%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 02:08:47 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 7 unt; 1 def)
% Number of atoms : 37 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 16 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
union(a,b,aUb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ subset(a,aUb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f18,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(member_of_1_not_of_2(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [Union,Element] :
( member(Element,Union)
| ! [Set1] :
( ~ member(Element,Set1)
| ! [Set2] : ~ union(Set1,Set2,Union) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f31,plain,
union(a,b,aUb),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
~ subset(a,aUb),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( subset(X3,X2)
| ~ member(member_of_1_not_of_2(X3,X2),X0)
| ~ union(X0,X1,X2) ),
inference(resolution,[status(thm)],[f25,f18]) ).
fof(f49,plain,
! [X0] :
( subset(X0,aUb)
| ~ member(member_of_1_not_of_2(X0,aUb),a) ),
inference(resolution,[status(thm)],[f41,f31]) ).
fof(f50,plain,
( subset(a,aUb)
| subset(a,aUb) ),
inference(resolution,[status(thm)],[f49,f17]) ).
fof(f54,definition,
( sQ0_spl
<=> subset(a,aUb) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ0_spl
| subset(a,aUb) ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f50,f54]) ).
fof(f58,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f32]) ).
fof(f59,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f58]) ).
fof(f60,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 04:41:06 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.032976 seconds
% 0.12/0.39 % CPU time: 0.078065 seconds
% 0.12/0.39 % Total memory used: 9.019 MB
% 0.12/0.39 % Net memory used: 8.785 MB
%------------------------------------------------------------------------------