%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 0.12s 5.95s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 13 unt; 2 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 44 ~; 48 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Xs,Ys] :
( member(X,intersection(Xs,Ys))
| ~ member(X,Ys)
| ~ member(X,Xs) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Xs,Ys] :
( member(X,Xs)
| ~ member(X,intersection(Xs,Ys)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Xs,Ys] :
( member(X,Ys)
| ~ member(X,intersection(Xs,Ys)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [Xs,Ys] :
( equal_sets(Ys,Xs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [Xs,Ys,Zs] :
( equal_sets(Xs,Zs)
| ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
equal_sets(intersection(as,bs),cs),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
equal_sets(intersection(bs,as),ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ equal_sets(cs,ds),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
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(f38,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f39,plain,
! [X,Xs] :
( member(X,Xs)
| ! [Ys] : ~ member(X,intersection(Xs,Ys)) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f40,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X,Ys] :
( member(X,Ys)
| ! [Xs] : ~ member(X,intersection(Xs,Ys)) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f42,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f47,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f48,plain,
! [Xs,Zs] :
( equal_sets(Xs,Zs)
| ! [Ys] :
( ~ equal_sets(Ys,Zs)
| ~ equal_sets(Xs,Ys) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f49,plain,
! [X0,X1,X2] :
( equal_sets(X0,X2)
| ~ equal_sets(X1,X2)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f54,plain,
equal_sets(intersection(as,bs),cs),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f55,plain,
equal_sets(intersection(bs,as),ds),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f56,plain,
~ equal_sets(cs,ds),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f58,plain,
equal_sets(cs,intersection(as,bs)),
inference(resolution,[status(thm)],[f54,f47]) ).
fof(f61,plain,
! [X0] :
( equal_sets(X0,intersection(as,bs))
| ~ equal_sets(X0,cs) ),
inference(resolution,[status(thm)],[f49,f58]) ).
fof(f62,plain,
! [X0] :
( equal_sets(X0,ds)
| ~ equal_sets(X0,intersection(bs,as)) ),
inference(resolution,[status(thm)],[f49,f55]) ).
fof(f63,plain,
! [X0] :
( equal_sets(X0,cs)
| ~ equal_sets(X0,intersection(as,bs)) ),
inference(resolution,[status(thm)],[f49,f54]) ).
fof(f68,plain,
! [X0] :
( equal_sets(intersection(as,bs),X0)
| ~ equal_sets(X0,cs) ),
inference(resolution,[status(thm)],[f61,f47]) ).
fof(f78,plain,
( equal_sets(intersection(as,bs),ds)
| ~ equal_sets(intersection(bs,as),cs) ),
inference(resolution,[status(thm)],[f68,f62]) ).
fof(f85,definition,
( sQ1_spl
<=> equal_sets(intersection(bs,as),cs) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f87,plain,
( sQ1_spl
| ~ equal_sets(intersection(bs,as),cs) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,definition,
( sQ2_spl
<=> equal_sets(intersection(as,bs),ds) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f89,plain,
( ~ sQ2_spl
| equal_sets(intersection(as,bs),ds) ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f78,f85,f88]) ).
fof(f218,plain,
( ~ sQ2_spl
| equal_sets(ds,intersection(as,bs)) ),
inference(resolution,[status(thm)],[f89,f47]) ).
fof(f228,plain,
( ~ sQ2_spl
| equal_sets(ds,cs) ),
inference(resolution,[status(thm)],[f218,f63]) ).
fof(f237,plain,
( ~ sQ2_spl
| equal_sets(cs,ds) ),
inference(resolution,[status(thm)],[f228,f47]) ).
fof(f238,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f56]) ).
fof(f239,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f238]) ).
fof(f249,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(member_of_1_not_of_2(intersection(X0,X1),X2),X0) ),
inference(resolution,[status(thm)],[f40,f28]) ).
fof(f250,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),X2)
| member(member_of_1_not_of_2(intersection(X0,X1),X2),X1) ),
inference(resolution,[status(thm)],[f42,f28]) ).
fof(f356,plain,
! [X0,X1,X2] :
( subset(X0,intersection(X1,X2))
| ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X2)
| ~ member(member_of_1_not_of_2(X0,intersection(X1,X2)),X1) ),
inference(resolution,[status(thm)],[f38,f29]) ).
fof(f740,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),intersection(X2,X0))
| subset(intersection(X0,X1),intersection(X2,X0))
| ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2) ),
inference(resolution,[status(thm)],[f356,f249]) ).
fof(f753,plain,
! [X0,X1,X2] :
( subset(intersection(X0,X1),intersection(X2,X0))
| ~ member(member_of_1_not_of_2(intersection(X0,X1),intersection(X2,X0)),X2) ),
inference(duplicate_literals_removal,[status(thm)],[f740]) ).
fof(f4502,plain,
! [X0,X1] :
( subset(intersection(X0,X1),intersection(X1,X0))
| subset(intersection(X0,X1),intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f753,f250]) ).
fof(f4536,plain,
! [X0,X1] : subset(intersection(X0,X1),intersection(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f4502]) ).
fof(f5061,plain,
! [X0,X1] :
( equal_sets(intersection(X1,X0),intersection(X0,X1))
| ~ subset(intersection(X0,X1),intersection(X1,X0)) ),
inference(resolution,[status(thm)],[f4536,f45]) ).
fof(f5063,plain,
! [X0,X1] : equal_sets(intersection(X0,X1),intersection(X1,X0)),
inference(forward_subsumption_resolution,[status(thm)],[f5061,f4536]) ).
fof(f5071,plain,
equal_sets(intersection(bs,as),cs),
inference(resolution,[status(thm)],[f5063,f63]) ).
fof(f5079,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5071,f87]) ).
fof(f5080,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f5079]) ).
fof(f5081,plain,
$false,
inference(sat_refutation,[status(thm)],[f91,f239,f5080]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET013-2 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.36 % Computer : n005.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Mon Sep 21 04:41:23 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.37 % Drodi V4.1.1
% 0.12/5.95 % Refutation found
% 0.12/5.95 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/5.95 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.97 % Elapsed time: 0.602595 seconds
% 0.12/5.97 % CPU time: 4.608249 seconds
% 0.12/5.97 % Total memory used: 56.647 MB
% 0.12/5.97 % Net memory used: 48.297 MB
%------------------------------------------------------------------------------