%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU372+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 : Sat Jun 21 05:27:44 AM UTC 2025
% Result : Theorem 3.51s 3.73s
% Output : Proof 3.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU372+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 06:57:16 EDT 2025
% 0.12/0.33 % CPUTime :
% 3.51/3.73 % SZS status Theorem
% 3.51/3.73 % SZS output start Proof
% 3.51/3.73 tff(disjoint_type, type, (
% 3.51/3.73 disjoint: ( $i * $i ) > $o)).
% 3.51/3.73 tff(tptp_fun_B_19_type, type, (
% 3.51/3.73 tptp_fun_B_19: $i)).
% 3.51/3.73 tff(tptp_fun_E_0_type, type, (
% 3.51/3.73 tptp_fun_E_0: ( $i * $i * $i ) > $i)).
% 3.51/3.73 tff(tptp_fun_A_18_type, type, (
% 3.51/3.73 tptp_fun_A_18: $i)).
% 3.51/3.73 tff(tptp_fun_C_20_type, type, (
% 3.51/3.73 tptp_fun_C_20: $i)).
% 3.51/3.73 tff(element_type, type, (
% 3.51/3.73 element: ( $i * $i ) > $o)).
% 3.51/3.73 tff(powerset_type, type, (
% 3.51/3.73 powerset: $i > $i)).
% 3.51/3.73 tff(the_carrier_type, type, (
% 3.51/3.73 the_carrier: $i > $i)).
% 3.51/3.73 tff(open_subset_type, type, (
% 3.51/3.73 open_subset: ( $i * $i ) > $o)).
% 3.51/3.73 tff(in_type, type, (
% 3.51/3.73 in: ( $i * $i ) > $o)).
% 3.51/3.73 tff(topstr_closure_type, type, (
% 3.51/3.73 topstr_closure: ( $i * $i ) > $i)).
% 3.51/3.73 tff(point_neighbourhood_type, type, (
% 3.51/3.73 point_neighbourhood: ( $i * $i * $i ) > $o)).
% 3.51/3.73 tff(tptp_fun_D_21_type, type, (
% 3.51/3.73 tptp_fun_D_21: $i)).
% 3.51/3.73 tff(top_str_type, type, (
% 3.51/3.73 top_str: $i > $o)).
% 3.51/3.73 tff(topological_space_type, type, (
% 3.51/3.73 topological_space: $i > $o)).
% 3.51/3.73 tff(empty_carrier_type, type, (
% 3.51/3.73 empty_carrier: $i > $o)).
% 3.51/3.73 tff(tptp_fun_D_1_type, type, (
% 3.51/3.73 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 3.51/3.73 tff(tptp_fun_E_2_type, type, (
% 3.51/3.73 tptp_fun_E_2: ( $i * $i * $i ) > $i)).
% 3.51/3.73 tff(empty_type, type, (
% 3.51/3.73 empty: $i > $o)).
% 3.51/3.73 tff(one_sorted_str_type, type, (
% 3.51/3.73 one_sorted_str: $i > $o)).
% 3.51/3.73 tff(interior_type, type, (
% 3.51/3.73 interior: ( $i * $i ) > $i)).
% 3.51/3.73 tff(subset_type, type, (
% 3.51/3.73 subset: ( $i * $i ) > $o)).
% 3.51/3.73 tff(1,plain,
% 3.51/3.73 ((((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(2,plain,
% 3.51/3.73 ((element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(3,plain,
% 3.51/3.73 ((element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(4,plain,
% 3.51/3.73 ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) <=> (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(5,plain,
% 3.51/3.73 (((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))) <=> ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(monotonicity,[status(thm)],[4])).
% 3.51/3.73 tff(6,plain,
% 3.51/3.73 ((element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 3.51/3.73 inference(monotonicity,[status(thm)],[5])).
% 3.51/3.73 tff(7,plain,
% 3.51/3.73 ((element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))) <=> (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(transitivity,[status(thm)],[6, 3])).
% 3.51/3.73 tff(8,plain,
% 3.51/3.73 ((element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 3.51/3.73 inference(monotonicity,[status(thm)],[7])).
% 3.51/3.73 tff(9,plain,
% 3.51/3.73 ((element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))) <=> (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(transitivity,[status(thm)],[8, 2])).
% 3.51/3.73 tff(10,plain,
% 3.51/3.73 ((((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))))) <=> (((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))))),
% 3.51/3.73 inference(monotonicity,[status(thm)],[9])).
% 3.51/3.73 tff(11,plain,
% 3.51/3.73 ((((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18)) & (element(B!19, powerset(the_carrier(A!18))) & (element(C!20, the_carrier(A!18)) & ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))))) <=> ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))))),
% 3.51/3.73 inference(transitivity,[status(thm)],[10, 1])).
% 3.51/3.73 tff(12,plain,
% 3.51/3.73 ((~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C))))))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(13,plain,
% 3.51/3.73 ((~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (point_neighbourhood(D, A, C) => (~disjoint(D, B)))))))) <=> (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C))))))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(14,axiom,(~![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (point_neighbourhood(D, A, C) => (~disjoint(D, B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t6_yellow_6')).
% 3.51/3.73 tff(15,plain,
% 3.51/3.73 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[14, 13])).
% 3.51/3.73 tff(16,plain,
% 3.51/3.73 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[15, 12])).
% 3.51/3.73 tff(17,plain,
% 3.51/3.73 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[16, 12])).
% 3.51/3.73 tff(18,plain,
% 3.51/3.73 (~![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : ((~disjoint(D, B)) | (~point_neighbourhood(D, A, C)))))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[17, 12])).
% 3.51/3.73 tff(19,plain,
% 3.51/3.73 ((~empty_carrier(A!18)) & topological_space(A!18) & top_str(A!18) & element(B!19, powerset(the_carrier(A!18))) & element(C!20, the_carrier(A!18)) & (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) & ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[18, 11])).
% 3.51/3.73 tff(20,plain,
% 3.51/3.73 (element(B!19, powerset(the_carrier(A!18)))),
% 3.51/3.73 inference(and_elim,[status(thm)],[19])).
% 3.51/3.73 tff(21,plain,
% 3.51/3.73 (top_str(A!18)),
% 3.51/3.73 inference(and_elim,[status(thm)],[19])).
% 3.51/3.73 tff(22,plain,
% 3.51/3.73 (^[A: $i, B: $i] : refl((element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 3.51/3.73 inference(bind,[status(th)],[])).
% 3.51/3.73 tff(23,plain,
% 3.51/3.73 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.51/3.73 inference(quant_intro,[status(thm)],[22])).
% 3.51/3.73 tff(24,plain,
% 3.51/3.73 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 3.51/3.73 inference(bind,[status(th)],[])).
% 3.51/3.73 tff(25,plain,
% 3.51/3.73 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.51/3.73 inference(quant_intro,[status(thm)],[24])).
% 3.51/3.73 tff(26,plain,
% 3.51/3.73 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(27,plain,
% 3.51/3.73 (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A)))))),
% 3.51/3.73 inference(bind,[status(th)],[])).
% 3.51/3.73 tff(28,plain,
% 3.51/3.73 (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 3.51/3.73 inference(quant_intro,[status(thm)],[27])).
% 3.51/3.73 tff(29,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(topstr_closure(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_pre_topc')).
% 3.51/3.73 tff(30,plain,
% 3.51/3.73 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[29, 28])).
% 3.51/3.73 tff(31,plain,
% 3.51/3.73 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[30, 26])).
% 3.51/3.73 tff(32,plain,(
% 3.51/3.73 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 3.51/3.73 inference(skolemize,[status(sab)],[31])).
% 3.51/3.73 tff(33,plain,
% 3.51/3.73 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[32, 25])).
% 3.51/3.73 tff(34,plain,
% 3.51/3.73 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[33, 23])).
% 3.51/3.73 tff(35,plain,
% 3.51/3.73 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(36,plain,
% 3.51/3.73 ((element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18))) <=> ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 3.51/3.73 inference(rewrite,[status(thm)],[])).
% 3.51/3.73 tff(37,plain,
% 3.51/3.73 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))))),
% 3.51/3.73 inference(monotonicity,[status(thm)],[36])).
% 3.51/3.73 tff(38,plain,
% 3.51/3.73 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))))),
% 3.51/3.73 inference(transitivity,[status(thm)],[37, 35])).
% 3.51/3.73 tff(39,plain,
% 3.51/3.73 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)))),
% 3.51/3.73 inference(quant_inst,[status(thm)],[])).
% 3.51/3.73 tff(40,plain,
% 3.51/3.73 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~element(B!19, powerset(the_carrier(A!18)))) | (~top_str(A!18)) | element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))),
% 3.51/3.73 inference(modus_ponens,[status(thm)],[39, 38])).
% 3.51/3.73 tff(41,plain,
% 3.51/3.73 (element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))),
% 3.51/3.73 inference(unit_resolution,[status(thm)],[40, 34, 21, 20])).
% 3.51/3.73 tff(42,plain,
% 3.51/3.73 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E)))))))))))))))),
% 3.51/3.73 inference(bind,[status(th)],[])).
% 3.51/3.73 tff(43,plain,
% 3.51/3.73 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))),
% 3.51/3.73 inference(quant_intro,[status(thm)],[42])).
% 3.51/3.73 tff(44,plain,
% 3.51/3.73 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 3.51/3.73 inference(bind,[status(th)],[])).
% 3.51/3.73 tff(45,plain,
% 3.51/3.73 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.73 inference(quant_intro,[status(thm)],[44])).
% 3.51/3.73 tff(46,plain,
% 3.51/3.74 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 3.51/3.74 inference(bind,[status(th)],[])).
% 3.51/3.74 tff(47,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.74 inference(quant_intro,[status(thm)],[46])).
% 3.51/3.74 tff(48,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.74 inference(transitivity,[status(thm)],[47, 45])).
% 3.51/3.74 tff(49,plain,
% 3.51/3.74 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A)))))))))))))))))),
% 3.51/3.74 inference(bind,[status(th)],[])).
% 3.51/3.74 tff(50,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.74 inference(quant_intro,[status(thm)],[49])).
% 3.51/3.74 tff(51,plain,
% 3.51/3.74 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 3.51/3.74 inference(bind,[status(th)],[])).
% 3.51/3.74 tff(52,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 3.51/3.74 inference(quant_intro,[status(thm)],[51])).
% 3.51/3.74 tff(53,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 3.51/3.74 inference(rewrite,[status(thm)],[])).
% 3.51/3.74 tff(54,plain,
% 3.51/3.74 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))) <=> ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), rewrite((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))), ((element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))))),
% 3.51/3.74 inference(bind,[status(th)],[])).
% 3.51/3.74 tff(55,plain,
% 3.51/3.74 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E)))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 3.51/3.74 inference(quant_intro,[status(thm)],[54])).
% 3.51/3.74 tff(56,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, powerset(the_carrier(A))) => ((C = topstr_closure(A, B)) <=> ![D: $i] : (in(D, the_carrier(A)) => (in(D, C) <=> ![E: $i] : (element(E, powerset(the_carrier(A))) => (~((open_subset(E, A) & in(D, E)) & disjoint(B, E))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d13_pre_topc')).
% 3.51/3.74 tff(57,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[56, 55])).
% 3.51/3.74 tff(58,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | ((C = topstr_closure(A, B)) <=> ![D: $i] : ((~in(D, the_carrier(A))) | (in(D, C) <=> ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[57, 53])).
% 3.51/3.74 tff(59,plain,(
% 3.51/3.74 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & ((in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A))))))))))))))),
% 3.51/3.74 inference(skolemize,[status(sab)],[58])).
% 3.51/3.74 tff(60,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (((~in(D, C)) | ![E: $i] : ((~(open_subset(E, A) & in(D, E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & (in(D, C) | (~((~(open_subset(tptp_fun_E_0(D, B, A), A) & in(D, tptp_fun_E_0(D, B, A)) & disjoint(B, tptp_fun_E_0(D, B, A)))) | (~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))))))))) & ((C = topstr_closure(A, B)) | (in(tptp_fun_D_1(C, B, A), the_carrier(A)) & (in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~(open_subset(E, A) & in(tptp_fun_D_1(C, B, A), E) & disjoint(B, E))) | (~element(E, powerset(the_carrier(A)))))) & ((~in(tptp_fun_D_1(C, B, A), C)) | (~((~(open_subset(tptp_fun_E_2(C, B, A), A) & in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A)) & disjoint(B, tptp_fun_E_2(C, B, A)))) | (~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[59, 52])).
% 3.51/3.74 tff(61,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[60, 50])).
% 3.51/3.74 tff(62,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[61, 48])).
% 3.51/3.74 tff(63,plain,
% 3.51/3.74 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))),
% 3.51/3.74 inference(modus_ponens,[status(thm)],[62, 43])).
% 3.51/3.74 tff(64,plain,
% 3.51/3.74 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))),
% 3.51/3.74 inference(rewrite,[status(thm)],[])).
% 3.51/3.74 tff(65,plain,
% 3.51/3.74 (((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)) | (~disjoint(B, E)))))))))))))) <=> ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))),
% 3.51/3.74 inference(rewrite,[status(thm)],[])).
% 3.51/3.74 tff(66,plain,
% 3.51/3.74 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)) | (~disjoint(B, E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))))),
% 3.51/3.74 inference(monotonicity,[status(thm)],[65])).
% 3.51/3.74 tff(67,plain,
% 3.51/3.74 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)) | (~disjoint(B, E))))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E))))))))))))))),
% 3.51/3.74 inference(transitivity,[status(thm)],[66, 64])).
% 3.51/3.74 tff(68,plain,
% 3.51/3.74 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~disjoint(B, tptp_fun_E_0(D, B, A!18)))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~disjoint(B, tptp_fun_E_2(C, B, A!18))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)) | (~disjoint(B, E))))))))))))))),
% 3.51/3.74 inference(quant_inst,[status(thm)],[])).
% 3.51/3.74 tff(69,plain,
% 3.51/3.74 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (~((~((~(C = topstr_closure(A, B))) | ![D: $i] : ((~in(D, the_carrier(A))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~disjoint(B, E))))) | (~(in(D, C) | (~((~element(tptp_fun_E_0(D, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_0(D, B, A), A)) | (~in(D, tptp_fun_E_0(D, B, A))) | (~disjoint(B, tptp_fun_E_0(D, B, A)))))))))))) | (~((C = topstr_closure(A, B)) | (~((~in(tptp_fun_D_1(C, B, A), the_carrier(A))) | (~((~in(tptp_fun_D_1(C, B, A), C)) | (~((~element(tptp_fun_E_2(C, B, A), powerset(the_carrier(A)))) | (~open_subset(tptp_fun_E_2(C, B, A), A)) | (~in(tptp_fun_D_1(C, B, A), tptp_fun_E_2(C, B, A))) | (~disjoint(B, tptp_fun_E_2(C, B, A))))))) | (~(in(tptp_fun_D_1(C, B, A), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A)))) | (~open_subset(E, A)) | (~in(tptp_fun_D_1(C, B, A), E)) | (~disjoint(B, E))))))))))))))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))),
% 3.51/3.75 inference(modus_ponens,[status(thm)],[68, 67])).
% 3.51/3.75 tff(70,plain,
% 3.51/3.75 (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))),
% 3.51/3.75 inference(unit_resolution,[status(thm)],[69, 63, 21])).
% 3.51/3.75 tff(71,plain,
% 3.51/3.75 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))),
% 3.51/3.75 inference(rewrite,[status(thm)],[])).
% 3.51/3.75 tff(72,plain,
% 3.51/3.75 (((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) <=> ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))),
% 3.51/3.75 inference(rewrite,[status(thm)],[])).
% 3.51/3.75 tff(73,plain,
% 3.51/3.75 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))))),
% 3.51/3.75 inference(monotonicity,[status(thm)],[72])).
% 3.51/3.75 tff(74,plain,
% 3.51/3.75 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))),
% 3.51/3.75 inference(transitivity,[status(thm)],[73, 71])).
% 3.51/3.75 tff(75,plain,
% 3.51/3.75 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | ((~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B!19, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B!19, A!18), E)))))))))))))),
% 3.51/3.75 inference(quant_inst,[status(thm)],[])).
% 3.51/3.75 tff(76,plain,
% 3.51/3.75 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18))))) | (~(in(D, C) | (~((~disjoint(B, tptp_fun_E_0(D, B, A!18))) | (~in(D, tptp_fun_E_0(D, B, A!18))) | (~open_subset(tptp_fun_E_0(D, B, A!18), A!18)) | (~element(tptp_fun_E_0(D, B, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B)) | (~((~in(tptp_fun_D_1(C, B, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B, A!18), C)) | (~((~disjoint(B, tptp_fun_E_2(C, B, A!18))) | (~in(tptp_fun_D_1(C, B, A!18), tptp_fun_E_2(C, B, A!18))) | (~open_subset(tptp_fun_E_2(C, B, A!18), A!18)) | (~element(tptp_fun_E_2(C, B, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~disjoint(B, E)) | (~open_subset(E, A!18)) | (~in(tptp_fun_D_1(C, B, A!18), E)))))))))))))) | (~element(B!19, powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))),
% 3.51/3.75 inference(modus_ponens,[status(thm)],[75, 74])).
% 3.51/3.75 tff(77,plain,
% 3.51/3.75 (![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))),
% 3.51/3.75 inference(unit_resolution,[status(thm)],[76, 20, 70])).
% 3.51/3.75 tff(78,plain,
% 3.51/3.75 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))),
% 3.51/3.75 inference(rewrite,[status(thm)],[])).
% 3.51/3.75 tff(79,plain,
% 3.51/3.75 (((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E)))))))))))) <=> ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(80,plain,
% 3.59/3.76 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))))),
% 3.59/3.76 inference(monotonicity,[status(thm)],[79])).
% 3.59/3.76 tff(81,plain,
% 3.59/3.76 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))),
% 3.59/3.76 inference(transitivity,[status(thm)],[80, 78])).
% 3.59/3.76 tff(82,plain,
% 3.59/3.76 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | ((~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | (~((~((~(topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((topstr_closure(A!18, B!19) = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19))) | (~((~disjoint(B!19, tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18))) | (~open_subset(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), A!18)) | (~element(tptp_fun_E_2(topstr_closure(A!18, B!19), B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), topstr_closure(A!18, B!19)) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(topstr_closure(A!18, B!19), B!19, A!18), E))))))))))))),
% 3.59/3.76 inference(quant_inst,[status(thm)],[])).
% 3.59/3.76 tff(83,plain,
% 3.59/3.76 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (~((~((~(C = topstr_closure(A!18, B!19))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, C)) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, C) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18))))))))))))) | (~((C = topstr_closure(A!18, B!19)) | (~((~in(tptp_fun_D_1(C, B!19, A!18), the_carrier(A!18))) | (~((~in(tptp_fun_D_1(C, B!19, A!18), C)) | (~((~disjoint(B!19, tptp_fun_E_2(C, B!19, A!18))) | (~in(tptp_fun_D_1(C, B!19, A!18), tptp_fun_E_2(C, B!19, A!18))) | (~open_subset(tptp_fun_E_2(C, B!19, A!18), A!18)) | (~element(tptp_fun_E_2(C, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~(in(tptp_fun_D_1(C, B!19, A!18), C) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(tptp_fun_D_1(C, B!19, A!18), E))))))))))))) | (~element(topstr_closure(A!18, B!19), powerset(the_carrier(A!18)))) | ![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[82, 81])).
% 3.59/3.76 tff(84,plain,
% 3.59/3.76 (![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.76 inference(unit_resolution,[status(thm)],[83, 77, 41])).
% 3.59/3.76 tff(85,plain,
% 3.59/3.76 (^[A: $i] : refl((one_sorted_str(A) | (~top_str(A))) <=> (one_sorted_str(A) | (~top_str(A))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(86,plain,
% 3.59/3.76 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[85])).
% 3.59/3.76 tff(87,plain,
% 3.59/3.76 (![A: $i] : (one_sorted_str(A) | (~top_str(A))) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(88,plain,
% 3.59/3.76 (^[A: $i] : rewrite((top_str(A) => one_sorted_str(A)) <=> (one_sorted_str(A) | (~top_str(A))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(89,plain,
% 3.59/3.76 (![A: $i] : (top_str(A) => one_sorted_str(A)) <=> ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[88])).
% 3.59/3.76 tff(90,axiom,(![A: $i] : (top_str(A) => one_sorted_str(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l1_pre_topc')).
% 3.59/3.76 tff(91,plain,
% 3.59/3.76 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[90, 89])).
% 3.59/3.76 tff(92,plain,
% 3.59/3.76 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[91, 87])).
% 3.59/3.76 tff(93,plain,(
% 3.59/3.76 ![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(skolemize,[status(sab)],[92])).
% 3.59/3.76 tff(94,plain,
% 3.59/3.76 (![A: $i] : (one_sorted_str(A) | (~top_str(A)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[93, 86])).
% 3.59/3.76 tff(95,plain,
% 3.59/3.76 (((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!18) | (~top_str(A!18)))) <=> ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!18) | (~top_str(A!18)))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(96,plain,
% 3.59/3.76 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | (one_sorted_str(A!18) | (~top_str(A!18)))),
% 3.59/3.76 inference(quant_inst,[status(thm)],[])).
% 3.59/3.76 tff(97,plain,
% 3.59/3.76 ((~![A: $i] : (one_sorted_str(A) | (~top_str(A)))) | one_sorted_str(A!18) | (~top_str(A!18))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[96, 95])).
% 3.59/3.76 tff(98,plain,
% 3.59/3.76 (one_sorted_str(A!18)),
% 3.59/3.76 inference(unit_resolution,[status(thm)],[97, 94, 21])).
% 3.59/3.76 tff(99,plain,
% 3.59/3.76 (~empty_carrier(A!18)),
% 3.59/3.76 inference(and_elim,[status(thm)],[19])).
% 3.59/3.76 tff(100,plain,
% 3.59/3.76 (^[A: $i] : refl((empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(101,plain,
% 3.59/3.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[100])).
% 3.59/3.76 tff(102,plain,
% 3.59/3.76 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & one_sorted_str(A)) <=> (~(empty_carrier(A) | (~one_sorted_str(A))))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (~(~(empty_carrier(A) | (~one_sorted_str(A))))))), rewrite((~(~(empty_carrier(A) | (~one_sorted_str(A))))) <=> (empty_carrier(A) | (~one_sorted_str(A)))), ((~((~empty_carrier(A)) & one_sorted_str(A))) <=> (empty_carrier(A) | (~one_sorted_str(A))))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))))), rewrite(((~empty(the_carrier(A))) | (empty_carrier(A) | (~one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))), (((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(103,plain,
% 3.59/3.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[102])).
% 3.59/3.76 tff(104,plain,
% 3.59/3.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(105,plain,
% 3.59/3.76 (^[A: $i] : rewrite((((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A)))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(106,plain,
% 3.59/3.76 (![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A)))) <=> ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[105])).
% 3.59/3.76 tff(107,axiom,(![A: $i] : (((~empty_carrier(A)) & one_sorted_str(A)) => (~empty(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 3.59/3.76 tff(108,plain,
% 3.59/3.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[107, 106])).
% 3.59/3.76 tff(109,plain,
% 3.59/3.76 (![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[108, 104])).
% 3.59/3.76 tff(110,plain,(
% 3.59/3.76 ![A: $i] : ((~empty(the_carrier(A))) | (~((~empty_carrier(A)) & one_sorted_str(A))))),
% 3.59/3.76 inference(skolemize,[status(sab)],[109])).
% 3.59/3.76 tff(111,plain,
% 3.59/3.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[110, 103])).
% 3.59/3.76 tff(112,plain,
% 3.59/3.76 (![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[111, 101])).
% 3.59/3.76 tff(113,plain,
% 3.59/3.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(114,plain,
% 3.59/3.76 ((empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18))) <=> (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(115,plain,
% 3.59/3.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18)))))),
% 3.59/3.76 inference(monotonicity,[status(thm)],[114])).
% 3.59/3.76 tff(116,plain,
% 3.59/3.76 (((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))) <=> ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18))))),
% 3.59/3.76 inference(transitivity,[status(thm)],[115, 113])).
% 3.59/3.76 tff(117,plain,
% 3.59/3.76 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | (empty_carrier(A!18) | (~empty(the_carrier(A!18))) | (~one_sorted_str(A!18)))),
% 3.59/3.76 inference(quant_inst,[status(thm)],[])).
% 3.59/3.76 tff(118,plain,
% 3.59/3.76 ((~![A: $i] : (empty_carrier(A) | (~empty(the_carrier(A))) | (~one_sorted_str(A)))) | empty_carrier(A!18) | (~one_sorted_str(A!18)) | (~empty(the_carrier(A!18)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[117, 116])).
% 3.59/3.76 tff(119,plain,
% 3.59/3.76 (~empty(the_carrier(A!18))),
% 3.59/3.76 inference(unit_resolution,[status(thm)],[118, 112, 99, 98])).
% 3.59/3.76 tff(120,plain,
% 3.59/3.76 (element(C!20, the_carrier(A!18))),
% 3.59/3.76 inference(and_elim,[status(thm)],[19])).
% 3.59/3.76 tff(121,plain,
% 3.59/3.76 (^[A: $i, B: $i] : refl((empty(B) | in(A, B) | (~element(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(122,plain,
% 3.59/3.76 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[121])).
% 3.59/3.76 tff(123,plain,
% 3.59/3.76 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(124,plain,
% 3.59/3.76 (^[A: $i, B: $i] : rewrite((element(A, B) => (empty(B) | in(A, B))) <=> (empty(B) | in(A, B) | (~element(A, B))))),
% 3.59/3.76 inference(bind,[status(th)],[])).
% 3.59/3.76 tff(125,plain,
% 3.59/3.76 (![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B))) <=> ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(quant_intro,[status(thm)],[124])).
% 3.59/3.76 tff(126,axiom,(![A: $i, B: $i] : (element(A, B) => (empty(B) | in(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2_subset')).
% 3.59/3.76 tff(127,plain,
% 3.59/3.76 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[126, 125])).
% 3.59/3.76 tff(128,plain,
% 3.59/3.76 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[127, 123])).
% 3.59/3.76 tff(129,plain,(
% 3.59/3.76 ![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(skolemize,[status(sab)],[128])).
% 3.59/3.76 tff(130,plain,
% 3.59/3.76 (![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[129, 122])).
% 3.59/3.76 tff(131,plain,
% 3.59/3.76 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(132,plain,
% 3.59/3.76 ((empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18)))) <=> ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(133,plain,
% 3.59/3.76 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | ((~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18))))),
% 3.59/3.76 inference(monotonicity,[status(thm)],[132])).
% 3.59/3.76 tff(134,plain,
% 3.59/3.76 (((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)))),
% 3.59/3.76 inference(transitivity,[status(thm)],[133, 131])).
% 3.59/3.76 tff(135,plain,
% 3.59/3.76 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18)) | (~element(C!20, the_carrier(A!18))))),
% 3.59/3.76 inference(quant_inst,[status(thm)],[])).
% 3.59/3.76 tff(136,plain,
% 3.59/3.76 ((~![A: $i, B: $i] : (empty(B) | in(A, B) | (~element(A, B)))) | (~element(C!20, the_carrier(A!18))) | empty(the_carrier(A!18)) | in(C!20, the_carrier(A!18))),
% 3.59/3.76 inference(modus_ponens,[status(thm)],[135, 134])).
% 3.59/3.76 tff(137,plain,
% 3.59/3.76 (in(C!20, the_carrier(A!18))),
% 3.59/3.76 inference(unit_resolution,[status(thm)],[136, 130, 120, 119])).
% 3.59/3.76 tff(138,plain,
% 3.59/3.76 (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.76 inference(rewrite,[status(thm)],[])).
% 3.59/3.76 tff(139,plain,
% 3.59/3.76 (((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))))) <=> ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(140,plain,
% 3.59/3.77 (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))))))),
% 3.59/3.77 inference(monotonicity,[status(thm)],[139])).
% 3.59/3.77 tff(141,plain,
% 3.59/3.77 (((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))) <=> ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.77 inference(transitivity,[status(thm)],[140, 138])).
% 3.59/3.77 tff(142,plain,
% 3.59/3.77 ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | ((~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(C!20, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))))),
% 3.59/3.77 inference(quant_inst,[status(thm)],[])).
% 3.59/3.77 tff(143,plain,
% 3.59/3.77 ((~![D: $i] : ((~in(D, the_carrier(A!18))) | (~((~((~in(D, topstr_closure(A!18, B!19))) | ![E: $i] : ((~in(D, E)) | (~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E))))) | (~(in(D, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(D, B!19, A!18))) | (~in(D, tptp_fun_E_0(D, B!19, A!18))) | (~open_subset(tptp_fun_E_0(D, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(D, B!19, A!18), powerset(the_carrier(A!18)))))))))))) | (~in(C!20, the_carrier(A!18))) | (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[142, 141])).
% 3.59/3.77 tff(144,plain,
% 3.59/3.77 (~((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))))),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[143, 137, 84])).
% 3.59/3.77 tff(145,plain,
% 3.59/3.77 (((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))) | (in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))),
% 3.59/3.77 inference(tautology,[status(thm)],[])).
% 3.59/3.77 tff(146,plain,
% 3.59/3.77 (in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[145, 144])).
% 3.59/3.77 tff(147,assumption,(~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))), introduced(assumption)).
% 3.59/3.77 tff(148,plain,
% 3.59/3.77 (((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))) | point_neighbourhood(D!21, A!18, C!20)),
% 3.59/3.77 inference(tautology,[status(thm)],[])).
% 3.59/3.77 tff(149,plain,
% 3.59/3.77 (point_neighbourhood(D!21, A!18, C!20)),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[148, 147])).
% 3.59/3.77 tff(150,plain,
% 3.59/3.77 (((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))) | disjoint(D!21, B!19)),
% 3.59/3.77 inference(tautology,[status(thm)],[])).
% 3.59/3.77 tff(151,plain,
% 3.59/3.77 (disjoint(D!21, B!19)),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[150, 147])).
% 3.59/3.77 tff(152,plain,
% 3.59/3.77 (topological_space(A!18)),
% 3.59/3.77 inference(and_elim,[status(thm)],[19])).
% 3.59/3.77 tff(153,plain,
% 3.59/3.77 (^[A: $i, B: $i] : rewrite((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(154,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[153])).
% 3.59/3.77 tff(155,plain,
% 3.59/3.77 (^[A: $i, B: $i] : refl((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(156,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[155])).
% 3.59/3.77 tff(157,plain,
% 3.59/3.77 (^[A: $i, B: $i] : rewrite((empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(158,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[157])).
% 3.59/3.77 tff(159,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(transitivity,[status(thm)],[158, 156])).
% 3.59/3.77 tff(160,plain,
% 3.59/3.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ((empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))), rewrite(((empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(161,plain,
% 3.59/3.77 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[160])).
% 3.59/3.77 tff(162,plain,
% 3.59/3.77 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(163,plain,
% 3.59/3.77 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))))), quant_intro(proof_bind(^[C: $i] : rewrite((point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))) <=> ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), (![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))) <=> ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) => ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A))) => ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))), ((((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(164,plain,
% 3.59/3.77 (![A: $i, B: $i] : (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A))))) <=> ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[163])).
% 3.59/3.77 tff(165,axiom,(![A: $i, B: $i] : (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) & element(B, the_carrier(A))) => ![C: $i] : (point_neighbourhood(C, A, B) => element(C, powerset(the_carrier(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_connsp_2')).
% 3.59/3.77 tff(166,plain,
% 3.59/3.77 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[165, 164])).
% 3.59/3.77 tff(167,plain,
% 3.59/3.77 (![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[166, 162])).
% 3.59/3.77 tff(168,plain,(
% 3.59/3.77 ![A: $i, B: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A) & element(B, the_carrier(A)))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(skolemize,[status(sab)],[167])).
% 3.59/3.77 tff(169,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[168, 161])).
% 3.59/3.77 tff(170,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))) | (~top_str(A)) | (~topological_space(A)))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[169, 159])).
% 3.59/3.77 tff(171,plain,
% 3.59/3.77 (![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[170, 154])).
% 3.59/3.77 tff(172,plain,
% 3.59/3.77 (((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(173,plain,
% 3.59/3.77 ((empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) <=> (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(174,plain,
% 3.59/3.77 (((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))))),
% 3.59/3.77 inference(monotonicity,[status(thm)],[173])).
% 3.59/3.77 tff(175,plain,
% 3.59/3.77 (((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))) <=> ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 3.59/3.77 inference(transitivity,[status(thm)],[174, 172])).
% 3.59/3.77 tff(176,plain,
% 3.59/3.77 ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | (empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18)))))),
% 3.59/3.77 inference(quant_inst,[status(thm)],[])).
% 3.59/3.77 tff(177,plain,
% 3.59/3.77 ((~![A: $i, B: $i] : (empty_carrier(A) | (~element(B, the_carrier(A))) | (~top_str(A)) | (~topological_space(A)) | ![C: $i] : ((~point_neighbourhood(C, A, B)) | element(C, powerset(the_carrier(A)))))) | empty_carrier(A!18) | (~element(C!20, the_carrier(A!18))) | (~topological_space(A!18)) | (~top_str(A!18)) | ![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[176, 175])).
% 3.59/3.77 tff(178,plain,
% 3.59/3.77 (![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[177, 171, 99, 152, 21, 120])).
% 3.59/3.77 tff(179,plain,
% 3.59/3.77 (((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | ((~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))) <=> ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | (~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(180,plain,
% 3.59/3.77 ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | ((~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18))))),
% 3.59/3.77 inference(quant_inst,[status(thm)],[])).
% 3.59/3.77 tff(181,plain,
% 3.59/3.77 ((~![C: $i] : ((~point_neighbourhood(C, A!18, C!20)) | element(C, powerset(the_carrier(A!18))))) | (~point_neighbourhood(D!21, A!18, C!20)) | element(D!21, powerset(the_carrier(A!18)))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[180, 179])).
% 3.59/3.77 tff(182,plain,
% 3.59/3.77 (element(D!21, powerset(the_carrier(A!18)))),
% 3.59/3.77 inference(unit_resolution,[status(thm)],[181, 149, 178])).
% 3.59/3.77 tff(183,plain,
% 3.59/3.77 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(184,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[183])).
% 3.59/3.77 tff(185,plain,
% 3.59/3.77 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(186,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[185])).
% 3.59/3.77 tff(187,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(transitivity,[status(thm)],[186, 184])).
% 3.59/3.77 tff(188,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(rewrite,[status(thm)],[])).
% 3.59/3.77 tff(189,plain,
% 3.59/3.77 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)) <=> ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))))),
% 3.59/3.77 inference(bind,[status(th)],[])).
% 3.59/3.77 tff(190,plain,
% 3.59/3.77 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(quant_intro,[status(thm)],[189])).
% 3.59/3.77 tff(191,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(interior(A, B), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t44_tops_1')).
% 3.59/3.77 tff(192,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[191, 190])).
% 3.59/3.77 tff(193,plain,
% 3.59/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.59/3.77 inference(modus_ponens,[status(thm)],[192, 188])).
% 3.59/3.77 tff(194,plain,(
% 3.59/3.77 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.61/3.77 inference(skolemize,[status(sab)],[193])).
% 3.61/3.77 tff(195,plain,
% 3.61/3.77 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[194, 187])).
% 3.61/3.77 tff(196,plain,
% 3.61/3.77 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))),
% 3.61/3.77 inference(rewrite,[status(thm)],[])).
% 3.61/3.77 tff(197,plain,
% 3.61/3.77 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | ((~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B)))),
% 3.61/3.77 inference(quant_inst,[status(thm)],[])).
% 3.61/3.77 tff(198,plain,
% 3.61/3.77 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(interior(A, B), B)))) | (~top_str(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[197, 196])).
% 3.61/3.77 tff(199,plain,
% 3.61/3.77 (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))),
% 3.61/3.77 inference(unit_resolution,[status(thm)],[198, 195, 21])).
% 3.61/3.77 tff(200,plain,
% 3.61/3.77 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | ((~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | (~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))),
% 3.61/3.77 inference(rewrite,[status(thm)],[])).
% 3.61/3.77 tff(201,plain,
% 3.61/3.77 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | ((~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21))),
% 3.61/3.77 inference(quant_inst,[status(thm)],[])).
% 3.61/3.77 tff(202,plain,
% 3.61/3.77 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | subset(interior(A!18, B), B))) | (~element(D!21, powerset(the_carrier(A!18)))) | subset(interior(A!18, D!21), D!21)),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[201, 200])).
% 3.61/3.77 tff(203,plain,
% 3.61/3.77 (subset(interior(A!18, D!21), D!21)),
% 3.61/3.77 inference(unit_resolution,[status(thm)],[202, 199, 182])).
% 3.61/3.77 tff(204,assumption,(~disjoint(interior(A!18, D!21), B!19)), introduced(assumption)).
% 3.61/3.77 tff(205,assumption,(subset(interior(A!18, D!21), D!21)), introduced(assumption)).
% 3.61/3.77 tff(206,assumption,(disjoint(D!21, B!19)), introduced(assumption)).
% 3.61/3.77 tff(207,plain,
% 3.61/3.77 (^[A: $i, B: $i, C: $i] : refl((disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))))),
% 3.61/3.77 inference(bind,[status(th)],[])).
% 3.61/3.77 tff(208,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B))) <=> ![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 3.61/3.77 inference(quant_intro,[status(thm)],[207])).
% 3.61/3.77 tff(209,plain,
% 3.61/3.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((subset(A, B) & disjoint(B, C)) <=> (~((~disjoint(B, C)) | (~subset(A, B))))), ((~(subset(A, B) & disjoint(B, C))) <=> (~(~((~disjoint(B, C)) | (~subset(A, B))))))), rewrite((~(~((~disjoint(B, C)) | (~subset(A, B))))) <=> ((~disjoint(B, C)) | (~subset(A, B)))), ((~(subset(A, B) & disjoint(B, C))) <=> ((~disjoint(B, C)) | (~subset(A, B))))), (((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> (((~disjoint(B, C)) | (~subset(A, B))) | disjoint(A, C)))), rewrite((((~disjoint(B, C)) | (~subset(A, B))) | disjoint(A, C)) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))), (((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))))),
% 3.61/3.77 inference(bind,[status(th)],[])).
% 3.61/3.77 tff(210,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 3.61/3.77 inference(quant_intro,[status(thm)],[209])).
% 3.61/3.77 tff(211,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 3.61/3.77 inference(rewrite,[status(thm)],[])).
% 3.61/3.77 tff(212,plain,
% 3.61/3.77 (^[A: $i, B: $i, C: $i] : rewrite(((subset(A, B) & disjoint(B, C)) => disjoint(A, C)) <=> ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C)))),
% 3.61/3.77 inference(bind,[status(th)],[])).
% 3.61/3.77 tff(213,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C)) <=> ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 3.61/3.77 inference(quant_intro,[status(thm)],[212])).
% 3.61/3.77 tff(214,axiom,(![A: $i, B: $i, C: $i] : ((subset(A, B) & disjoint(B, C)) => disjoint(A, C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_xboole_1')).
% 3.61/3.77 tff(215,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[214, 213])).
% 3.61/3.77 tff(216,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[215, 211])).
% 3.61/3.77 tff(217,plain,(
% 3.61/3.77 ![A: $i, B: $i, C: $i] : ((~(subset(A, B) & disjoint(B, C))) | disjoint(A, C))),
% 3.61/3.77 inference(skolemize,[status(sab)],[216])).
% 3.61/3.77 tff(218,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[217, 210])).
% 3.61/3.77 tff(219,plain,
% 3.61/3.77 (![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[218, 208])).
% 3.61/3.77 tff(220,plain,
% 3.61/3.77 (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 3.61/3.77 inference(rewrite,[status(thm)],[])).
% 3.61/3.77 tff(221,plain,
% 3.61/3.77 ((disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21))) <=> ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 3.61/3.77 inference(rewrite,[status(thm)],[])).
% 3.61/3.77 tff(222,plain,
% 3.61/3.77 (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | ((~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19)))),
% 3.61/3.77 inference(monotonicity,[status(thm)],[221])).
% 3.61/3.77 tff(223,plain,
% 3.61/3.77 (((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))) <=> ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19))),
% 3.61/3.77 inference(transitivity,[status(thm)],[222, 220])).
% 3.61/3.77 tff(224,plain,
% 3.61/3.77 ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)))),
% 3.61/3.77 inference(quant_inst,[status(thm)],[])).
% 3.61/3.77 tff(225,plain,
% 3.61/3.77 ((~![A: $i, B: $i, C: $i] : (disjoint(A, C) | (~disjoint(B, C)) | (~subset(A, B)))) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21)) | disjoint(interior(A!18, D!21), B!19)),
% 3.61/3.77 inference(modus_ponens,[status(thm)],[224, 223])).
% 3.61/3.77 tff(226,plain,
% 3.61/3.77 ($false),
% 3.61/3.77 inference(unit_resolution,[status(thm)],[225, 219, 206, 205, 204])).
% 3.61/3.77 tff(227,plain,(disjoint(interior(A!18, D!21), B!19) | (~disjoint(D!21, B!19)) | (~subset(interior(A!18, D!21), D!21))), inference(lemma,lemma(discharge,[]))).
% 3.61/3.78 tff(228,plain,
% 3.61/3.78 (disjoint(interior(A!18, D!21), B!19)),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[227, 151, 203])).
% 3.61/3.78 tff(229,plain,
% 3.61/3.78 (^[A: $i, B: $i] : refl(((~disjoint(A, B)) | disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(230,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[229])).
% 3.61/3.78 tff(231,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(232,plain,
% 3.61/3.78 (^[A: $i, B: $i] : rewrite((disjoint(A, B) => disjoint(B, A)) <=> ((~disjoint(A, B)) | disjoint(B, A)))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(233,plain,
% 3.61/3.78 (![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A)) <=> ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[232])).
% 3.61/3.78 tff(234,axiom,(![A: $i, B: $i] : (disjoint(A, B) => disjoint(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_xboole_0')).
% 3.61/3.78 tff(235,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[234, 233])).
% 3.61/3.78 tff(236,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[235, 231])).
% 3.61/3.78 tff(237,plain,(
% 3.61/3.78 ![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(skolemize,[status(sab)],[236])).
% 3.61/3.78 tff(238,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[237, 230])).
% 3.61/3.78 tff(239,plain,
% 3.61/3.78 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(240,plain,
% 3.61/3.78 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21)))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(241,plain,
% 3.61/3.78 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(interior(A!18, D!21), B!19)) | disjoint(B!19, interior(A!18, D!21))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[240, 239])).
% 3.61/3.78 tff(242,plain,
% 3.61/3.78 (disjoint(B!19, interior(A!18, D!21))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[241, 238, 228])).
% 3.61/3.78 tff(243,plain,
% 3.61/3.78 (^[A: $i, B: $i] : refl((element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(244,plain,
% 3.61/3.78 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[243])).
% 3.61/3.78 tff(245,plain,
% 3.61/3.78 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((top_str(A) & element(B, powerset(the_carrier(A)))) <=> (~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> (~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A)))))), ((~(top_str(A) & element(B, powerset(the_carrier(A))))) <=> ((~top_str(A)) | (~element(B, powerset(the_carrier(A))))))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))), rewrite((((~top_str(A)) | (~element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))), (((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(246,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[245])).
% 3.61/3.78 tff(247,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(248,plain,
% 3.61/3.78 (^[A: $i, B: $i] : rewrite(((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A)))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(249,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A)))) <=> ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[248])).
% 3.61/3.78 tff(250,axiom,(![A: $i, B: $i] : ((top_str(A) & element(B, powerset(the_carrier(A)))) => element(interior(A, B), powerset(the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_tops_1')).
% 3.61/3.78 tff(251,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[250, 249])).
% 3.61/3.78 tff(252,plain,
% 3.61/3.78 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[251, 247])).
% 3.61/3.78 tff(253,plain,(
% 3.61/3.78 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(interior(A, B), powerset(the_carrier(A))))),
% 3.61/3.78 inference(skolemize,[status(sab)],[252])).
% 3.61/3.78 tff(254,plain,
% 3.61/3.78 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[253, 246])).
% 3.61/3.78 tff(255,plain,
% 3.61/3.78 (![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[254, 244])).
% 3.61/3.78 tff(256,plain,
% 3.61/3.78 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(257,plain,
% 3.61/3.78 ((element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18))) <=> ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(258,plain,
% 3.61/3.78 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18)))))),
% 3.61/3.78 inference(monotonicity,[status(thm)],[257])).
% 3.61/3.78 tff(259,plain,
% 3.61/3.78 (((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))) <=> ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18))))),
% 3.61/3.78 inference(transitivity,[status(thm)],[258, 256])).
% 3.61/3.78 tff(260,plain,
% 3.61/3.78 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (element(interior(A!18, D!21), powerset(the_carrier(A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | (~top_str(A!18)))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(261,plain,
% 3.61/3.78 ((~![A: $i, B: $i] : (element(interior(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!18)) | (~element(D!21, powerset(the_carrier(A!18)))) | element(interior(A!18, D!21), powerset(the_carrier(A!18)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[260, 259])).
% 3.61/3.78 tff(262,plain,
% 3.61/3.78 (element(interior(A!18, D!21), powerset(the_carrier(A!18)))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[261, 255, 21, 182])).
% 3.61/3.78 tff(263,plain,
% 3.61/3.78 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(264,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[263])).
% 3.61/3.78 tff(265,plain,
% 3.61/3.78 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(266,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[265])).
% 3.61/3.78 tff(267,plain,
% 3.61/3.78 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(268,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[267])).
% 3.61/3.78 tff(269,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(transitivity,[status(thm)],[268, 266])).
% 3.61/3.78 tff(270,plain,
% 3.61/3.78 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((topological_space(A) & top_str(A)) <=> (~((~top_str(A)) | (~topological_space(A))))), ((~(topological_space(A) & top_str(A))) <=> (~(~((~top_str(A)) | (~topological_space(A))))))), rewrite((~(~((~top_str(A)) | (~topological_space(A))))) <=> ((~top_str(A)) | (~topological_space(A)))), ((~(topological_space(A) & top_str(A))) <=> ((~top_str(A)) | (~topological_space(A))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> (((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))), rewrite((((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(271,plain,
% 3.61/3.78 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[270])).
% 3.61/3.78 tff(272,plain,
% 3.61/3.78 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(273,plain,
% 3.61/3.78 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)) <=> ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))))), rewrite(((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(274,plain,
% 3.61/3.78 (![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[273])).
% 3.61/3.78 tff(275,axiom,(![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => open_subset(interior(A, B), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t51_tops_1')).
% 3.61/3.78 tff(276,plain,
% 3.61/3.78 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[275, 274])).
% 3.61/3.78 tff(277,plain,
% 3.61/3.78 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[276, 272])).
% 3.61/3.78 tff(278,plain,(
% 3.61/3.78 ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(skolemize,[status(sab)],[277])).
% 3.61/3.78 tff(279,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[278, 271])).
% 3.61/3.78 tff(280,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)) | (~topological_space(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[279, 269])).
% 3.61/3.78 tff(281,plain,
% 3.61/3.78 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[280, 264])).
% 3.61/3.78 tff(282,plain,
% 3.61/3.78 (((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | ((~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))) <=> ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(283,plain,
% 3.61/3.78 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | ((~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18)))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(284,plain,
% 3.61/3.78 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | open_subset(interior(A, B), A)))) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[283, 282])).
% 3.61/3.78 tff(285,plain,
% 3.61/3.78 (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[284, 281, 152, 21])).
% 3.61/3.78 tff(286,plain,
% 3.61/3.78 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | ((~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(287,plain,
% 3.61/3.78 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | ((~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(288,plain,
% 3.61/3.78 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, B), A!18))) | (~element(D!21, powerset(the_carrier(A!18)))) | open_subset(interior(A!18, D!21), A!18)),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[287, 286])).
% 3.61/3.78 tff(289,plain,
% 3.61/3.78 (open_subset(interior(A!18, D!21), A!18)),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[288, 285, 182])).
% 3.61/3.78 tff(290,plain,
% 3.61/3.78 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(291,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[290])).
% 3.61/3.78 tff(292,plain,
% 3.61/3.78 (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(293,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[292])).
% 3.61/3.78 tff(294,plain,
% 3.61/3.78 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(295,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[294])).
% 3.61/3.78 tff(296,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(transitivity,[status(thm)],[295, 293])).
% 3.61/3.78 tff(297,plain,
% 3.61/3.78 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(298,plain,
% 3.61/3.78 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[297])).
% 3.61/3.78 tff(299,plain,
% 3.61/3.78 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(300,plain,
% 3.61/3.78 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))) <=> ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))))),
% 3.61/3.78 inference(bind,[status(th)],[])).
% 3.61/3.78 tff(301,plain,
% 3.61/3.78 (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(quant_intro,[status(thm)],[300])).
% 3.61/3.78 tff(302,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, powerset(the_carrier(A))) => (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_connsp_2')).
% 3.61/3.78 tff(303,plain,
% 3.61/3.78 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[302, 301])).
% 3.61/3.78 tff(304,plain,
% 3.61/3.78 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[303, 299])).
% 3.61/3.78 tff(305,plain,(
% 3.61/3.78 ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(skolemize,[status(sab)],[304])).
% 3.61/3.78 tff(306,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[305, 298])).
% 3.61/3.78 tff(307,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))) | (~topological_space(A)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[306, 296])).
% 3.61/3.78 tff(308,plain,
% 3.61/3.78 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[307, 291])).
% 3.61/3.78 tff(309,plain,
% 3.61/3.78 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(310,plain,
% 3.61/3.78 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C))))))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(311,plain,
% 3.61/3.78 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, powerset(the_carrier(A)))) | (point_neighbourhood(C, A, B) <=> in(B, interior(A, C))))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[310, 309])).
% 3.61/3.78 tff(312,plain,
% 3.61/3.78 (![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[311, 308, 99, 152, 21])).
% 3.61/3.78 tff(313,plain,
% 3.61/3.78 (((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | ((~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | (~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(314,plain,
% 3.61/3.78 ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | ((~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C)))))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(315,plain,
% 3.61/3.78 ((~![B: $i] : ((~element(B, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, B) <=> in(B, interior(A!18, C)))))) | (~element(C!20, the_carrier(A!18))) | ![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[314, 313])).
% 3.61/3.78 tff(316,plain,
% 3.61/3.78 (![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[315, 120, 312])).
% 3.61/3.78 tff(317,plain,
% 3.61/3.78 (((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | ((~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))) <=> ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | (~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(318,plain,
% 3.61/3.78 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | ((~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))))),
% 3.61/3.78 inference(quant_inst,[status(thm)],[])).
% 3.61/3.78 tff(319,plain,
% 3.61/3.78 ((~![C: $i] : ((~element(C, powerset(the_carrier(A!18)))) | (point_neighbourhood(C, A!18, C!20) <=> in(C!20, interior(A!18, C))))) | (~element(D!21, powerset(the_carrier(A!18)))) | (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))),
% 3.61/3.78 inference(modus_ponens,[status(thm)],[318, 317])).
% 3.61/3.78 tff(320,plain,
% 3.61/3.78 (point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[319, 316, 182])).
% 3.61/3.78 tff(321,plain,
% 3.61/3.78 ((~(point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))) | (~point_neighbourhood(D!21, A!18, C!20)) | in(C!20, interior(A!18, D!21))),
% 3.61/3.78 inference(tautology,[status(thm)],[])).
% 3.61/3.78 tff(322,plain,
% 3.61/3.78 ((~(point_neighbourhood(D!21, A!18, C!20) <=> in(C!20, interior(A!18, D!21)))) | in(C!20, interior(A!18, D!21))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[321, 149])).
% 3.61/3.78 tff(323,plain,
% 3.61/3.78 (in(C!20, interior(A!18, D!21))),
% 3.61/3.78 inference(unit_resolution,[status(thm)],[322, 320])).
% 3.61/3.78 tff(324,assumption,(![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), introduced(assumption)).
% 3.61/3.78 tff(325,assumption,(disjoint(B!19, interior(A!18, D!21))), introduced(assumption)).
% 3.61/3.78 tff(326,assumption,(element(interior(A!18, D!21), powerset(the_carrier(A!18)))), introduced(assumption)).
% 3.61/3.78 tff(327,assumption,(open_subset(interior(A!18, D!21), A!18)), introduced(assumption)).
% 3.61/3.78 tff(328,assumption,(in(C!20, interior(A!18, D!21))), introduced(assumption)).
% 3.61/3.78 tff(329,plain,
% 3.61/3.78 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.78 tff(330,plain,
% 3.61/3.78 (((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21)))) <=> ((~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21))))),
% 3.61/3.78 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(331,plain,
% 3.61/3.79 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21)))))),
% 3.61/3.79 inference(monotonicity,[status(thm)],[330])).
% 3.61/3.79 tff(332,plain,
% 3.61/3.79 (((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))) <=> ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21))))),
% 3.61/3.79 inference(transitivity,[status(thm)],[331, 329])).
% 3.61/3.79 tff(333,plain,
% 3.61/3.79 ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | ((~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~open_subset(interior(A!18, D!21), A!18)) | (~disjoint(B!19, interior(A!18, D!21))) | (~in(C!20, interior(A!18, D!21))))),
% 3.61/3.79 inference(quant_inst,[status(thm)],[])).
% 3.61/3.79 tff(334,plain,
% 3.61/3.79 ((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21)))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[333, 332])).
% 3.61/3.79 tff(335,plain,
% 3.61/3.79 ($false),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[334, 328, 327, 326, 325, 324])).
% 3.61/3.79 tff(336,plain,((~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))) | (~in(C!20, interior(A!18, D!21))) | (~open_subset(interior(A!18, D!21), A!18)) | (~element(interior(A!18, D!21), powerset(the_carrier(A!18)))) | (~disjoint(B!19, interior(A!18, D!21)))), inference(lemma,lemma(discharge,[]))).
% 3.61/3.79 tff(337,plain,
% 3.61/3.79 (~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[336, 323, 289, 262, 242])).
% 3.61/3.79 tff(338,assumption,(~![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), introduced(assumption)).
% 3.61/3.79 tff(339,assumption,(in(C!20, topstr_closure(A!18, B!19))), introduced(assumption)).
% 3.61/3.79 tff(340,plain,
% 3.61/3.79 ((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(341,plain,
% 3.61/3.79 (~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[340, 339, 338])).
% 3.61/3.79 tff(342,plain,
% 3.61/3.79 (((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))) | ((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(343,plain,
% 3.61/3.79 ((~((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E))))) | (~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[342, 341])).
% 3.61/3.79 tff(344,plain,
% 3.61/3.79 ($false),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[143, 137, 84, 343])).
% 3.61/3.79 tff(345,plain,((~in(C!20, topstr_closure(A!18, B!19))) | ![E: $i] : ((~element(E, powerset(the_carrier(A!18)))) | (~open_subset(E, A!18)) | (~disjoint(B!19, E)) | (~in(C!20, E)))), inference(lemma,lemma(discharge,[]))).
% 3.61/3.79 tff(346,plain,
% 3.61/3.79 (~in(C!20, topstr_closure(A!18, B!19))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[345, 337])).
% 3.61/3.79 tff(347,plain,
% 3.61/3.79 ((in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) <=> (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(348,plain,
% 3.61/3.79 (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 3.61/3.79 inference(and_elim,[status(thm)],[19])).
% 3.61/3.79 tff(349,plain,
% 3.61/3.79 (in(C!20, topstr_closure(A!18, B!19)) | ![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[348, 347])).
% 3.61/3.79 tff(350,plain,
% 3.61/3.79 (![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[349, 346])).
% 3.61/3.79 tff(351,plain,
% 3.61/3.79 (((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))) <=> ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(352,plain,
% 3.61/3.79 ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20)))),
% 3.61/3.79 inference(quant_inst,[status(thm)],[])).
% 3.61/3.79 tff(353,plain,
% 3.61/3.79 ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[352, 351])).
% 3.61/3.79 tff(354,plain,
% 3.61/3.79 ($false),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[353, 350, 151, 149])).
% 3.61/3.79 tff(355,plain,((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))), inference(lemma,lemma(discharge,[]))).
% 3.61/3.79 tff(356,plain,
% 3.61/3.79 ((~in(C!20, topstr_closure(A!18, B!19))) | (~((~disjoint(D!21, B!19)) | (~point_neighbourhood(D!21, A!18, C!20))))),
% 3.61/3.79 inference(and_elim,[status(thm)],[19])).
% 3.61/3.79 tff(357,plain,
% 3.61/3.79 (~in(C!20, topstr_closure(A!18, B!19))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[356, 355])).
% 3.61/3.79 tff(358,plain,
% 3.61/3.79 ((~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))) | in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(359,plain,
% 3.61/3.79 ((~(in(C!20, topstr_closure(A!18, B!19)) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))))) | (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[358, 357])).
% 3.61/3.79 tff(360,plain,
% 3.61/3.79 (~((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[359, 146])).
% 3.61/3.79 tff(361,plain,
% 3.61/3.79 (((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))) | disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(362,plain,
% 3.61/3.79 (disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[361, 360])).
% 3.61/3.79 tff(363,plain,
% 3.61/3.79 (((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))) <=> ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(364,plain,
% 3.61/3.79 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | ((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19))),
% 3.61/3.79 inference(quant_inst,[status(thm)],[])).
% 3.61/3.79 tff(365,plain,
% 3.61/3.79 ((~![A: $i, B: $i] : ((~disjoint(A, B)) | disjoint(B, A))) | (~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[364, 363])).
% 3.61/3.79 tff(366,plain,
% 3.61/3.79 (disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[365, 238, 362])).
% 3.61/3.79 tff(367,plain,
% 3.61/3.79 (((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))) | element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(368,plain,
% 3.61/3.79 (element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[367, 360])).
% 3.61/3.79 tff(369,plain,
% 3.61/3.79 (^[A: $i] : refl((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))),
% 3.61/3.79 inference(bind,[status(th)],[])).
% 3.61/3.79 tff(370,plain,
% 3.61/3.79 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(quant_intro,[status(thm)],[369])).
% 3.61/3.79 tff(371,plain,
% 3.61/3.79 (^[A: $i] : rewrite((empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))),
% 3.61/3.79 inference(bind,[status(th)],[])).
% 3.61/3.79 tff(372,plain,
% 3.61/3.79 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(quant_intro,[status(thm)],[371])).
% 3.61/3.79 tff(373,plain,
% 3.61/3.79 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(transitivity,[status(thm)],[372, 370])).
% 3.61/3.79 tff(374,plain,
% 3.61/3.79 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & topological_space(A) & top_str(A)) <=> (~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))))), rewrite((~(~(empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)))), ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))))), rewrite(((empty_carrier(A) | (~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))), (((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))))),
% 3.61/3.79 inference(bind,[status(th)],[])).
% 3.61/3.79 tff(375,plain,
% 3.61/3.79 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(quant_intro,[status(thm)],[374])).
% 3.61/3.79 tff(376,plain,
% 3.61/3.79 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(377,plain,
% 3.61/3.79 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) <=> ((~empty_carrier(A)) & topological_space(A) & top_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)) <=> ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))), ((element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> (element(C, the_carrier(A)) => ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))))), rewrite((element(C, the_carrier(A)) => ((~(open_subset(B, A) & in(C, B))) | point_neighbourhood(B, A, C))) <=> (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))), ((element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))) <=> ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> (((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))))), rewrite((((~empty_carrier(A)) & topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A)))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))), (((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))))),
% 3.61/3.79 inference(bind,[status(th)],[])).
% 3.61/3.79 tff(378,plain,
% 3.61/3.79 (![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 3.61/3.79 inference(quant_intro,[status(thm)],[377])).
% 3.61/3.79 tff(379,axiom,(![A: $i] : ((((~empty_carrier(A)) & topological_space(A)) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (element(C, the_carrier(A)) => ((open_subset(B, A) & in(C, B)) => point_neighbourhood(B, A, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t5_connsp_2')).
% 3.61/3.79 tff(380,plain,
% 3.61/3.79 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[379, 378])).
% 3.61/3.79 tff(381,plain,
% 3.61/3.79 (![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[380, 376])).
% 3.61/3.79 tff(382,plain,(
% 3.61/3.79 ![A: $i] : ((~((~empty_carrier(A)) & topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : (point_neighbourhood(B, A, C) | (~(open_subset(B, A) & in(C, B))) | (~element(C, the_carrier(A))))))),
% 3.61/3.79 inference(skolemize,[status(sab)],[381])).
% 3.61/3.79 tff(383,plain,
% 3.61/3.79 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[382, 375])).
% 3.61/3.79 tff(384,plain,
% 3.61/3.79 (![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[383, 373])).
% 3.61/3.79 tff(385,plain,
% 3.61/3.79 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(386,plain,
% 3.61/3.79 ((empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18))))) <=> (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(387,plain,
% 3.61/3.79 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))))),
% 3.61/3.79 inference(monotonicity,[status(thm)],[386])).
% 3.61/3.79 tff(388,plain,
% 3.61/3.79 (((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18)))))),
% 3.61/3.79 inference(transitivity,[status(thm)],[387, 385])).
% 3.61/3.79 tff(389,plain,
% 3.61/3.79 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | (empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A!18, C) | (~element(C, the_carrier(A!18))) | (~open_subset(B, A!18)))))),
% 3.61/3.79 inference(quant_inst,[status(thm)],[])).
% 3.61/3.79 tff(390,plain,
% 3.61/3.79 ((~![A: $i] : (empty_carrier(A) | (~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, B)) | point_neighbourhood(B, A, C) | (~element(C, the_carrier(A))) | (~open_subset(B, A)))))) | empty_carrier(A!18) | (~top_str(A!18)) | (~topological_space(A!18)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[389, 388])).
% 3.61/3.79 tff(391,plain,
% 3.61/3.79 (![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[390, 384, 99, 152, 21])).
% 3.61/3.79 tff(392,plain,
% 3.61/3.79 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(393,plain,
% 3.61/3.79 (((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(394,plain,
% 3.61/3.79 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))))),
% 3.61/3.79 inference(monotonicity,[status(thm)],[393])).
% 3.61/3.79 tff(395,plain,
% 3.61/3.79 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 3.61/3.79 inference(transitivity,[status(thm)],[394, 392])).
% 3.61/3.79 tff(396,plain,
% 3.61/3.79 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | ((~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | (~element(C, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))))),
% 3.61/3.79 inference(quant_inst,[status(thm)],[])).
% 3.61/3.79 tff(397,plain,
% 3.61/3.79 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!18)))) | ![C: $i] : ((~in(C, B)) | (~element(C, the_carrier(A!18))) | point_neighbourhood(B, A!18, C) | (~open_subset(B, A!18))))) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18)))) | ![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 3.61/3.79 inference(modus_ponens,[status(thm)],[396, 395])).
% 3.61/3.79 tff(398,plain,
% 3.61/3.79 (![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[397, 391, 368])).
% 3.61/3.79 tff(399,plain,
% 3.61/3.79 (((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))) | open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(400,plain,
% 3.61/3.79 (open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[399, 360])).
% 3.61/3.79 tff(401,plain,
% 3.61/3.79 (((~disjoint(B!19, tptp_fun_E_0(C!20, B!19, A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~element(tptp_fun_E_0(C!20, B!19, A!18), powerset(the_carrier(A!18))))) | in(C!20, tptp_fun_E_0(C!20, B!19, A!18))),
% 3.61/3.79 inference(tautology,[status(thm)],[])).
% 3.61/3.79 tff(402,plain,
% 3.61/3.79 (in(C!20, tptp_fun_E_0(C!20, B!19, A!18))),
% 3.61/3.79 inference(unit_resolution,[status(thm)],[401, 360])).
% 3.61/3.79 tff(403,plain,
% 3.61/3.79 (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(404,plain,
% 3.61/3.79 (((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18))) <=> ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 3.61/3.79 inference(rewrite,[status(thm)],[])).
% 3.61/3.79 tff(405,plain,
% 3.61/3.79 (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18)))))),
% 3.65/3.82 inference(monotonicity,[status(thm)],[404])).
% 3.65/3.82 tff(406,plain,
% 3.65/3.82 (((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) <=> ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))))),
% 3.65/3.82 inference(transitivity,[status(thm)],[405, 403])).
% 3.65/3.82 tff(407,plain,
% 3.65/3.82 ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | ((~element(C!20, the_carrier(A!18))) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))),
% 3.65/3.82 inference(quant_inst,[status(thm)],[])).
% 3.65/3.82 tff(408,plain,
% 3.65/3.82 ((~![C: $i] : ((~element(C, the_carrier(A!18))) | (~in(C, tptp_fun_E_0(C!20, B!19, A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)))) | (~element(C!20, the_carrier(A!18))) | point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20) | (~open_subset(tptp_fun_E_0(C!20, B!19, A!18), A!18)) | (~in(C!20, tptp_fun_E_0(C!20, B!19, A!18)))),
% 3.65/3.82 inference(modus_ponens,[status(thm)],[407, 406])).
% 3.65/3.82 tff(409,plain,
% 3.65/3.82 (point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)),
% 3.65/3.82 inference(unit_resolution,[status(thm)],[408, 120, 402, 400, 398])).
% 3.65/3.82 tff(410,plain,
% 3.65/3.82 (![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))),
% 3.65/3.82 inference(unit_resolution,[status(thm)],[349, 357])).
% 3.65/3.82 tff(411,plain,
% 3.65/3.82 (((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))) <=> ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))),
% 3.65/3.82 inference(rewrite,[status(thm)],[])).
% 3.65/3.82 tff(412,plain,
% 3.65/3.82 ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | ((~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20)))),
% 3.65/3.82 inference(quant_inst,[status(thm)],[])).
% 3.65/3.82 tff(413,plain,
% 3.65/3.82 ((~![D: $i] : ((~disjoint(D, B!19)) | (~point_neighbourhood(D, A!18, C!20)))) | (~disjoint(tptp_fun_E_0(C!20, B!19, A!18), B!19)) | (~point_neighbourhood(tptp_fun_E_0(C!20, B!19, A!18), A!18, C!20))),
% 3.65/3.82 inference(modus_ponens,[status(thm)],[412, 411])).
% 3.65/3.82 tff(414,plain,
% 3.65/3.82 ($false),
% 3.65/3.82 inference(unit_resolution,[status(thm)],[413, 410, 409, 366])).
% 3.65/3.82 % SZS output end Proof
% 3.65/3.82 % E exiting
%------------------------------------------------------------------------------