%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 02:08:48 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 40 ( 11 unt; 1 def)
% Number of atoms : 88 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 89 ( 41 ~; 47 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 68 ( 68 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Element,Subset,Superset] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f7,axiom,
! [Set1,Set2,Difference,Element] :
( member(Element,Set1)
| ~ member(Element,Difference)
| ~ difference(Set1,Set2,Difference) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Element,Set1,Set2,A_set] :
( ~ difference(A_set,Set1,Set2)
| ~ member(Element,Set2)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Element,Set1,Set2,Difference] :
( member(Element,Set2)
| member(Element,Difference)
| ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
subset(d,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
difference(b,a,bDa),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
difference(b,d,bDd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ subset(bDa,bDd),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [Element,Superset] :
( member(Element,Superset)
| ! [Subset] :
( ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ subset(X1,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(member_of_1_not_of_2(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f20,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,
! [Set1,Element] :
( member(Element,Set1)
| ! [Difference] :
( ~ member(Element,Difference)
| ! [Set2] : ~ difference(Set1,Set2,Difference) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ difference(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f26,plain,
! [Set1,Set2] :
( ! [A_set] : ~ difference(A_set,Set1,Set2)
| ! [Element] :
( ~ member(Element,Set2)
| ~ member(Element,Set1) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ difference(X3,X1,X2)
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [Element,Set2] :
( member(Element,Set2)
| ! [Difference] :
( member(Element,Difference)
| ! [Set1] :
( ~ difference(Set1,Set2,Difference)
| ~ member(Element,Set1) ) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( member(X0,X2)
| member(X0,X3)
| ~ difference(X1,X2,X3)
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f33,plain,
subset(d,a),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
difference(b,a,bDa),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
difference(b,d,bDd),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
~ subset(bDa,bDd),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
! [X0] :
( member(X0,a)
| ~ member(X0,d) ),
inference(resolution,[status(thm)],[f33,f18]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ~ difference(X3,X2,X0)
| ~ member(member_of_1_not_of_2(X0,X1),X2)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f19,f27]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( member(member_of_1_not_of_2(X0,X1),X2)
| ~ difference(X2,X3,X0)
| subset(X0,X1) ),
inference(resolution,[status(thm)],[f19,f25]) ).
fof(f75,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(bDa,X0),a)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f58,f34]) ).
fof(f77,plain,
! [X0] :
( ~ member(member_of_1_not_of_2(bDa,X0),d)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f75,f37]) ).
fof(f85,plain,
! [X0] :
( member(member_of_1_not_of_2(bDa,X0),b)
| subset(bDa,X0) ),
inference(resolution,[status(thm)],[f59,f34]) ).
fof(f119,plain,
! [X0] :
( member(X0,d)
| member(X0,bDd)
| ~ member(X0,b) ),
inference(resolution,[status(thm)],[f29,f35]) ).
fof(f121,plain,
! [X0] :
( subset(bDa,X0)
| member(member_of_1_not_of_2(bDa,X0),d)
| member(member_of_1_not_of_2(bDa,X0),bDd) ),
inference(resolution,[status(thm)],[f119,f85]) ).
fof(f125,plain,
! [X0] :
( subset(bDa,X0)
| member(member_of_1_not_of_2(bDa,X0),bDd) ),
inference(forward_subsumption_resolution,[status(thm)],[f121,f77]) ).
fof(f127,plain,
( subset(bDa,bDd)
| subset(bDa,bDd) ),
inference(resolution,[status(thm)],[f125,f20]) ).
fof(f132,definition,
( sQ7_spl
<=> subset(bDa,bDd) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f133,plain,
( ~ sQ7_spl
| subset(bDa,bDd) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,plain,
sQ7_spl,
inference(split_clause,[status(thm)],[f127,f132]) ).
fof(f136,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f36]) ).
fof(f137,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f136]) ).
fof(f138,plain,
$false,
inference(sat_refutation,[status(thm)],[f135,f137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.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 04:42:03 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.39 % Refutation found
% 0.12/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.41 % Elapsed time: 0.051394 seconds
% 0.12/0.41 % CPU time: 0.134409 seconds
% 0.12/0.41 % Total memory used: 17.365 MB
% 0.12/0.41 % Net memory used: 16.937 MB
%------------------------------------------------------------------------------