%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 02:08:46 PM UTC 2026
% Result : Unsatisfiable 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 35 ( 8 unt; 3 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 32 ~; 38 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 4 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [Subset,Superset] :
( member(member_of_1_not_of_2(Subset,Superset),Subset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Subset,Superset] :
( subset(Subset,Superset)
| ~ member(member_of_1_not_of_2(Subset,Superset),Superset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Set1,Set2] :
( equal_sets(Set2,Set1)
| ~ subset(Set2,Set1)
| ~ subset(Set1,Set2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
union(a,a,aUa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ equal_sets(aUa,a),
file('/export/starexec/sandbox/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(f21,plain,
! [X0,X1] :
( equal_sets(X1,X0)
| ~ subset(X1,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f22,plain,
! [Set2,Element] :
( member(Element,Set2)
| ! [Set1] :
( member(Element,Set1)
| ! [Union] :
( ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f23,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
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,a,aUa),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
~ equal_sets(aUa,a),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f41,plain,
! [X0] :
( member(X0,a)
| member(X0,a)
| ~ member(X0,aUa) ),
inference(resolution,[status(thm)],[f23,f31]) ).
fof(f42,plain,
! [X0] :
( member(X0,a)
| ~ member(X0,aUa) ),
inference(duplicate_literals_removal,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0] :
( subset(aUa,X0)
| member(member_of_1_not_of_2(aUa,X0),a) ),
inference(resolution,[status(thm)],[f42,f17]) ).
fof(f45,plain,
! [X0] :
( member(X0,aUa)
| ~ member(X0,a) ),
inference(resolution,[status(thm)],[f25,f31]) ).
fof(f46,plain,
! [X0] :
( subset(X0,aUa)
| ~ member(member_of_1_not_of_2(X0,aUa),a) ),
inference(resolution,[status(thm)],[f45,f18]) ).
fof(f49,plain,
( subset(aUa,a)
| subset(aUa,a) ),
inference(resolution,[status(thm)],[f43,f18]) ).
fof(f50,definition,
( sQ0_spl
<=> subset(aUa,a) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f51,plain,
( ~ sQ0_spl
| subset(aUa,a) ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
sQ0_spl,
inference(split_clause,[status(thm)],[f49,f50]) ).
fof(f55,plain,
( ~ sQ0_spl
| equal_sets(aUa,a)
| ~ subset(a,aUa) ),
inference(resolution,[status(thm)],[f51,f21]) ).
fof(f56,definition,
( sQ1_spl
<=> subset(a,aUa) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f59,definition,
( sQ2_spl
<=> equal_sets(aUa,a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( ~ sQ2_spl
| equal_sets(aUa,a) ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ sQ0_spl
| sQ2_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f55,f56,f59,f50]) ).
fof(f65,plain,
( subset(a,aUa)
| subset(a,aUa) ),
inference(resolution,[status(thm)],[f46,f17]) ).
fof(f71,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f65,f56]) ).
fof(f72,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f32]) ).
fof(f73,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f72]) ).
fof(f74,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f62,f71,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.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
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 04:40:47 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.41 % Elapsed time: 0.039730 seconds
% 0.15/0.41 % CPU time: 0.113753 seconds
% 0.15/0.41 % Total memory used: 16.915 MB
% 0.15/0.41 % Net memory used: 16.458 MB
%------------------------------------------------------------------------------