TSTP Solution File: TOP004-1 by ConnectPP---0.3.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ConnectPP---0.3.0
% Problem : TOP004-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Mar 25 14:45:31 EDT 2024
% Result : Unsatisfiable 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : TOP004-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13 % Command : connect++ --verbosity 0 --no-colour --tptp-proof --schedule default %s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Mar 20 23:32:18 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.35 % SZS output start Proof for theBenchmark
% 0.13/0.35
% 0.13/0.35 % Problem matrix:
% 0.13/0.35 cnf(matrix-0, plain, ( ~element_of_set(U, union_of_members(Vf)) | element_of_set(U, f1(Vf, U)) )).
% 0.13/0.35 cnf(matrix-1, plain, ( ~element_of_set(U, union_of_members(Vf)) | element_of_collection(f1(Vf, U), Vf) )).
% 0.13/0.35 cnf(matrix-2, plain, ( element_of_set(U, union_of_members(Vf)) | ~element_of_set(U, Uu1) | ~element_of_collection(Uu1, Vf) )).
% 0.13/0.35 cnf(matrix-3, plain, ( ~element_of_set(U, intersection_of_members(Vf)) | ~element_of_collection(Va, Vf) | element_of_set(U, Va) )).
% 0.13/0.35 cnf(matrix-4, plain, ( element_of_set(U, intersection_of_members(Vf)) | element_of_collection(f2(Vf, U), Vf) )).
% 0.13/0.35 cnf(matrix-5, plain, ( element_of_set(U, intersection_of_members(Vf)) | ~element_of_set(U, f2(Vf, U)) )).
% 0.13/0.35 cnf(matrix-6, plain, ( ~topological_space(X, Vt) | equal_sets(union_of_members(Vt), X) )).
% 0.13/0.35 cnf(matrix-7, plain, ( ~topological_space(X, Vt) | element_of_collection(empty_set, Vt) )).
% 0.13/0.35 cnf(matrix-8, plain, ( ~topological_space(X, Vt) | element_of_collection(X, Vt) )).
% 0.13/0.35 cnf(matrix-9, plain, ( ~topological_space(X, Vt) | ~element_of_collection(Y, Vt) | ~element_of_collection(Z, Vt) | element_of_collection(intersection_of_sets(Y, Z), Vt) )).
% 0.13/0.35 cnf(matrix-10, plain, ( ~topological_space(X, Vt) | ~subset_collections(Vf, Vt) | element_of_collection(union_of_members(Vf), Vt) )).
% 0.13/0.35 cnf(matrix-11, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | element_of_collection(f3(X, Vt), Vt) | subset_collections(f5(X, Vt), Vt) )).
% 0.13/0.35 cnf(matrix-12, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | element_of_collection(f3(X, Vt), Vt) | ~element_of_collection(union_of_members(f5(X, Vt)), Vt) )).
% 0.13/0.35 cnf(matrix-13, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | element_of_collection(f4(X, Vt), Vt) | subset_collections(f5(X, Vt), Vt) )).
% 0.13/0.35 cnf(matrix-14, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | element_of_collection(f4(X, Vt), Vt) | ~element_of_collection(union_of_members(f5(X, Vt)), Vt) )).
% 0.13/0.35 cnf(matrix-15, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | ~element_of_collection(intersection_of_sets(f3(X, Vt), f4(X, Vt)), Vt) | subset_collections(f5(X, Vt), Vt) )).
% 0.13/0.35 cnf(matrix-16, plain, ( topological_space(X, Vt) | ~equal_sets(union_of_members(Vt), X) | ~element_of_collection(empty_set, Vt) | ~element_of_collection(X, Vt) | ~element_of_collection(intersection_of_sets(f3(X, Vt), f4(X, Vt)), Vt) | ~element_of_collection(union_of_members(f5(X, Vt)), Vt) )).
% 0.13/0.35 cnf(matrix-17, plain, ( ~open(U, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-18, plain, ( ~open(U, X, Vt) | element_of_collection(U, Vt) )).
% 0.13/0.35 cnf(matrix-19, plain, ( open(U, X, Vt) | ~topological_space(X, Vt) | ~element_of_collection(U, Vt) )).
% 0.13/0.35 cnf(matrix-20, plain, ( ~closed(U, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-21, plain, ( ~closed(U, X, Vt) | open(relative_complement_sets(U, X), X, Vt) )).
% 0.13/0.35 cnf(matrix-22, plain, ( closed(U, X, Vt) | ~topological_space(X, Vt) | ~open(relative_complement_sets(U, X), X, Vt) )).
% 0.13/0.35 cnf(matrix-23, plain, ( ~finer(Vt, Vs, X) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-24, plain, ( ~finer(Vt, Vs, X) | topological_space(X, Vs) )).
% 0.13/0.35 cnf(matrix-25, plain, ( ~finer(Vt, Vs, X) | subset_collections(Vs, Vt) )).
% 0.13/0.35 cnf(matrix-26, plain, ( finer(Vt, Vs, X) | ~topological_space(X, Vt) | ~topological_space(X, Vs) | ~subset_collections(Vs, Vt) )).
% 0.13/0.35 cnf(matrix-27, plain, ( ~basis(X, Vf) | equal_sets(union_of_members(Vf), X) )).
% 0.13/0.35 cnf(matrix-28, plain, ( ~basis(X, Vf) | ~element_of_set(Y, X) | ~element_of_collection(Vb1, Vf) | ~element_of_collection(Vb2, Vf) | ~element_of_set(Y, intersection_of_sets(Vb1, Vb2)) | element_of_set(Y, f6(X, Vf, Y, Vb1, Vb2)) )).
% 0.13/0.35 cnf(matrix-29, plain, ( ~basis(X, Vf) | ~element_of_set(Y, X) | ~element_of_collection(Vb1, Vf) | ~element_of_collection(Vb2, Vf) | ~element_of_set(Y, intersection_of_sets(Vb1, Vb2)) | element_of_collection(f6(X, Vf, Y, Vb1, Vb2), Vf) )).
% 0.13/0.35 cnf(matrix-30, plain, ( ~basis(X, Vf) | ~element_of_set(Y, X) | ~element_of_collection(Vb1, Vf) | ~element_of_collection(Vb2, Vf) | ~element_of_set(Y, intersection_of_sets(Vb1, Vb2)) | subset_sets(f6(X, Vf, Y, Vb1, Vb2), intersection_of_sets(Vb1, Vb2)) )).
% 0.13/0.35 cnf(matrix-31, plain, ( basis(X, Vf) | ~equal_sets(union_of_members(Vf), X) | element_of_set(f7(X, Vf), X) )).
% 0.13/0.35 cnf(matrix-32, plain, ( basis(X, Vf) | ~equal_sets(union_of_members(Vf), X) | element_of_collection(f8(X, Vf), Vf) )).
% 0.13/0.35 cnf(matrix-33, plain, ( basis(X, Vf) | ~equal_sets(union_of_members(Vf), X) | element_of_collection(f9(X, Vf), Vf) )).
% 0.13/0.35 cnf(matrix-34, plain, ( basis(X, Vf) | ~equal_sets(union_of_members(Vf), X) | element_of_set(f7(X, Vf), intersection_of_sets(f8(X, Vf), f9(X, Vf))) )).
% 0.13/0.35 cnf(matrix-35, plain, ( basis(X, Vf) | ~equal_sets(union_of_members(Vf), X) | ~element_of_set(f7(X, Vf), Uu9) | ~element_of_collection(Uu9, Vf) | ~subset_sets(Uu9, intersection_of_sets(f8(X, Vf), f9(X, Vf))) )).
% 0.13/0.35 cnf(matrix-36, plain, ( ~element_of_collection(U, top_of_basis(Vf)) | ~element_of_set(X, U) | element_of_set(X, f10(Vf, U, X)) )).
% 0.13/0.35 cnf(matrix-37, plain, ( ~element_of_collection(U, top_of_basis(Vf)) | ~element_of_set(X, U) | element_of_collection(f10(Vf, U, X), Vf) )).
% 0.13/0.35 cnf(matrix-38, plain, ( ~element_of_collection(U, top_of_basis(Vf)) | ~element_of_set(X, U) | subset_sets(f10(Vf, U, X), U) )).
% 0.13/0.35 cnf(matrix-39, plain, ( element_of_collection(U, top_of_basis(Vf)) | element_of_set(f11(Vf, U), U) )).
% 0.13/0.35 cnf(matrix-40, plain, ( element_of_collection(U, top_of_basis(Vf)) | ~element_of_set(f11(Vf, U), Uu11) | ~element_of_collection(Uu11, Vf) | ~subset_sets(Uu11, U) )).
% 0.13/0.35 cnf(matrix-41, plain, ( ~element_of_collection(U, subspace_topology(X, Vt, Y)) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-42, plain, ( ~element_of_collection(U, subspace_topology(X, Vt, Y)) | subset_sets(Y, X) )).
% 0.13/0.35 cnf(matrix-43, plain, ( ~element_of_collection(U, subspace_topology(X, Vt, Y)) | element_of_collection(f12(X, Vt, Y, U), Vt) )).
% 0.13/0.35 cnf(matrix-44, plain, ( ~element_of_collection(U, subspace_topology(X, Vt, Y)) | equal_sets(U, intersection_of_sets(Y, f12(X, Vt, Y, U))) )).
% 0.13/0.35 cnf(matrix-45, plain, ( element_of_collection(U, subspace_topology(X, Vt, Y)) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | ~element_of_collection(Uu12, Vt) | ~equal_sets(U, intersection_of_sets(Y, Uu12)) )).
% 0.13/0.35 cnf(matrix-46, plain, ( ~element_of_set(U, interior(Y, X, Vt)) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-47, plain, ( ~element_of_set(U, interior(Y, X, Vt)) | subset_sets(Y, X) )).
% 0.13/0.35 cnf(matrix-48, plain, ( ~element_of_set(U, interior(Y, X, Vt)) | element_of_set(U, f13(Y, X, Vt, U)) )).
% 0.13/0.35 cnf(matrix-49, plain, ( ~element_of_set(U, interior(Y, X, Vt)) | subset_sets(f13(Y, X, Vt, U), Y) )).
% 0.13/0.35 cnf(matrix-50, plain, ( ~element_of_set(U, interior(Y, X, Vt)) | open(f13(Y, X, Vt, U), X, Vt) )).
% 0.13/0.35 cnf(matrix-51, plain, ( element_of_set(U, interior(Y, X, Vt)) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | ~element_of_set(U, Uu13) | ~subset_sets(Uu13, Y) | ~open(Uu13, X, Vt) )).
% 0.13/0.35 cnf(matrix-52, plain, ( ~element_of_set(U, closure(Y, X, Vt)) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-53, plain, ( ~element_of_set(U, closure(Y, X, Vt)) | subset_sets(Y, X) )).
% 0.13/0.35 cnf(matrix-54, plain, ( ~element_of_set(U, closure(Y, X, Vt)) | ~subset_sets(Y, V) | ~closed(V, X, Vt) | element_of_set(U, V) )).
% 0.13/0.35 cnf(matrix-55, plain, ( element_of_set(U, closure(Y, X, Vt)) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | subset_sets(Y, f14(Y, X, Vt, U)) )).
% 0.13/0.35 cnf(matrix-56, plain, ( element_of_set(U, closure(Y, X, Vt)) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | closed(f14(Y, X, Vt, U), X, Vt) )).
% 0.13/0.35 cnf(matrix-57, plain, ( element_of_set(U, closure(Y, X, Vt)) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | ~element_of_set(U, f14(Y, X, Vt, U)) )).
% 0.13/0.35 cnf(matrix-58, plain, ( ~neighborhood(U, Y, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-59, plain, ( ~neighborhood(U, Y, X, Vt) | open(U, X, Vt) )).
% 0.13/0.35 cnf(matrix-60, plain, ( ~neighborhood(U, Y, X, Vt) | element_of_set(Y, U) )).
% 0.13/0.35 cnf(matrix-61, plain, ( neighborhood(U, Y, X, Vt) | ~topological_space(X, Vt) | ~open(U, X, Vt) | ~element_of_set(Y, U) )).
% 0.13/0.35 cnf(matrix-62, plain, ( ~limit_point(Z, Y, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-63, plain, ( ~limit_point(Z, Y, X, Vt) | subset_sets(Y, X) )).
% 0.13/0.35 cnf(matrix-64, plain, ( ~limit_point(Z, Y, X, Vt) | ~neighborhood(U, Z, X, Vt) | element_of_set(f15(Z, Y, X, Vt, U), intersection_of_sets(U, Y)) )).
% 0.13/0.35 cnf(matrix-65, plain, ( ~limit_point(Z, Y, X, Vt) | ~neighborhood(U, Z, X, Vt) | ~eq_p(f15(Z, Y, X, Vt, U), Z) )).
% 0.13/0.35 cnf(matrix-66, plain, ( limit_point(Z, Y, X, Vt) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | neighborhood(f16(Z, Y, X, Vt), Z, X, Vt) )).
% 0.13/0.35 cnf(matrix-67, plain, ( limit_point(Z, Y, X, Vt) | ~topological_space(X, Vt) | ~subset_sets(Y, X) | ~element_of_set(Uu16, intersection_of_sets(f16(Z, Y, X, Vt), Y)) | eq_p(Uu16, Z) )).
% 0.13/0.35 cnf(matrix-68, plain, ( ~element_of_set(U, boundary(Y, X, Vt)) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-69, plain, ( ~element_of_set(U, boundary(Y, X, Vt)) | element_of_set(U, closure(Y, X, Vt)) )).
% 0.13/0.35 cnf(matrix-70, plain, ( ~element_of_set(U, boundary(Y, X, Vt)) | element_of_set(U, closure(relative_complement_sets(Y, X), X, Vt)) )).
% 0.13/0.35 cnf(matrix-71, plain, ( element_of_set(U, boundary(Y, X, Vt)) | ~topological_space(X, Vt) | ~element_of_set(U, closure(Y, X, Vt)) | ~element_of_set(U, closure(relative_complement_sets(Y, X), X, Vt)) )).
% 0.13/0.35 cnf(matrix-72, plain, ( ~hausdorff(X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-73, plain, ( ~hausdorff(X, Vt) | ~element_of_set(X_1, X) | ~element_of_set(X_2, X) | eq_p(X_1, X_2) | neighborhood(f17(X, Vt, X_1, X_2), X_1, X, Vt) )).
% 0.13/0.35 cnf(matrix-74, plain, ( ~hausdorff(X, Vt) | ~element_of_set(X_1, X) | ~element_of_set(X_2, X) | eq_p(X_1, X_2) | neighborhood(f18(X, Vt, X_1, X_2), X_2, X, Vt) )).
% 0.13/0.35 cnf(matrix-75, plain, ( ~hausdorff(X, Vt) | ~element_of_set(X_1, X) | ~element_of_set(X_2, X) | eq_p(X_1, X_2) | disjoint_s(f17(X, Vt, X_1, X_2), f18(X, Vt, X_1, X_2)) )).
% 0.13/0.35 cnf(matrix-76, plain, ( hausdorff(X, Vt) | ~topological_space(X, Vt) | element_of_set(f19(X, Vt), X) )).
% 0.13/0.35 cnf(matrix-77, plain, ( hausdorff(X, Vt) | ~topological_space(X, Vt) | element_of_set(f20(X, Vt), X) )).
% 0.13/0.35 cnf(matrix-78, plain, ( hausdorff(X, Vt) | ~topological_space(X, Vt) | ~eq_p(f19(X, Vt), f20(X, Vt)) )).
% 0.13/0.35 cnf(matrix-79, plain, ( hausdorff(X, Vt) | ~topological_space(X, Vt) | ~neighborhood(Uu19, f19(X, Vt), X, Vt) | ~neighborhood(Uu20, f20(X, Vt), X, Vt) | ~disjoint_s(Uu19, Uu20) )).
% 0.13/0.35 cnf(matrix-80, plain, ( ~separation(Va1, Va2, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-81, plain, ( ~separation(Va1, Va2, X, Vt) | ~equal_sets(Va1, empty_set) )).
% 0.13/0.35 cnf(matrix-82, plain, ( ~separation(Va1, Va2, X, Vt) | ~equal_sets(Va2, empty_set) )).
% 0.13/0.35 cnf(matrix-83, plain, ( ~separation(Va1, Va2, X, Vt) | element_of_collection(Va1, Vt) )).
% 0.13/0.35 cnf(matrix-84, plain, ( ~separation(Va1, Va2, X, Vt) | element_of_collection(Va2, Vt) )).
% 0.13/0.35 cnf(matrix-85, plain, ( ~separation(Va1, Va2, X, Vt) | equal_sets(union_of_sets(Va1, Va2), X) )).
% 0.13/0.35 cnf(matrix-86, plain, ( ~separation(Va1, Va2, X, Vt) | disjoint_s(Va1, Va2) )).
% 0.13/0.35 cnf(matrix-87, plain, ( separation(Va1, Va2, X, Vt) | ~topological_space(X, Vt) | equal_sets(Va1, empty_set) | equal_sets(Va2, empty_set) | ~element_of_collection(Va1, Vt) | ~element_of_collection(Va2, Vt) | ~equal_sets(union_of_sets(Va1, Va2), X) | ~disjoint_s(Va1, Va2) )).
% 0.13/0.35 cnf(matrix-88, plain, ( ~connected_space(X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-89, plain, ( ~connected_space(X, Vt) | ~separation(Va1, Va2, X, Vt) )).
% 0.13/0.35 cnf(matrix-90, plain, ( connected_space(X, Vt) | ~topological_space(X, Vt) | separation(f21(X, Vt), f22(X, Vt), X, Vt) )).
% 0.13/0.35 cnf(matrix-91, plain, ( ~connected_set(Va, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-92, plain, ( ~connected_set(Va, X, Vt) | subset_sets(Va, X) )).
% 0.13/0.35 cnf(matrix-93, plain, ( ~connected_set(Va, X, Vt) | connected_space(Va, subspace_topology(X, Vt, Va)) )).
% 0.13/0.35 cnf(matrix-94, plain, ( connected_set(Va, X, Vt) | ~topological_space(X, Vt) | ~subset_sets(Va, X) | ~connected_space(Va, subspace_topology(X, Vt, Va)) )).
% 0.13/0.35 cnf(matrix-95, plain, ( ~open_covering(Vf, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-96, plain, ( ~open_covering(Vf, X, Vt) | subset_collections(Vf, Vt) )).
% 0.13/0.35 cnf(matrix-97, plain, ( ~open_covering(Vf, X, Vt) | equal_sets(union_of_members(Vf), X) )).
% 0.13/0.35 cnf(matrix-98, plain, ( open_covering(Vf, X, Vt) | ~topological_space(X, Vt) | ~subset_collections(Vf, Vt) | ~equal_sets(union_of_members(Vf), X) )).
% 0.13/0.35 cnf(matrix-99, plain, ( ~compact_space(X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-100, plain, ( ~compact_space(X, Vt) | ~open_covering(Vf1, X, Vt) | finite(f23(X, Vt, Vf1)) )).
% 0.13/0.35 cnf(matrix-101, plain, ( ~compact_space(X, Vt) | ~open_covering(Vf1, X, Vt) | subset_collections(f23(X, Vt, Vf1), Vf1) )).
% 0.13/0.35 cnf(matrix-102, plain, ( ~compact_space(X, Vt) | ~open_covering(Vf1, X, Vt) | open_covering(f23(X, Vt, Vf1), X, Vt) )).
% 0.13/0.35 cnf(matrix-103, plain, ( compact_space(X, Vt) | ~topological_space(X, Vt) | open_covering(f24(X, Vt), X, Vt) )).
% 0.13/0.35 cnf(matrix-104, plain, ( compact_space(X, Vt) | ~topological_space(X, Vt) | ~finite(Uu24) | ~subset_collections(Uu24, f24(X, Vt)) | ~open_covering(Uu24, X, Vt) )).
% 0.13/0.35 cnf(matrix-105, plain, ( ~compact_set(Va, X, Vt) | topological_space(X, Vt) )).
% 0.13/0.35 cnf(matrix-106, plain, ( ~compact_set(Va, X, Vt) | subset_sets(Va, X) )).
% 0.13/0.35 cnf(matrix-107, plain, ( ~compact_set(Va, X, Vt) | compact_space(Va, subspace_topology(X, Vt, Va)) )).
% 0.13/0.35 cnf(matrix-108, plain, ( compact_set(Va, X, Vt) | ~topological_space(X, Vt) | ~subset_sets(Va, X) | ~compact_space(Va, subspace_topology(X, Vt, Va)) )).
% 0.13/0.35 cnf(matrix-109, plain, ( basis(cx, f) )).
% 0.13/0.35 cnf(matrix-110, plain, ( element_of_collection(U, top_of_basis(f)) )).
% 0.13/0.35 cnf(matrix-111, plain, ( element_of_collection(V, top_of_basis(f)) )).
% 0.13/0.35 cnf(matrix-112, plain, ( ~element_of_collection(intersection_of_sets(U, V), top_of_basis(f)) )).
% 0.13/0.35
% 0.13/0.35 % Proof stack:
% 0.13/0.35 cnf(proof-stack, plain,
% 0.13/0.35 proof_stack(
% 0.13/0.35 start(112),
% 0.13/0.35 left_branch(0, 111, 0, 2),
% 0.13/0.35 right_branch(2)
% 0.13/0.35 )).
% 0.13/0.35 % SZS output end Proof for theBenchmark
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