%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 03:53:23 PM UTC 2026
% Result : Unsatisfiable 0.15s 5.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 16
% Syntax : Number of formulae : 61 ( 14 unt; 5 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 137 ( 65 ~; 67 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 10 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U,Vf] :
( element_of_set(U,f1(Vf,U))
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Vf] :
( element_of_collection(f1(Vf,U),Vf)
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U,Vf,X] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U,Vf,X] :
( element_of_collection(f10(Vf,U,X),Vf)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U,Vf,X] :
( subset_sets(f10(Vf,U,X),U)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U,Vf,Uu11] :
( ~ subset_sets(Uu11,U)
| ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] :
( subset_sets(X,union_of_members(Z))
| ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y,U] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1] :
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0,X1,X2] :
( element_of_set(X2,f10(X1,X0,X2))
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( element_of_collection(f10(X1,X0,X2),X1)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f17,plain,
! [X0,X1,X2] :
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f19,plain,
! [U,Uu11] :
( ~ subset_sets(Uu11,U)
| ! [Vf] :
( ~ element_of_collection(Uu11,Vf)
| ~ element_of_set(f11(Vf,U),Uu11)
| element_of_collection(U,top_of_basis(Vf)) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ subset_sets(X2,X0)
| ~ element_of_collection(X2,X1)
| ~ element_of_set(f11(X1,X0),X2)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [X,Z] :
( subset_sets(X,union_of_members(Z))
| ! [Y] :
( ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f24,plain,
! [X0,X1,X2] :
( subset_sets(X0,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ subset_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f25,plain,
! [Y,U] :
( element_of_collection(U,Y)
| ! [X] :
( ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1,X2] :
( element_of_collection(X2,X1)
| ~ element_of_collection(X2,X0)
| ~ subset_collections(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f27,plain,
subset_collections(g,top_of_basis(f)),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
element_of_set(f11(f,union_of_members(g)),union_of_members(g)),
inference(resolution,[status(thm)],[f18,f28]) ).
fof(f32,plain,
element_of_collection(f1(g,f11(f,union_of_members(g))),g),
inference(resolution,[status(thm)],[f29,f14]) ).
fof(f33,plain,
element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))),
inference(resolution,[status(thm)],[f29,f13]) ).
fof(f35,definition,
( sQ0_spl
<=> element_of_collection(union_of_members(g),top_of_basis(f)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f45,plain,
! [X0] :
( element_of_collection(f1(g,f11(f,union_of_members(g))),X0)
| ~ subset_collections(g,X0) ),
inference(resolution,[status(thm)],[f32,f26]) ).
fof(f56,plain,
( ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f36,f28]) ).
fof(f57,plain,
~ sQ0_spl,
inference(contradiction_clause,[status(thm)],[f56]) ).
fof(f60,plain,
! [X0,X1] :
( ~ subset_collections(g,top_of_basis(X1))
| element_of_set(X0,f10(X1,f1(g,f11(f,union_of_members(g))),X0))
| ~ element_of_set(X0,f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f15,f45]) ).
fof(f62,plain,
! [X0] :
( element_of_set(X0,f10(f,f1(g,f11(f,union_of_members(g))),X0))
| ~ element_of_set(X0,f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f60,f27]) ).
fof(f63,plain,
element_of_set(f11(f,union_of_members(g)),f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g)))),
inference(resolution,[status(thm)],[f62,f33]) ).
fof(f64,plain,
( ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(resolution,[status(thm)],[f63,f20]) ).
fof(f66,definition,
( sQ5_spl
<=> element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f68,plain,
( sQ5_spl
| ~ element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f) ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,definition,
( sQ6_spl
<=> subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( sQ6_spl
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),union_of_members(g)) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f35,f66,f69]) ).
fof(f73,plain,
! [X0,X1] :
( ~ subset_collections(g,top_of_basis(X1))
| element_of_collection(f10(X1,f1(g,f11(f,union_of_members(g))),X0),X1)
| ~ element_of_set(X0,f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f16,f45]) ).
fof(f77,plain,
! [X0] :
( element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),X0),f)
| ~ element_of_set(X0,f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f73,f27]) ).
fof(f78,plain,
element_of_collection(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f),
inference(resolution,[status(thm)],[f77,f33]) ).
fof(f79,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f78,f68]) ).
fof(f80,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f79]) ).
fof(f83,plain,
! [X0] :
( sQ6_spl
| ~ element_of_collection(X0,g)
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),X0) ),
inference(resolution,[status(thm)],[f71,f24]) ).
fof(f84,plain,
( sQ6_spl
| ~ subset_sets(f10(f,f1(g,f11(f,union_of_members(g))),f11(f,union_of_members(g))),f1(g,f11(f,union_of_members(g)))) ),
inference(resolution,[status(thm)],[f83,f32]) ).
fof(f94,plain,
( sQ6_spl
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g))))
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) ),
inference(resolution,[status(thm)],[f84,f17]) ).
fof(f95,definition,
( sQ9_spl
<=> element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( sQ9_spl
| ~ element_of_collection(f1(g,f11(f,union_of_members(g))),top_of_basis(f)) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,definition,
( sQ10_spl
<=> element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f100,plain,
( sQ10_spl
| ~ element_of_set(f11(f,union_of_members(g)),f1(g,f11(f,union_of_members(g)))) ),
inference(component_clause,[status(thm)],[f98]) ).
fof(f101,plain,
( sQ6_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f94,f95,f98,f69]) ).
fof(f102,plain,
( sQ9_spl
| ~ subset_collections(g,top_of_basis(f)) ),
inference(resolution,[status(thm)],[f97,f45]) ).
fof(f104,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f27]) ).
fof(f105,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f104]) ).
fof(f106,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f33]) ).
fof(f107,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f106]) ).
fof(f108,plain,
$false,
inference(sat_refutation,[status(thm)],[f57,f72,f80,f101,f105,f107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n004.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Mon Sep 21 12:38:10 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.39 % Drodi V4.1.1
% 0.15/5.42 % Refutation found
% 0.15/5.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/5.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/5.46 % Elapsed time: 0.061356 seconds
% 0.15/5.46 % CPU time: 0.172893 seconds
% 0.15/5.46 % Total memory used: 18.036 MB
% 0.15/5.46 % Net memory used: 17.609 MB
%------------------------------------------------------------------------------