%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : SEU400+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n011.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 : Thu Aug 31 16:31:23 EDT 2023

% Result   : Theorem 0.20s 0.48s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : SEU400+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14  % Command    : do_cvc5 %s %d
% 0.13/0.35  % Computer : n011.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Wed Aug 23 17:33:07 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.20/0.44  %----Proving TF0_NAR, FOF, or CNF
% 0.20/0.48  ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.VQG951YpGW/cvc5---1.0.5_11358.p...
% 0.20/0.48  ------- get file name : TPTP file name is SEU400+1
% 0.20/0.48  ------- cvc5-fof : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_11358.smt2...
% 0.20/0.48  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.20/0.48  % SZS status Theorem for SEU400+1
% 0.20/0.48  % SZS output start Proof for SEU400+1
% 0.20/0.48  (
% 0.20/0.48  (let ((_let_1 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((D $$unsorted)) (=> (forall ((E $$unsorted) (F $$unsorted) (G $$unsorted)) (=> (and (= E F) (exists ((H $$unsorted) (I $$unsorted)) (and (= (tptp.ordered_pair H I) F) (tptp.in H C) (exists ((J $$unsorted)) (and (= I J) (forall ((K $$unsorted)) (= (tptp.in K J) (and (tptp.in K (tptp.the_carrier B)) (exists ((L $$unsorted)) (and (tptp.netstr_induced_subset L A B) (exists ((M $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B M))) (and (tptp.element M (tptp.the_carrier B)) (= H (tptp.topstr_closure A L)) (= K M) (= L (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1))))))))))))))) (= E G) (exists ((N $$unsorted) (O $$unsorted)) (and (= (tptp.ordered_pair N O) G) (tptp.in N C) (exists ((P $$unsorted)) (and (= O P) (forall ((Q $$unsorted)) (= (tptp.in Q P) (and (tptp.in Q (tptp.the_carrier B)) (exists ((R $$unsorted)) (and (tptp.netstr_induced_subset R A B) (exists ((S $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B S))) (and (tptp.element S (tptp.the_carrier B)) (= N (tptp.topstr_closure A R)) (= Q S) (= R (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1)))))))))))))))) (= F G))) (exists ((E $$unsorted)) (forall ((F $$unsorted)) (= (tptp.in F E) (exists ((G $$unsorted)) (and (tptp.in G (tptp.cartesian_product2 C D)) (= G F) (exists ((T $$unsorted) (U $$unsorted)) (and (= (tptp.ordered_pair T U) F) (tptp.in T C) (exists ((V $$unsorted)) (and (= U V) (forall ((W $$unsorted)) (= (tptp.in W V) (and (tptp.in W (tptp.the_carrier B)) (exists ((X $$unsorted)) (and (tptp.netstr_induced_subset X A B) (exists ((Y $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B Y))) (and (tptp.element Y (tptp.the_carrier B)) (= T (tptp.topstr_closure A X)) (= W Y) (= X (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1)))))))))))))))))))))))))) (let ((_let_2 (not (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((D $$unsorted)) (exists ((E $$unsorted)) (forall ((F $$unsorted)) (= (tptp.in F E) (and (tptp.in F (tptp.cartesian_product2 C D)) (exists ((G $$unsorted) (H $$unsorted)) (and (= (tptp.ordered_pair G H) F) (tptp.in G C) (exists ((I $$unsorted)) (and (= H I) (forall ((J $$unsorted)) (= (tptp.in J I) (and (tptp.in J (tptp.the_carrier B)) (exists ((K $$unsorted)) (and (tptp.netstr_induced_subset K A B) (exists ((L $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B L))) (and (tptp.element L (tptp.the_carrier B)) (= G (tptp.topstr_closure A K)) (= J L) (= K (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1))))))))))))))))))))))))) (let ((_let_3 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_3012 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (tptp.empty_carrier B) (not (tptp.transitive_relstr B)) (not (tptp.directed_relstr B)) (not (tptp.net_str B A)) (not (forall ((E $$unsorted)) (not (forall ((F $$unsorted)) (= (tptp.in F E) (and (not (forall ((T $$unsorted) (U $$unsorted)) (or (not (= F (tptp.ordered_pair T U))) (not (tptp.in T C)) (not (forall ((W $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B W))) (let ((_let_2 (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1)))) (let ((_let_3 (tptp.the_carrier B))) (= (and (tptp.in W _let_3) (tptp.element W _let_3) (tptp.netstr_induced_subset _let_2 A B) (= T (tptp.topstr_closure A _let_2))) (tptp.in W U)))))))))) (tptp.in F (tptp.cartesian_product2 C BOUND_VARIABLE_3012)))))))))))) (let ((_let_4 (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_1833 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (tptp.empty_carrier B) (not (tptp.transitive_relstr B)) (not (tptp.directed_relstr B)) (not (tptp.net_str B A)) (not (forall ((E $$unsorted)) (not (forall ((F $$unsorted)) (= (tptp.in F E) (and (tptp.in F (tptp.cartesian_product2 C BOUND_VARIABLE_1833)) (not (forall ((G $$unsorted) (H $$unsorted)) (or (not (= F (tptp.ordered_pair G H))) (not (tptp.in G C)) (not (forall ((J $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B J))) (let ((_let_2 (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1)))) (let ((_let_3 (tptp.the_carrier B))) (= (and (tptp.in J _let_3) (tptp.element J _let_3) (tptp.netstr_induced_subset _let_2 A B) (= G (tptp.topstr_closure A _let_2))) (tptp.in J H)))))))))))))))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (ASSUME :args (_let_1)) (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (TRANS (ALPHA_EQUIV :args (_let_4 (= A A) (= B B) (= E E) (= F F) (= G T) (= H U) (= J W) (= C C) (= BOUND_VARIABLE_1833 BOUND_VARIABLE_3012))) (MACRO_SR_PRED_INTRO :args ((= (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (BOUND_VARIABLE_3012 $$unsorted)) (or (tptp.empty_carrier A) (not (tptp.topological_space A)) (not (tptp.top_str A)) (tptp.empty_carrier B) (not (tptp.transitive_relstr B)) (not (tptp.directed_relstr B)) (not (tptp.net_str B A)) (not (forall ((E $$unsorted)) (not (forall ((F $$unsorted)) (= (tptp.in F E) (and (tptp.in F (tptp.cartesian_product2 C BOUND_VARIABLE_3012)) (not (forall ((T $$unsorted) (U $$unsorted)) (or (not (= F (tptp.ordered_pair T U))) (not (tptp.in T C)) (not (forall ((W $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B W))) (let ((_let_2 (tptp.relation_rng_as_subset (tptp.the_carrier _let_1) (tptp.the_carrier A) (tptp.the_mapping A _let_1)))) (let ((_let_3 (tptp.the_carrier B))) (= (and (tptp.in W _let_3) (tptp.element W _let_3) (tptp.netstr_induced_subset _let_2 A B) (= T (tptp.topstr_closure A _let_2))) (tptp.in W U)))))))))))))))))) _let_3) SB_DEFAULT SBA_SEQUENTIAL RW_EXT_REWRITE)))) (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) :args ((not _let_3) true _let_4)) :args (false true _let_3)) :args (_let_2 (forall ((A $$unsorted)) (=> (tptp.top_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.empty B) (tptp.open_subset B A) (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) (tptp.nowhere_dense B A))))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.finite A))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (tptp.finite A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset A)) (tptp.finite B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.finite A) (tptp.finite B)) (tptp.finite (tptp.cartesian_product2 A B)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.open_subset B A) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.open_subset B A) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.nowhere_dense B A) (tptp.boundary_set B A)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.boundary_set B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and (tptp.closed_subset B A) _let_1) (and _let_1 (tptp.nowhere_dense B A)))))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (let ((_let_1 (tptp.nowhere_dense B A))) (let ((_let_2 (tptp.open_subset B A))) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (and _let_2 _let_1) (and (tptp.empty B) _let_2 (tptp.closed_subset B A) (tptp.v1_membered B) (tptp.v2_membered B) (tptp.v3_membered B) (tptp.v4_membered B) (tptp.v5_membered B) (tptp.boundary_set B A) _let_1)))))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset A))) (not (tptp.empty B)) (tptp.finite B)))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.powerset (tptp.the_carrier A)))) (not (tptp.empty B)) (tptp.finite B))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_1) (tptp.relation_of2 D B _let_1)) (forall ((E $$unsorted) (F $$unsorted) (G $$unsorted) (H $$unsorted)) (=> (= (tptp.net_str_of A B C D) (tptp.net_str_of E F G H)) (and (= A E) (= B F) (= C G) (= D H))))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A)))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (=> (tptp.rel_str A) (tptp.relation_of2_as_subset (tptp.the_InternalRel A) _let_1 _let_1)))) (forall ((A $$unsorted)) (=> (not (tptp.empty A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (not (tptp.empty B)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty A)) (not (tptp.empty B))) (not (tptp.empty (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset A)) (tptp.empty B)))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.finite A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.topological_space A) (tptp.top_str A)) (exists ((B $$unsorted)) (and (tptp.element B (tptp.powerset (tptp.the_carrier A))) (not (tptp.empty B)) (tptp.closed_subset B A))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (and (tptp.open_subset B A) (tptp.closed_subset B A))))))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.boundary_set B A)))))) (forall ((A $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A)) (forall ((B $$unsorted)) (=> (tptp.element B (tptp.powerset (tptp.the_carrier A))) (=> (tptp.empty B) (tptp.nowhere_dense B A)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted) (D $$unsorted)) (let ((_let_1 (tptp.net_str_of A B C D))) (let ((_let_2 (tptp.the_carrier A))) (=> (and (tptp.one_sorted_str A) (not (tptp.empty B)) (tptp.relation_of2 C B B) (tptp.function D) (tptp.quasi_total D B _let_2) (tptp.relation_of2 D B _let_2)) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A)))))) (exists ((A $$unsorted)) (and (tptp.empty A) (tptp.relation A))) (forall ((A $$unsorted)) (=> (tptp.empty A) (tptp.relation A))) (exists ((A $$unsorted)) (and (not (tptp.empty A)) (tptp.relation A))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty A)) (tptp.relation A)) (not (tptp.empty (tptp.relation_rng A))))) (forall ((A $$unsorted)) (let ((_let_1 (tptp.relation_rng A))) (=> (tptp.empty A) (and (tptp.empty _let_1) (tptp.relation _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (=> (tptp.strict_net_str B A) (= B (tptp.net_str_of A (tptp.the_carrier B) (tptp.the_InternalRel B) (tptp.the_mapping A B)))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (= (tptp.relation_of2_as_subset C A B) (tptp.relation_of2 C A B))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.net_str _let_1 A))))) (forall ((A $$unsorted)) (=> (tptp.rel_str A) (tptp.one_sorted_str A))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2_as_subset C A B) (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.subnet C A B) (and (not (tptp.empty_carrier C)) (tptp.transitive_relstr C) (tptp.directed_relstr C) (tptp.net_str C A)))))) (forall ((A $$unsorted)) (not (tptp.empty (tptp.powerset A)))) (exists ((A $$unsorted)) (and (tptp.one_sorted_str A) (not (tptp.empty_carrier A)))) (forall ((A $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A)) (not (tptp.empty (tptp.the_carrier A))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (tptp.topological_space A) (tptp.top_str A) (tptp.element B (tptp.powerset (tptp.the_carrier A)))) (tptp.closed_subset (tptp.topstr_closure A B) A))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.element C (tptp.powerset (tptp.cartesian_product2 A B))) (tptp.relation C))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (exists ((B $$unsorted)) (and (tptp.net_str B A) (tptp.strict_net_str B A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.strict_net_str _let_1 A))))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.netstr_restr_to_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (not (tptp.empty_carrier _let_1)) (tptp.transitive_relstr _let_1) (tptp.strict_net_str _let_1 A) (tptp.directed_relstr _let_1))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A)) (exists ((C $$unsorted)) (and (tptp.subnet C A B) (not (tptp.empty_carrier C)) (tptp.transitive_relstr C) (tptp.strict_net_str C A) (tptp.directed_relstr C))))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_mapping A B))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (and (not (tptp.empty _let_1)) (tptp.relation _let_1) (tptp.function _let_1) (tptp.quasi_total _let_1 (tptp.the_carrier B) (tptp.the_carrier A)))))) (forall ((A $$unsorted) (B $$unsorted)) (=> (tptp.in A B) (not (tptp.in B A)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (= (tptp.relation_rng_as_subset A B C) (tptp.relation_rng C)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (= (tptp.subnetstr_of_element A B C) (tptp.netstr_restr_to_element A B C)))) true true (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (=> (tptp.relation_of2 C A B) (tptp.element (tptp.relation_rng_as_subset A B C) (tptp.powerset B)))) (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.powerset (tptp.the_carrier A)))) (=> (and (tptp.top_str A) (tptp.element B _let_1)) (tptp.element (tptp.topstr_closure A B) _let_1)))) (forall ((A $$unsorted) (B $$unsorted) (C $$unsorted)) (let ((_let_1 (tptp.subnetstr_of_element A B C))) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.transitive_relstr B) (tptp.directed_relstr B) (tptp.net_str B A) (tptp.element C (tptp.the_carrier B))) (and (tptp.strict_net_str _let_1 A) (tptp.subnet _let_1 A B))))) (forall ((A $$unsorted)) (=> (tptp.top_str A) (tptp.one_sorted_str A))) (forall ((A $$unsorted)) (=> (tptp.one_sorted_str A) (forall ((B $$unsorted)) (=> (tptp.net_str B A) (tptp.rel_str B))))) true (forall ((A $$unsorted) (B $$unsorted)) (=> (and (not (tptp.empty_carrier A)) (tptp.one_sorted_str A) (not (tptp.empty_carrier B)) (tptp.net_str B A)) (forall ((C $$unsorted)) (=> (tptp.netstr_induced_subset C A B) (tptp.element C (tptp.powerset (tptp.the_carrier A))))))) true (forall ((A $$unsorted) (B $$unsorted)) (let ((_let_1 (tptp.the_carrier A))) (let ((_let_2 (tptp.the_carrier B))) (let ((_let_3 (tptp.the_mapping A B))) (=> (and (tptp.one_sorted_str A) (tptp.net_str B A)) (and (tptp.function _let_3) (tptp.quasi_total _let_3 _let_2 _let_1) (tptp.relation_of2_as_subset _let_3 _let_2 _let_1))))))) _let_1 true)))))))
% 0.20/0.48  )
% 0.20/0.48  % SZS output end Proof for SEU400+1
% 0.20/0.48  % cvc5---1.0.5 exiting
% 0.20/0.48  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------