%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 03:53:22 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 8 unt; 1 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 132 ( 65 ~; 66 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 93 ( 93 !; 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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U,Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Vf] :
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,U] :
( element_of_set(U,Y)
| ~ element_of_set(U,X)
| ~ subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y] :
( subset_sets(X,Y)
| ~ equal_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] :
( element_of_set(in_1st_set(X,Y),X)
| subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] :
( ~ element_of_set(in_1st_set(X,Y),Y)
| subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
basis(cx,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,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(f15,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(f16,plain,
! [Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ! [U] :
( ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ) ),
inference(miniscoping,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X2,X1)
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( equal_sets(union_of_members(X1),X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f19,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)],[f5]) ).
fof(f20,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)],[f6]) ).
fof(f22,plain,
! [Y,U] :
( element_of_set(U,Y)
| ! [X] :
( ~ element_of_set(U,X)
| ~ subset_sets(X,Y) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f23,plain,
! [X0,X1,X2] :
( element_of_set(X2,X1)
| ~ element_of_set(X2,X0)
| ~ subset_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset_sets(X0,X1)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f25,plain,
! [X0,X1] :
( element_of_set(in_1st_set(X0,X1),X0)
| subset_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( ~ element_of_set(in_1st_set(X0,X1),X1)
| subset_sets(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
basis(cx,f),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f28,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ element_of_collection(X2,X1)
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),X2)
| subset_sets(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f26,f17]) ).
fof(f33,plain,
! [X0,X1,X2] :
( ~ element_of_set(in_1st_set(X0,X1),X2)
| ~ subset_sets(X2,X1)
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f26,f23]) ).
fof(f35,plain,
! [X0,X1,X2] :
( ~ equal_sets(X2,X1)
| ~ element_of_set(in_1st_set(X0,X1),X2)
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f33,f24]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ basis(X1,X2)
| ~ element_of_set(in_1st_set(X0,X1),union_of_members(X2))
| subset_sets(X0,X1) ),
inference(resolution,[status(thm)],[f35,f18]) ).
fof(f38,plain,
! [X0] :
( ~ element_of_set(in_1st_set(X0,cx),union_of_members(f))
| subset_sets(X0,cx) ),
inference(resolution,[status(thm)],[f37,f27]) ).
fof(f41,plain,
! [X0,X1] :
( ~ element_of_set(in_1st_set(X0,cx),X1)
| ~ subset_sets(X1,union_of_members(f))
| subset_sets(X0,cx) ),
inference(resolution,[status(thm)],[f38,f23]) ).
fof(f49,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X3,X2)
| ~ element_of_collection(X2,top_of_basis(X1))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f10(X1,X2,X3))
| subset_sets(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f32,f20]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ element_of_set(X2,union_of_members(top_of_basis(X1)))
| ~ element_of_set(X3,f1(top_of_basis(X1),X2))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f10(X1,f1(top_of_basis(X1),X2),X3))
| subset_sets(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f49,f15]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f1(top_of_basis(X1),X2))
| ~ element_of_collection(f1(top_of_basis(X1),X2),top_of_basis(X1))
| ~ element_of_set(X2,union_of_members(top_of_basis(X1)))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f1(top_of_basis(X1),X2))
| subset_sets(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f52,f19]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ element_of_collection(f1(top_of_basis(X1),X2),top_of_basis(X1))
| ~ element_of_set(X2,union_of_members(top_of_basis(X1)))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f1(top_of_basis(X1),X2))
| subset_sets(X0,union_of_members(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f78]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ~ element_of_set(X2,union_of_members(top_of_basis(X1)))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),f1(top_of_basis(X1),X2))
| subset_sets(X0,union_of_members(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f81,f15]) ).
fof(f86,plain,
! [X0,X1] :
( ~ element_of_set(in_1st_set(X0,union_of_members(X1)),union_of_members(top_of_basis(X1)))
| ~ element_of_set(in_1st_set(X0,union_of_members(X1)),union_of_members(top_of_basis(X1)))
| subset_sets(X0,union_of_members(X1)) ),
inference(resolution,[status(thm)],[f82,f14]) ).
fof(f89,plain,
! [X0,X1] :
( ~ element_of_set(in_1st_set(X0,union_of_members(X1)),union_of_members(top_of_basis(X1)))
| subset_sets(X0,union_of_members(X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f86]) ).
fof(f92,plain,
! [X0] :
( subset_sets(union_of_members(top_of_basis(X0)),union_of_members(X0))
| subset_sets(union_of_members(top_of_basis(X0)),union_of_members(X0)) ),
inference(resolution,[status(thm)],[f89,f25]) ).
fof(f95,plain,
! [X0] : subset_sets(union_of_members(top_of_basis(X0)),union_of_members(X0)),
inference(duplicate_literals_removal,[status(thm)],[f92]) ).
fof(f96,plain,
! [X0] :
( ~ element_of_set(in_1st_set(X0,cx),union_of_members(top_of_basis(f)))
| subset_sets(X0,cx) ),
inference(resolution,[status(thm)],[f95,f41]) ).
fof(f98,plain,
( subset_sets(union_of_members(top_of_basis(f)),cx)
| subset_sets(union_of_members(top_of_basis(f)),cx) ),
inference(resolution,[status(thm)],[f96,f25]) ).
fof(f101,definition,
( sQ1_spl
<=> subset_sets(union_of_members(top_of_basis(f)),cx) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f102,plain,
( ~ sQ1_spl
| subset_sets(union_of_members(top_of_basis(f)),cx) ),
inference(component_clause,[status(thm)],[f101]) ).
fof(f104,plain,
sQ1_spl,
inference(split_clause,[status(thm)],[f98,f101]) ).
fof(f105,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f102,f28]) ).
fof(f106,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f107,plain,
$false,
inference(sat_refutation,[status(thm)],[f104,f106]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 12:41:06 UTC 2026
% 0.12/0.35 % 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: 0.043697 seconds
% 0.12/0.41 % CPU time: 0.131024 seconds
% 0.12/0.41 % Total memory used: 17.264 MB
% 0.12/0.41 % Net memory used: 16.837 MB
%------------------------------------------------------------------------------