%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 03:54:38 PM UTC 2026
% Result : Unsatisfiable 5.86s 1.34s
% Output : Proof 5.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 65 ( 11 unt; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 136 ( 60 ~; 76 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 123 ( 0 sgn 48 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
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(f9,axiom,
( element_of_set(in_1st_set(X,Y),X)
| subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_4) ).
fof(f9_nnf,plain,
! [X,Y] :
( element_of_set(in_1st_set(X,Y),X)
| subset_sets(X,Y) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y] :
( element_of_set(in_1st_set(X,Y),X)
| subset_sets(X,Y) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( element_of_set(in_1st_set(X0,X1),X0)
| subset_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p16,plain,
( subset_sets(union_of_members(X0),X1)
| element_of_collection(f1(X0,in_1st_set(union_of_members(X0),X1)),X0) ),
inference(resolution,[status(thm)],[c1,c9]) ).
cnf(p22,plain,
( subset_sets(union_of_members(top_of_basis(X1)),X2)
| element_of_set(X0,f10(X1,f1(top_of_basis(X1),in_1st_set(union_of_members(top_of_basis(X1)),X2)),X0))
| ~ element_of_set(X0,f1(top_of_basis(X1),in_1st_set(union_of_members(top_of_basis(X1)),X2))) ),
inference(resolution,[status(thm)],[c4,p16]) ).
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(p15,plain,
( element_of_set(in_1st_set(union_of_members(X0),X1),f1(X0,in_1st_set(union_of_members(X0),X1)))
| subset_sets(union_of_members(X0),X1) ),
inference(resolution,[status(thm)],[c9,c0]) ).
cnf(p33,plain,
( subset_sets(union_of_members(top_of_basis(X0)),X1)
| subset_sets(union_of_members(top_of_basis(X0)),X1)
| element_of_set(in_1st_set(union_of_members(top_of_basis(X0)),X1),f10(X0,f1(top_of_basis(X0),in_1st_set(union_of_members(top_of_basis(X0)),X1)),in_1st_set(union_of_members(top_of_basis(X0)),X1))) ),
inference(resolution,[status(thm)],[p22,p15]) ).
cnf(p48,plain,
( subset_sets(union_of_members(top_of_basis(X0)),X1)
| element_of_set(in_1st_set(union_of_members(top_of_basis(X0)),X1),f10(X0,f1(top_of_basis(X0),in_1st_set(union_of_members(top_of_basis(X0)),X1)),in_1st_set(union_of_members(top_of_basis(X0)),X1))) ),
inference(factoring,[status(thm)],[p33]) ).
cnf(f2,axiom,
( ~ 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',union_of_members_3) ).
fof(f2_nnf,plain,
! [U,Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [U,Vf,Uu1] :
( ~ element_of_collection(Uu1,Vf)
| ~ element_of_set(U,Uu1)
| element_of_set(U,union_of_members(Vf)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ element_of_collection(X2,X1)
| ~ element_of_set(X0,X2)
| element_of_set(X0,union_of_members(X1)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p50,plain,
( ~ element_of_collection(f10(X0,f1(top_of_basis(X0),in_1st_set(union_of_members(top_of_basis(X0)),X1)),in_1st_set(union_of_members(top_of_basis(X0)),X1)),X2)
| element_of_set(in_1st_set(union_of_members(top_of_basis(X0)),X1),union_of_members(X2))
| subset_sets(union_of_members(top_of_basis(X0)),X1) ),
inference(resolution,[status(thm)],[p48,c2]) ).
cnf(f5,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(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,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)],[f5_sk]) ).
cnf(p23,plain,
( subset_sets(union_of_members(top_of_basis(X1)),X2)
| element_of_collection(f10(X1,f1(top_of_basis(X1),in_1st_set(union_of_members(top_of_basis(X1)),X2)),X0),X1)
| ~ element_of_set(X0,f1(top_of_basis(X1),in_1st_set(union_of_members(top_of_basis(X1)),X2))) ),
inference(resolution,[status(thm)],[c5,p16]) ).
cnf(p37,plain,
( subset_sets(union_of_members(top_of_basis(X0)),X1)
| subset_sets(union_of_members(top_of_basis(X0)),X1)
| element_of_collection(f10(X0,f1(top_of_basis(X0),in_1st_set(union_of_members(top_of_basis(X0)),X1)),in_1st_set(union_of_members(top_of_basis(X0)),X1)),X0) ),
inference(resolution,[status(thm)],[p23,p15]) ).
cnf(p44,plain,
( subset_sets(union_of_members(top_of_basis(X0)),X1)
| element_of_collection(f10(X0,f1(top_of_basis(X0),in_1st_set(union_of_members(top_of_basis(X0)),X1)),in_1st_set(union_of_members(top_of_basis(X0)),X1)),X0) ),
inference(factoring,[status(thm)],[p37]) ).
cnf(p51,plain,
( subset_sets(union_of_members(top_of_basis(X0)),X1)
| element_of_set(in_1st_set(union_of_members(top_of_basis(X0)),X1),union_of_members(X0))
| subset_sets(union_of_members(top_of_basis(X0)),X1) ),
inference(resolution,[status(thm)],[p50,p44]) ).
cnf(p52,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(X0)),X1),union_of_members(X0))
| subset_sets(union_of_members(top_of_basis(X0)),X1) ),
inference(factoring,[status(thm)],[p51]) ).
cnf(f7,axiom,
( element_of_set(U,Y)
| ~ element_of_set(U,X)
| ~ subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_2) ).
fof(f7_nnf,plain,
! [X,Y,U] :
( element_of_set(U,Y)
| ~ element_of_set(U,X)
| ~ subset_sets(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U] :
( element_of_set(U,Y)
| ~ element_of_set(U,X)
| ~ subset_sets(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( element_of_set(X2,X1)
| ~ element_of_set(X2,X0)
| ~ subset_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(f3,axiom,
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',basis_for_topology_28) ).
fof(f3_nnf,plain,
! [X,Vf] :
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Vf] :
( equal_sets(union_of_members(Vf),X)
| ~ basis(X,Vf) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( equal_sets(union_of_members(X1),X0)
| ~ basis(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(f11,negated_conjecture,
basis(cx,f),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1a_1) ).
fof(f11_nnf,plain,
basis(cx,f),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
basis(cx,f),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(p13,plain,
equal_sets(union_of_members(f),cx),
inference(resolution,[status(thm)],[c3,c11]) ).
cnf(f8,axiom,
( subset_sets(X,Y)
| ~ equal_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_3) ).
fof(f8_nnf,plain,
! [X,Y] :
( subset_sets(X,Y)
| ~ equal_sets(X,Y) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y] :
( subset_sets(X,Y)
| ~ equal_sets(X,Y) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( subset_sets(X0,X1)
| ~ equal_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p14,plain,
subset_sets(union_of_members(f),cx),
inference(resolution,[status(thm)],[p13,c8]) ).
cnf(p17,plain,
( element_of_set(X0,cx)
| ~ element_of_set(X0,union_of_members(f)) ),
inference(resolution,[status(thm)],[c7,p14]) ).
cnf(p56,plain,
( element_of_set(in_1st_set(union_of_members(top_of_basis(f)),X0),cx)
| subset_sets(union_of_members(top_of_basis(f)),X0) ),
inference(resolution,[status(thm)],[p52,p17]) ).
cnf(f10,axiom,
( ~ element_of_set(in_1st_set(X,Y),Y)
| subset_sets(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_theory_5) ).
fof(f10_nnf,plain,
! [X,Y] :
( ~ element_of_set(in_1st_set(X,Y),Y)
| subset_sets(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] :
( ~ element_of_set(in_1st_set(X,Y),Y)
| subset_sets(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ element_of_set(in_1st_set(X0,X1),X1)
| subset_sets(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p61,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)],[p56,c10]) ).
cnf(p63,plain,
subset_sets(union_of_members(top_of_basis(f)),cx),
inference(factoring,[status(thm)],[p61]) ).
cnf(f12,negated_conjecture,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lemma_1a_2) ).
fof(f12_nnf,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ subset_sets(union_of_members(top_of_basis(f)),cx),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(p64,plain,
$false,
inference(resolution,[status(thm)],[p63,c12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : TOP001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n002.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 04:09:49 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.86/1.34 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.86/1.34 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------