%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 : Fri Sep 25 03:54:39 PM UTC 2026
% Result : Unsatisfiable 4.68s 1.09s
% Output : Proof 4.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 9 unt; 0 def)
% Number of atoms : 163 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 172 ( 75 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 120 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_40) ).
fof(f5_nnf,plain,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [U,Vf] :
( element_of_set(f11(Vf,U),U)
| element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( element_of_set(f11(X1,X0),X0)
| element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f0,axiom,
( element_of_set(U,f1(Vf,U))
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_1) ).
fof(f0_nnf,plain,
! [U,Vf] :
( element_of_set(U,f1(Vf,U))
| ~ element_of_set(U,union_of_members(Vf)) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [U,Vf] :
( element_of_set(U,f1(Vf,U))
| ~ element_of_set(U,union_of_members(Vf)) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( element_of_set(X0,f1(X1,X0))
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p12,plain,
( element_of_set(f11(X1,union_of_members(X0)),f1(X0,f11(X1,union_of_members(X0))))
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(f1,axiom,
( element_of_collection(f1(Vf,U),Vf)
| ~ element_of_set(U,union_of_members(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_of_members_2) ).
fof(f1_nnf,plain,
! [U,Vf] :
( element_of_collection(f1(Vf,U),Vf)
| ~ element_of_set(U,union_of_members(Vf)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [U,Vf] :
( element_of_collection(f1(Vf,U),Vf)
| ~ element_of_set(U,union_of_members(Vf)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( element_of_collection(f1(X1,X0),X1)
| ~ element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p13,plain,
( element_of_collection(f1(X0,f11(X1,union_of_members(X0))),X0)
| element_of_collection(union_of_members(X0),top_of_basis(X1)) ),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(f9,axiom,
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_21) ).
fof(f9_nnf,plain,
! [X,Y,U] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,U] :
( element_of_collection(U,Y)
| ~ element_of_collection(U,X)
| ~ subset_collections(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( element_of_collection(X2,X1)
| ~ element_of_collection(X2,X0)
| ~ subset_collections(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(f10,negated_conjecture,
subset_collections(g,top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_2) ).
fof(f10_nnf,plain,
subset_collections(g,top_of_basis(f)),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
subset_collections(g,top_of_basis(f)),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(p15,plain,
( element_of_collection(X0,top_of_basis(f))
| ~ element_of_collection(X0,g) ),
inference(resolution,[status(thm)],[c9,c10]) ).
cnf(p17,plain,
( element_of_collection(f1(g,f11(X0,union_of_members(g))),top_of_basis(f))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p13,p15]) ).
cnf(f2,axiom,
( 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',topology_generated_37) ).
fof(f2_nnf,plain,
! [U,Vf,X] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U,Vf,X] :
( element_of_set(X,f10(Vf,U,X))
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( 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(esa)],[f2_sk]) ).
cnf(p19,plain,
( element_of_set(X1,f10(f,f1(g,f11(X0,union_of_members(g))),X1))
| ~ element_of_set(X1,f1(g,f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p17,c2]) ).
cnf(p35,plain,
( element_of_set(f11(X0,union_of_members(g)),f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p12,p19]) ).
cnf(p40,plain,
( element_of_set(f11(X0,union_of_members(g)),f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(factoring,[status(thm)],[p35]) ).
cnf(f6,axiom,
( ~ 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/sandbox2/benchmark/theBenchmark.p',topology_generated_41) ).
fof(f6_nnf,plain,
! [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)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [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)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ 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(esa)],[f6_sk]) ).
cnf(p42,plain,
( ~ subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),X0)
| element_of_collection(union_of_members(g),top_of_basis(X0))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p40,c6]) ).
cnf(p86,plain,
( ~ subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),union_of_members(g))
| ~ element_of_collection(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),X0)
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(factoring,[status(thm)],[p42]) ).
cnf(f3,axiom,
( 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',topology_generated_38) ).
fof(f3_nnf,plain,
! [U,Vf,X] :
( element_of_collection(f10(Vf,U,X),Vf)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [U,Vf,X] :
( element_of_collection(f10(Vf,U,X),Vf)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( 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(esa)],[f3_sk]) ).
cnf(p20,plain,
( element_of_collection(f10(f,f1(g,f11(X0,union_of_members(g))),X1),f)
| ~ element_of_set(X1,f1(g,f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p17,c3]) ).
cnf(p36,plain,
( element_of_collection(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(X0))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p12,p20]) ).
cnf(p39,plain,
( element_of_collection(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),f)
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(factoring,[status(thm)],[p36]) ).
cnf(p87,plain,
( element_of_collection(union_of_members(g),top_of_basis(f))
| ~ 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(union_of_members(g),top_of_basis(f)) ),
inference(resolution,[status(thm)],[p86,p39]) ).
cnf(p88,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(union_of_members(g),top_of_basis(f)) ),
inference(factoring,[status(thm)],[p87]) ).
cnf(f4,axiom,
( subset_sets(f10(Vf,U,X),U)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',topology_generated_39) ).
fof(f4_nnf,plain,
! [U,Vf,X] :
( subset_sets(f10(Vf,U,X),U)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [U,Vf,X] :
( subset_sets(f10(Vf,U,X),U)
| ~ element_of_set(X,U)
| ~ element_of_collection(U,top_of_basis(Vf)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( subset_sets(f10(X1,X0,X2),X0)
| ~ element_of_set(X2,X0)
| ~ element_of_collection(X0,top_of_basis(X1)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p23,plain,
( element_of_collection(union_of_members(g),top_of_basis(X1))
| subset_sets(f10(f,f1(g,f11(X1,union_of_members(g))),X0),f1(g,f11(X1,union_of_members(g))))
| ~ element_of_set(X0,f1(g,f11(X1,union_of_members(g)))) ),
inference(resolution,[status(thm)],[c4,p17]) ).
cnf(p37,plain,
( element_of_collection(union_of_members(g),top_of_basis(X0))
| subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),f1(g,f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p12,p23]) ).
cnf(p51,plain,
( subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),f1(g,f11(X0,union_of_members(g))))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(f8,axiom,
( subset_sets(X,union_of_members(Z))
| ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_20) ).
fof(f8_nnf,plain,
! [X,Y,Z] :
( subset_sets(X,union_of_members(Z))
| ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] :
( subset_sets(X,union_of_members(Z))
| ~ element_of_collection(Y,Z)
| ~ subset_sets(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( subset_sets(X0,union_of_members(X2))
| ~ element_of_collection(X1,X2)
| ~ subset_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p52,plain,
( subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),union_of_members(X1))
| ~ element_of_collection(f1(g,f11(X0,union_of_members(g))),X1)
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p51,c8]) ).
cnf(p53,plain,
( element_of_collection(union_of_members(g),top_of_basis(X0))
| subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),union_of_members(g))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(resolution,[status(thm)],[p52,p13]) ).
cnf(p58,plain,
( subset_sets(f10(f,f1(g,f11(X0,union_of_members(g))),f11(X0,union_of_members(g))),union_of_members(g))
| element_of_collection(union_of_members(g),top_of_basis(X0)) ),
inference(factoring,[status(thm)],[p53]) ).
cnf(p89,plain,
( element_of_collection(union_of_members(g),top_of_basis(f))
| element_of_collection(union_of_members(g),top_of_basis(f)) ),
inference(resolution,[status(thm)],[p88,p58]) ).
cnf(p91,plain,
element_of_collection(union_of_members(g),top_of_basis(f)),
inference(factoring,[status(thm)],[p89]) ).
cnf(f11,negated_conjecture,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1e_3) ).
fof(f11_nnf,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
~ element_of_collection(union_of_members(g),top_of_basis(f)),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(p92,plain,
$false,
inference(resolution,[status(thm)],[p91,c11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP005-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 04:06:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.68/1.09 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.68/1.09 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------