%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU318+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:27:35 AM UTC 2025
% Result : Theorem 0.99s 1.19s
% Output : Proof 1.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SEU318+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 06:44:09 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.99/1.19 % SZS status Theorem
% 0.99/1.19 % SZS output start Proof
% 0.99/1.19 tff(subset_type, type, (
% 0.99/1.19 subset: ( $i * $i ) > $o)).
% 0.99/1.19 tff(tptp_fun_B_12_type, type, (
% 0.99/1.19 tptp_fun_B_12: $i)).
% 0.99/1.19 tff(in_type, type, (
% 0.99/1.19 in: ( $i * $i ) > $o)).
% 0.99/1.19 tff(tptp_fun_C_0_type, type, (
% 0.99/1.19 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.99/1.19 tff(topstr_closure_type, type, (
% 0.99/1.19 topstr_closure: ( $i * $i ) > $i)).
% 0.99/1.19 tff(tptp_fun_A_11_type, type, (
% 0.99/1.19 tptp_fun_A_11: $i)).
% 0.99/1.19 tff(closed_subset_type, type, (
% 0.99/1.19 closed_subset: ( $i * $i ) > $o)).
% 0.99/1.19 tff(element_type, type, (
% 0.99/1.19 element: ( $i * $i ) > $o)).
% 0.99/1.19 tff(powerset_type, type, (
% 0.99/1.19 powerset: $i > $i)).
% 0.99/1.19 tff(the_carrier_type, type, (
% 0.99/1.19 the_carrier: $i > $i)).
% 0.99/1.19 tff(tptp_fun_D_9_type, type, (
% 0.99/1.19 tptp_fun_D_9: ( $i * $i * $i ) > $i)).
% 0.99/1.19 tff(topological_space_type, type, (
% 0.99/1.19 topological_space: $i > $o)).
% 0.99/1.19 tff(tptp_fun_C_10_type, type, (
% 0.99/1.19 tptp_fun_C_10: ( $i * $i ) > $i)).
% 0.99/1.19 tff(tptp_fun_C_8_type, type, (
% 0.99/1.19 tptp_fun_C_8: ( $i * $i ) > $i)).
% 0.99/1.19 tff(meet_of_subsets_type, type, (
% 0.99/1.19 meet_of_subsets: ( $i * $i ) > $i)).
% 0.99/1.19 tff(top_str_type, type, (
% 0.99/1.19 top_str: $i > $o)).
% 0.99/1.19 tff(1,plain,
% 0.99/1.19 (^[A: $i, B: $i] : refl((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(2,plain,
% 0.99/1.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[1])).
% 0.99/1.19 tff(3,plain,
% 0.99/1.19 (^[A: $i, B: $i] : rewrite((~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(4,plain,
% 0.99/1.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[3])).
% 0.99/1.19 tff(5,plain,
% 0.99/1.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[4, 2])).
% 0.99/1.19 tff(6,plain,
% 0.99/1.19 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))), rewrite((subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))) <=> (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))))), rewrite((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))), ((((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(7,plain,
% 0.99/1.19 (![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B))))) <=> ![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[6])).
% 0.99/1.19 tff(8,plain,
% 0.99/1.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(9,plain,
% 0.99/1.19 (^[A: $i, B: $i] : rewrite((subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(10,plain,
% 0.99/1.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B))) <=> ![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[9])).
% 0.99/1.19 tff(11,axiom,(![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : (in(C, A) => in(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_tarski')).
% 0.99/1.19 tff(12,plain,
% 0.99/1.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.99/1.19 tff(13,plain,
% 0.99/1.19 (![A: $i, B: $i] : (subset(A, B) <=> ![C: $i] : ((~in(C, A)) | in(C, B)))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.99/1.19 tff(14,plain,(
% 0.99/1.19 ![A: $i, B: $i] : (((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B))) & (subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))),
% 0.99/1.19 inference(skolemize,[status(sab)],[13])).
% 0.99/1.19 tff(15,plain,
% 0.99/1.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.99/1.19 tff(16,plain,
% 0.99/1.19 (![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.99/1.19 tff(17,plain,
% 0.99/1.19 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(topstr_closure(A!11, B!12), B!12)) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, B!12)))) | (~(subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(18,plain,
% 0.99/1.19 (~((~((~subset(topstr_closure(A!11, B!12), B!12)) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, B!12)))) | (~(subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.99/1.19 tff(19,plain,
% 0.99/1.19 (((~((~subset(topstr_closure(A!11, B!12), B!12)) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, B!12)))) | (~(subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)))))) | (subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))))),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.19 tff(20,plain,
% 0.99/1.19 (subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[19, 18])).
% 0.99/1.19 tff(21,assumption,(~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))), introduced(assumption)).
% 0.99/1.19 tff(22,plain,
% 0.99/1.19 ((closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))) | (topstr_closure(A!11, B!12) = B!12)),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.19 tff(23,plain,
% 0.99/1.19 (topstr_closure(A!11, B!12) = B!12),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[22, 21])).
% 0.99/1.19 tff(24,plain,
% 0.99/1.19 ((closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))) | topological_space(A!11)),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.19 tff(25,plain,
% 0.99/1.19 (topological_space(A!11)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[24, 21])).
% 0.99/1.19 tff(26,plain,
% 0.99/1.19 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(27,plain,
% 0.99/1.19 ((~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))))) <=> (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(28,axiom,(~![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ((closed_subset(B, A) => (topstr_closure(A, B) = B)) & ((topological_space(A) & (topstr_closure(A, B) = B)) => closed_subset(B, A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t52_pre_topc')).
% 0.99/1.19 tff(29,plain,
% 0.99/1.19 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.99/1.19 tff(30,plain,
% 0.99/1.19 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[29, 26])).
% 0.99/1.19 tff(31,plain,
% 0.99/1.19 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[30, 26])).
% 0.99/1.19 tff(32,plain,
% 0.99/1.19 (~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (((~closed_subset(B, A)) | (topstr_closure(A, B) = B)) & ((~(topological_space(A) & (topstr_closure(A, B) = B))) | closed_subset(B, A)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[31, 26])).
% 0.99/1.19 tff(33,plain,
% 0.99/1.19 (top_str(A!11)),
% 0.99/1.19 inference(and_elim,[status(thm)],[32])).
% 0.99/1.19 tff(34,plain,
% 0.99/1.19 (^[A: $i] : rewrite(((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(35,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[34])).
% 0.99/1.19 tff(36,plain,
% 0.99/1.19 (^[A: $i] : refl(((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(37,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[36])).
% 0.99/1.19 tff(38,plain,
% 0.99/1.19 (^[A: $i] : rewrite(((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(39,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[38])).
% 0.99/1.19 tff(40,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(transitivity,[status(thm)],[39, 37])).
% 0.99/1.19 tff(41,plain,
% 0.99/1.19 (^[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))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A))))) <=> ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))), (![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))))) <=> (((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))))), rewrite((((~top_str(A)) | (~topological_space(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(42,plain,
% 0.99/1.19 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[41])).
% 0.99/1.19 tff(43,plain,
% 0.99/1.19 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(44,plain,
% 0.99/1.19 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) <=> (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))))), (((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))) <=> ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))), rewrite(((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))) <=> (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))), (((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))) <=> (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))), (?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))) <=> ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))), ((element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))) <=> (element(B, powerset(the_carrier(A))) => ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))), rewrite((element(B, powerset(the_carrier(A))) => ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))) <=> ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))), ((element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))) <=> ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))) <=> ((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))))), rewrite(((topological_space(A) & top_str(A)) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))))),
% 0.99/1.19 inference(bind,[status(th)],[])).
% 0.99/1.19 tff(45,plain,
% 0.99/1.19 (![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))),
% 0.99/1.19 inference(quant_intro,[status(thm)],[44])).
% 0.99/1.19 tff(46,axiom,(![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ?[C: $i] : ((element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : (element(D, powerset(the_carrier(A))) => (in(D, C) <=> (closed_subset(D, A) & subset(B, D))))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_pre_topc')).
% 0.99/1.19 tff(47,plain,
% 0.99/1.19 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.99/1.19 tff(48,plain,
% 0.99/1.19 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ?[C: $i] : (element(C, powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, C) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), C)))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[47, 43])).
% 0.99/1.19 tff(49,plain,(
% 0.99/1.19 ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))) & ![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (in(D, tptp_fun_C_10(B, A)) <=> (closed_subset(D, A) & subset(B, D)))) & (topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A))))))),
% 0.99/1.19 inference(skolemize,[status(sab)],[48])).
% 0.99/1.19 tff(50,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[49, 42])).
% 0.99/1.19 tff(51,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A)))))) | (~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[50, 40])).
% 0.99/1.19 tff(52,plain,
% 0.99/1.19 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[51, 35])).
% 0.99/1.19 tff(53,plain,
% 0.99/1.19 (((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))) | ((~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))) | (~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11))))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(54,plain,
% 0.99/1.19 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))) | ((~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11))))))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(55,plain,
% 0.99/1.19 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | (~((~(topstr_closure(A, B) = meet_of_subsets(the_carrier(A), tptp_fun_C_10(B, A)))) | (~element(tptp_fun_C_10(B, A), powerset(powerset(the_carrier(A))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A)))) | (~(((~closed_subset(D, A)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A))))))))))) | (~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.99/1.19 tff(56,plain,
% 0.99/1.19 ((~topological_space(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[55, 52, 33])).
% 0.99/1.19 tff(57,plain,
% 0.99/1.19 (![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[56, 25])).
% 0.99/1.19 tff(58,plain,
% 0.99/1.19 (~((~element(B!12, powerset(the_carrier(A!11)))) | (((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11))))),
% 0.99/1.19 inference(and_elim,[status(thm)],[32])).
% 0.99/1.19 tff(59,plain,
% 0.99/1.19 (element(B!12, powerset(the_carrier(A!11)))),
% 0.99/1.19 inference(or_elim,[status(thm)],[58])).
% 0.99/1.19 tff(60,plain,
% 0.99/1.19 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))))))),
% 0.99/1.19 inference(rewrite,[status(thm)],[])).
% 0.99/1.19 tff(61,plain,
% 0.99/1.19 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))))))),
% 0.99/1.19 inference(quant_inst,[status(thm)],[])).
% 0.99/1.19 tff(62,plain,
% 0.99/1.19 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B, A!11)))) | (~element(tptp_fun_C_10(B, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B, D))) <=> in(D, tptp_fun_C_10(B, A!11)))))))))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11))))))))),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[61, 60])).
% 0.99/1.19 tff(63,plain,
% 0.99/1.19 (~((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[62, 59, 57])).
% 0.99/1.19 tff(64,plain,
% 0.99/1.19 (((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11))))))) | (topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.19 tff(65,plain,
% 0.99/1.19 (topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11))),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.99/1.19 tff(66,plain,
% 0.99/1.19 (meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)) = topstr_closure(A!11, B!12)),
% 0.99/1.19 inference(symmetry,[status(thm)],[65])).
% 0.99/1.19 tff(67,plain,
% 0.99/1.19 (meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)) = B!12),
% 0.99/1.19 inference(transitivity,[status(thm)],[66, 23])).
% 0.99/1.19 tff(68,plain,
% 0.99/1.19 (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) <=> closed_subset(B!12, A!11)),
% 0.99/1.19 inference(monotonicity,[status(thm)],[67])).
% 0.99/1.19 tff(69,plain,
% 0.99/1.19 (closed_subset(B!12, A!11) <=> closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11)),
% 0.99/1.19 inference(symmetry,[status(thm)],[68])).
% 0.99/1.19 tff(70,plain,
% 0.99/1.19 ((~closed_subset(B!12, A!11)) <=> (~closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11))),
% 0.99/1.19 inference(monotonicity,[status(thm)],[69])).
% 0.99/1.19 tff(71,plain,
% 0.99/1.19 ((closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))) | (~closed_subset(B!12, A!11))),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.19 tff(72,plain,
% 0.99/1.19 (~closed_subset(B!12, A!11)),
% 0.99/1.19 inference(unit_resolution,[status(thm)],[71, 21])).
% 0.99/1.19 tff(73,plain,
% 0.99/1.19 (~closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11)),
% 0.99/1.19 inference(modus_ponens,[status(thm)],[72, 70])).
% 0.99/1.19 tff(74,plain,
% 0.99/1.19 (((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11))))))) | element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))),
% 0.99/1.19 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(75,plain,
% 0.99/1.20 (element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[74, 63])).
% 0.99/1.20 tff(76,plain,
% 0.99/1.20 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(77,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[76])).
% 0.99/1.20 tff(78,plain,
% 0.99/1.20 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(79,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[78])).
% 0.99/1.20 tff(80,plain,
% 0.99/1.20 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(81,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[80])).
% 0.99/1.20 tff(82,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(transitivity,[status(thm)],[81, 79])).
% 0.99/1.20 tff(83,plain,
% 0.99/1.20 (^[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] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))) <=> (((~top_str(A)) | (~topological_space(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))))), rewrite((((~top_str(A)) | (~topological_space(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))) <=> ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))), (((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))) <=> ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(84,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[83])).
% 0.99/1.20 tff(85,plain,
% 0.99/1.20 (^[A: $i] : rewrite(((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(86,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[85])).
% 0.99/1.20 tff(87,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(88,plain,
% 0.99/1.20 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, B) => closed_subset(C, A)) <=> ((~in(C, B)) | closed_subset(C, A))), ((element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) <=> (element(C, powerset(the_carrier(A))) => ((~in(C, B)) | closed_subset(C, A))))), rewrite((element(C, powerset(the_carrier(A))) => ((~in(C, B)) | closed_subset(C, A))) <=> ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))), ((element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) <=> ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))))), (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) <=> ![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A))))))), ((![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)) <=> (![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A))))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)))), rewrite((![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A))))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)) <=> ((~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | closed_subset(meet_of_subsets(the_carrier(A), B), A))), ((![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)) <=> ((~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | closed_subset(meet_of_subsets(the_carrier(A), B), A)))), ((element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A))) <=> (element(B, powerset(powerset(the_carrier(A)))) => ((~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | closed_subset(meet_of_subsets(the_carrier(A), B), A))))), rewrite((element(B, powerset(powerset(the_carrier(A)))) => ((~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | closed_subset(meet_of_subsets(the_carrier(A), B), A))) <=> (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))), ((element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A))) <=> (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))))), (![B: $i] : (element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A))) <=> ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)))) <=> ((topological_space(A) & top_str(A)) => ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))))), rewrite(((topological_space(A) & top_str(A)) => ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A))))))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))), (((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)))) <=> ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))))),
% 0.99/1.20 inference(bind,[status(th)],[])).
% 0.99/1.20 tff(89,plain,
% 0.99/1.20 (![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A)))) <=> ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))),
% 0.99/1.20 inference(quant_intro,[status(thm)],[88])).
% 0.99/1.20 tff(90,axiom,(![A: $i] : ((topological_space(A) & top_str(A)) => ![B: $i] : (element(B, powerset(powerset(the_carrier(A)))) => (![C: $i] : (element(C, powerset(the_carrier(A))) => (in(C, B) => closed_subset(C, A))) => closed_subset(meet_of_subsets(the_carrier(A), B), A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t44_pre_topc')).
% 0.99/1.20 tff(91,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.99/1.20 tff(92,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~![C: $i] : ((~in(C, B)) | closed_subset(C, A) | (~element(C, powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.99/1.20 tff(93,plain,(
% 0.99/1.20 ![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A)))))) | (~element(B, powerset(powerset(the_carrier(A)))))))),
% 0.99/1.20 inference(skolemize,[status(sab)],[92])).
% 0.99/1.20 tff(94,plain,
% 0.99/1.20 (![A: $i] : ((~(topological_space(A) & top_str(A))) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.99/1.20 tff(95,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.99/1.20 tff(96,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))) | (~topological_space(A)))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[95, 82])).
% 0.99/1.20 tff(97,plain,
% 0.99/1.20 (![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[96, 77])).
% 0.99/1.20 tff(98,plain,
% 0.99/1.20 (((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))) | ((~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11))))))))) <=> ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))) | (~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11))))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(99,plain,
% 0.99/1.20 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))) | ((~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11))))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(100,plain,
% 0.99/1.20 ((~![A: $i] : ((~top_str(A)) | (~topological_space(A)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A), B), A) | (~element(B, powerset(powerset(the_carrier(A))))) | (~((~in(tptp_fun_C_8(B, A), B)) | closed_subset(tptp_fun_C_8(B, A), A) | (~element(tptp_fun_C_8(B, A), powerset(the_carrier(A))))))))) | (~top_str(A!11)) | (~topological_space(A!11)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.99/1.20 tff(101,plain,
% 0.99/1.20 ((~topological_space(A!11)) | ![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[100, 97, 33])).
% 0.99/1.20 tff(102,plain,
% 0.99/1.20 (![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[101, 25])).
% 0.99/1.20 tff(103,plain,
% 0.99/1.20 (((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | ((~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))) <=> ((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(104,plain,
% 0.99/1.20 ((closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))) <=> ((~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(105,plain,
% 0.99/1.20 ((~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))) <=> (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(106,plain,
% 0.99/1.20 ((closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))) <=> (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[105])).
% 0.99/1.20 tff(107,plain,
% 0.99/1.20 ((closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))) <=> ((~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[106, 104])).
% 0.99/1.20 tff(108,plain,
% 0.99/1.20 (((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))) <=> ((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | ((~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))))),
% 0.99/1.20 inference(monotonicity,[status(thm)],[107])).
% 0.99/1.20 tff(109,plain,
% 0.99/1.20 (((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))) <=> ((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(transitivity,[status(thm)],[108, 103])).
% 0.99/1.20 tff(110,plain,
% 0.99/1.20 ((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))))),
% 0.99/1.20 inference(quant_inst,[status(thm)],[])).
% 0.99/1.20 tff(111,plain,
% 0.99/1.20 ((~![B: $i] : (closed_subset(meet_of_subsets(the_carrier(A!11), B), A!11) | (~element(B, powerset(powerset(the_carrier(A!11))))) | (~((~in(tptp_fun_C_8(B, A!11), B)) | closed_subset(tptp_fun_C_8(B, A!11), A!11) | (~element(tptp_fun_C_8(B, A!11), powerset(the_carrier(A!11)))))))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))),
% 0.99/1.20 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.99/1.20 tff(112,plain,
% 0.99/1.20 (closed_subset(meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)), A!11) | (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[111, 102, 75])).
% 0.99/1.20 tff(113,plain,
% 0.99/1.20 (~((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[112, 73])).
% 0.99/1.20 tff(114,plain,
% 0.99/1.20 (((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))) | (~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11))),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(115,plain,
% 0.99/1.20 (~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[114, 113])).
% 0.99/1.20 tff(116,plain,
% 0.99/1.20 (((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(117,plain,
% 0.99/1.20 ((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[116, 115])).
% 0.99/1.20 tff(118,plain,
% 0.99/1.20 (((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))) | in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(119,plain,
% 0.99/1.20 (in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[118, 113])).
% 0.99/1.20 tff(120,plain,
% 0.99/1.20 ((((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | (~((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11))))) | (~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11)))),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(121,plain,
% 0.99/1.20 (((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[120, 119, 117])).
% 0.99/1.20 tff(122,plain,
% 0.99/1.20 (((~in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))) | closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11))))) | element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(123,plain,
% 0.99/1.20 (element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[122, 113])).
% 0.99/1.20 tff(124,plain,
% 0.99/1.20 (((~(topstr_closure(A!11, B!12) = meet_of_subsets(the_carrier(A!11), tptp_fun_C_10(B!12, A!11)))) | (~element(tptp_fun_C_10(B!12, A!11), powerset(powerset(the_carrier(A!11))))) | (~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11))))))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))),
% 0.99/1.20 inference(tautology,[status(thm)],[])).
% 0.99/1.20 tff(125,plain,
% 0.99/1.20 (![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))),
% 0.99/1.20 inference(unit_resolution,[status(thm)],[124, 63])).
% 0.99/1.20 tff(126,plain,
% 0.99/1.20 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))) | ((~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))) | (~(((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11)))))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))) | (~(((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11)))))),
% 0.99/1.20 inference(rewrite,[status(thm)],[])).
% 0.99/1.20 tff(127,plain,
% 0.99/1.20 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))) | ((~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))) | (~(((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11)))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(128,plain,
% 0.99/1.21 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~(((~closed_subset(D, A!11)) | (~subset(B!12, D))) <=> in(D, tptp_fun_C_10(B!12, A!11)))))) | (~element(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), powerset(the_carrier(A!11)))) | (~(((~closed_subset(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), A!11)) | (~subset(B!12, tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11)))) <=> in(tptp_fun_C_8(tptp_fun_C_10(B!12, A!11), A!11), tptp_fun_C_10(B!12, A!11))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.99/1.21 tff(129,plain,
% 0.99/1.21 ($false),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[128, 125, 123, 121])).
% 0.99/1.21 tff(130,plain,(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))), inference(lemma,lemma(discharge,[]))).
% 0.99/1.21 tff(131,plain,
% 0.99/1.21 ((~(~((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))))) <=> ((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(132,plain,
% 0.99/1.21 ((((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & (closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))) <=> (~((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(133,plain,
% 0.99/1.21 ((((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)) <=> (closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(134,plain,
% 0.99/1.21 ((~(~((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))) <=> ((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(135,plain,
% 0.99/1.21 ((topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12)) <=> (~((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(136,plain,
% 0.99/1.21 ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) <=> (~(~((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[135])).
% 0.99/1.21 tff(137,plain,
% 0.99/1.21 ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) <=> ((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(transitivity,[status(thm)],[136, 134])).
% 0.99/1.21 tff(138,plain,
% 0.99/1.21 (((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)) <=> (((~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[137])).
% 0.99/1.21 tff(139,plain,
% 0.99/1.21 (((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)) <=> (closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(transitivity,[status(thm)],[138, 133])).
% 0.99/1.21 tff(140,plain,
% 0.99/1.21 ((((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11))) <=> (((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & (closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[139])).
% 0.99/1.21 tff(141,plain,
% 0.99/1.21 ((((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11))) <=> (~((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[140, 132])).
% 0.99/1.21 tff(142,plain,
% 0.99/1.21 ((~(((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)))) <=> (~(~((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[141])).
% 0.99/1.21 tff(143,plain,
% 0.99/1.21 ((~(((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)))) <=> ((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12)))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[142, 131])).
% 0.99/1.21 tff(144,plain,
% 0.99/1.21 (~(((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) & ((~(topological_space(A!11) & (topstr_closure(A!11, B!12) = B!12))) | closed_subset(B!12, A!11)))),
% 0.99/1.21 inference(or_elim,[status(thm)],[58])).
% 0.99/1.21 tff(145,plain,
% 0.99/1.21 ((~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))) | (~(closed_subset(B!12, A!11) | (~topological_space(A!11)) | (~(topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.99/1.21 tff(146,plain,
% 0.99/1.21 (~((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[145, 130])).
% 0.99/1.21 tff(147,plain,
% 0.99/1.21 (((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) | (~(topstr_closure(A!11, B!12) = B!12))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(148,plain,
% 0.99/1.21 (~(topstr_closure(A!11, B!12) = B!12)),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[147, 146])).
% 0.99/1.21 tff(149,plain,
% 0.99/1.21 (^[A: $i, B: $i] : refl((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(150,plain,
% 0.99/1.21 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[149])).
% 0.99/1.21 tff(151,plain,
% 0.99/1.21 (^[A: $i, B: $i] : trans(trans(monotonicity(rewrite((subset(A, B) & subset(B, A)) <=> (~((~subset(A, B)) | (~subset(B, A))))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> ((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))))), rewrite(((A = B) <=> (~((~subset(A, B)) | (~subset(B, A))))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))))), rewrite((~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))), (((A = B) <=> (subset(A, B) & subset(B, A))) <=> (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(152,plain,
% 0.99/1.21 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[151])).
% 0.99/1.21 tff(153,plain,
% 0.99/1.21 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A))) <=> ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(154,axiom,(![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_xboole_0')).
% 0.99/1.21 tff(155,plain,
% 0.99/1.21 (![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.99/1.21 tff(156,plain,(
% 0.99/1.21 ![A: $i, B: $i] : ((A = B) <=> (subset(A, B) & subset(B, A)))),
% 0.99/1.21 inference(skolemize,[status(sab)],[155])).
% 0.99/1.21 tff(157,plain,
% 0.99/1.21 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[156, 152])).
% 0.99/1.21 tff(158,plain,
% 0.99/1.21 (![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.99/1.21 tff(159,plain,
% 0.99/1.21 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(160,plain,
% 0.99/1.21 ((~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))) <=> (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(161,plain,
% 0.99/1.21 ((((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12)) <=> (((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(162,plain,
% 0.99/1.21 ((~(((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12))) <=> (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[161])).
% 0.99/1.21 tff(163,plain,
% 0.99/1.21 ((~(((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12))) <=> (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(transitivity,[status(thm)],[162, 160])).
% 0.99/1.21 tff(164,plain,
% 0.99/1.21 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[163])).
% 0.99/1.21 tff(165,plain,
% 0.99/1.21 (((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12)))) <=> ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[164, 159])).
% 0.99/1.21 tff(166,plain,
% 0.99/1.21 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(topstr_closure(A!11, B!12), B!12)) | (~subset(B!12, topstr_closure(A!11, B!12)))) <=> (topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(167,plain,
% 0.99/1.21 ((~![A: $i, B: $i] : (~(((~subset(A, B)) | (~subset(B, A))) <=> (A = B)))) | (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.99/1.21 tff(168,plain,
% 0.99/1.21 (~(((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[167, 158])).
% 0.99/1.21 tff(169,plain,
% 0.99/1.21 ((((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) <=> (topstr_closure(A!11, B!12) = B!12)) | ((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) | (topstr_closure(A!11, B!12) = B!12)),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(170,plain,
% 0.99/1.21 (((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))) | (topstr_closure(A!11, B!12) = B!12)),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.99/1.21 tff(171,plain,
% 0.99/1.21 ((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[170, 148])).
% 0.99/1.21 tff(172,plain,
% 0.99/1.21 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(173,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[172])).
% 0.99/1.21 tff(174,plain,
% 0.99/1.21 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(175,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[174])).
% 0.99/1.21 tff(176,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[175, 173])).
% 0.99/1.21 tff(177,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(178,plain,
% 0.99/1.21 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(179,plain,
% 0.99/1.21 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B)))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[178])).
% 0.99/1.21 tff(180,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => subset(B, topstr_closure(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t48_pre_topc')).
% 0.99/1.21 tff(181,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.99/1.21 tff(182,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[181, 177])).
% 0.99/1.21 tff(183,plain,(
% 0.99/1.21 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(skolemize,[status(sab)],[182])).
% 0.99/1.21 tff(184,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[183, 176])).
% 0.99/1.21 tff(185,plain,
% 0.99/1.21 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(186,plain,
% 0.99/1.21 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(187,plain,
% 0.99/1.21 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | subset(B, topstr_closure(A, B))))) | (~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.99/1.21 tff(188,plain,
% 0.99/1.21 (![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[187, 184, 33])).
% 0.99/1.21 tff(189,plain,
% 0.99/1.21 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))) | ((~element(B!12, powerset(the_carrier(A!11)))) | subset(B!12, topstr_closure(A!11, B!12)))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))) | (~element(B!12, powerset(the_carrier(A!11)))) | subset(B!12, topstr_closure(A!11, B!12)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(190,plain,
% 0.99/1.21 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))) | ((~element(B!12, powerset(the_carrier(A!11)))) | subset(B!12, topstr_closure(A!11, B!12)))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(191,plain,
% 0.99/1.21 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | subset(B, topstr_closure(A!11, B)))) | (~element(B!12, powerset(the_carrier(A!11)))) | subset(B!12, topstr_closure(A!11, B!12))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[190, 189])).
% 0.99/1.21 tff(192,plain,
% 0.99/1.21 (subset(B!12, topstr_closure(A!11, B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[191, 59, 188])).
% 0.99/1.21 tff(193,plain,
% 0.99/1.21 ((~((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12)))) | (~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(194,plain,
% 0.99/1.21 ((~((~subset(B!12, topstr_closure(A!11, B!12))) | (~subset(topstr_closure(A!11, B!12), B!12)))) | (~subset(topstr_closure(A!11, B!12), B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[193, 192])).
% 0.99/1.21 tff(195,plain,
% 0.99/1.21 (~subset(topstr_closure(A!11, B!12), B!12)),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[194, 171])).
% 0.99/1.21 tff(196,plain,
% 0.99/1.21 ((~(subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))))) | subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(197,plain,
% 0.99/1.21 ((~(subset(topstr_closure(A!11, B!12), B!12) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))))) | (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[196, 195])).
% 0.99/1.21 tff(198,plain,
% 0.99/1.21 (~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[197, 20])).
% 0.99/1.21 tff(199,plain,
% 0.99/1.21 (((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(200,plain,
% 0.99/1.21 (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.99/1.21 tff(201,plain,
% 0.99/1.21 ((~![A: $i, B: $i] : (~((~((~subset(A, B)) | ![C: $i] : ((~in(C, A)) | in(C, B)))) | (~(subset(A, B) | (~((~in(tptp_fun_C_0(B, A), A)) | in(tptp_fun_C_0(B, A), B)))))))) | (~((~((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))) | (~(subset(topstr_closure(A!11, B!12), the_carrier(A!11)) | (~((~in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), the_carrier(A!11))))))))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(202,plain,
% 0.99/1.21 (~((~((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))) | (~(subset(topstr_closure(A!11, B!12), the_carrier(A!11)) | (~((~in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), the_carrier(A!11)))))))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[201, 16])).
% 0.99/1.21 tff(203,plain,
% 0.99/1.21 (((~((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))) | (~(subset(topstr_closure(A!11, B!12), the_carrier(A!11)) | (~((~in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(the_carrier(A!11), topstr_closure(A!11, B!12)), the_carrier(A!11))))))) | ((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(204,plain,
% 0.99/1.21 ((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[203, 202])).
% 0.99/1.21 tff(205,plain,
% 0.99/1.21 (^[A: $i, B: $i] : refl((element(A, powerset(B)) <=> subset(A, B)) <=> (element(A, powerset(B)) <=> subset(A, B)))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(206,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[205])).
% 0.99/1.21 tff(207,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B)) <=> ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(208,axiom,(![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 0.99/1.21 tff(209,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[208, 207])).
% 0.99/1.21 tff(210,plain,(
% 0.99/1.21 ![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.99/1.21 inference(skolemize,[status(sab)],[209])).
% 0.99/1.21 tff(211,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[210, 206])).
% 0.99/1.21 tff(212,plain,
% 0.99/1.21 ((~![A: $i, B: $i] : (element(A, powerset(B)) <=> subset(A, B))) | (element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))) <=> subset(topstr_closure(A!11, B!12), the_carrier(A!11)))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(213,plain,
% 0.99/1.21 (element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))) <=> subset(topstr_closure(A!11, B!12), the_carrier(A!11))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[212, 211])).
% 0.99/1.21 tff(214,plain,
% 0.99/1.21 (^[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))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(215,plain,
% 0.99/1.21 (![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)))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[214])).
% 0.99/1.21 tff(216,plain,
% 0.99/1.21 (^[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)))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(217,plain,
% 0.99/1.21 (![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)))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[216])).
% 0.99/1.21 tff(218,plain,
% 0.99/1.21 (![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))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(219,plain,
% 0.99/1.21 (^[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)))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(220,plain,
% 0.99/1.21 (![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))))),
% 0.99/1.21 inference(quant_intro,[status(thm)],[219])).
% 0.99/1.21 tff(221,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/sandbox2/benchmark/theBenchmark.p','dt_k6_pre_topc')).
% 0.99/1.21 tff(222,plain,
% 0.99/1.21 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[221, 220])).
% 0.99/1.21 tff(223,plain,
% 0.99/1.21 (![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[222, 218])).
% 0.99/1.21 tff(224,plain,(
% 0.99/1.21 ![A: $i, B: $i] : ((~(top_str(A) & element(B, powerset(the_carrier(A))))) | element(topstr_closure(A, B), powerset(the_carrier(A))))),
% 0.99/1.21 inference(skolemize,[status(sab)],[223])).
% 0.99/1.21 tff(225,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[224, 217])).
% 0.99/1.21 tff(226,plain,
% 0.99/1.21 (![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[225, 215])).
% 0.99/1.21 tff(227,plain,
% 0.99/1.21 (((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(228,plain,
% 0.99/1.21 ((element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~top_str(A!11))) <=> ((~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(229,plain,
% 0.99/1.21 (((~![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!11, B!12), powerset(the_carrier(A!11))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~top_str(A!11)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | ((~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11)))))),
% 0.99/1.21 inference(monotonicity,[status(thm)],[228])).
% 0.99/1.21 tff(230,plain,
% 0.99/1.21 (((~![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!11, B!12), powerset(the_carrier(A!11))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~top_str(A!11)))) <=> ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))))),
% 0.99/1.21 inference(transitivity,[status(thm)],[229, 227])).
% 0.99/1.21 tff(231,plain,
% 0.99/1.21 ((~![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!11, B!12), powerset(the_carrier(A!11))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~top_str(A!11)))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(232,plain,
% 0.99/1.21 ((~![A: $i, B: $i] : (element(topstr_closure(A, B), powerset(the_carrier(A))) | (~element(B, powerset(the_carrier(A)))) | (~top_str(A)))) | (~top_str(A!11)) | (~element(B!12, powerset(the_carrier(A!11)))) | element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11)))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.99/1.21 tff(233,plain,
% 0.99/1.21 (element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[232, 226, 33, 59])).
% 0.99/1.21 tff(234,plain,
% 0.99/1.21 ((~(element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))) <=> subset(topstr_closure(A!11, B!12), the_carrier(A!11)))) | (~element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11)))) | subset(topstr_closure(A!11, B!12), the_carrier(A!11))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(235,plain,
% 0.99/1.21 ((~(element(topstr_closure(A!11, B!12), powerset(the_carrier(A!11))) <=> subset(topstr_closure(A!11, B!12), the_carrier(A!11)))) | subset(topstr_closure(A!11, B!12), the_carrier(A!11))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.99/1.21 tff(236,plain,
% 0.99/1.21 (subset(topstr_closure(A!11, B!12), the_carrier(A!11))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[235, 213])).
% 0.99/1.21 tff(237,plain,
% 0.99/1.21 ((~((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))) | (~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))),
% 0.99/1.21 inference(tautology,[status(thm)],[])).
% 0.99/1.21 tff(238,plain,
% 0.99/1.21 ((~((~subset(topstr_closure(A!11, B!12), the_carrier(A!11))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11))))) | ![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[237, 236])).
% 0.99/1.21 tff(239,plain,
% 0.99/1.21 (![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[238, 204])).
% 0.99/1.21 tff(240,plain,
% 0.99/1.21 (((~![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11)))) <=> ((~![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11)))),
% 0.99/1.21 inference(rewrite,[status(thm)],[])).
% 0.99/1.21 tff(241,plain,
% 0.99/1.21 ((~![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11)))),
% 0.99/1.21 inference(quant_inst,[status(thm)],[])).
% 0.99/1.21 tff(242,plain,
% 0.99/1.21 ((~![C: $i] : ((~in(C, topstr_closure(A!11, B!12))) | in(C, the_carrier(A!11)))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))),
% 0.99/1.21 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.99/1.21 tff(243,plain,
% 0.99/1.21 (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))),
% 0.99/1.21 inference(unit_resolution,[status(thm)],[242, 239, 200])).
% 0.99/1.21 tff(244,plain,
% 0.99/1.21 (^[A: $i] : refl(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))))),
% 0.99/1.21 inference(bind,[status(th)],[])).
% 0.99/1.21 tff(245,plain,
% 0.99/1.21 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[244])).
% 0.99/1.22 tff(246,plain,
% 0.99/1.22 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))))),
% 0.99/1.22 inference(bind,[status(th)],[])).
% 0.99/1.22 tff(247,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[246])).
% 0.99/1.22 tff(248,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[247, 245])).
% 0.99/1.22 tff(249,plain,
% 0.99/1.22 (^[A: $i] : rewrite(((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~(closed_subset(tptp_fun_D_9(C, B, A), A) & subset(B, tptp_fun_D_9(C, B, A)))) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A))))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A)))))))))))))),
% 0.99/1.22 inference(bind,[status(th)],[])).
% 0.99/1.22 tff(250,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~(closed_subset(tptp_fun_D_9(C, B, A), A) & subset(B, tptp_fun_D_9(C, B, A)))) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A))))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[249])).
% 0.99/1.22 tff(251,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(252,plain,
% 0.99/1.22 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))) <=> (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), rewrite((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))), ((in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), (![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))) <=> ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> (element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), rewrite((element(B, powerset(the_carrier(A))) => ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))), ((element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), (![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))) <=> ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> (top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))))), rewrite((top_str(A) => ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A))))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))), ((top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))))),
% 0.99/1.22 inference(bind,[status(th)],[])).
% 0.99/1.22 tff(253,plain,
% 0.99/1.22 (![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D))))))) <=> ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.99/1.22 inference(quant_intro,[status(thm)],[252])).
% 0.99/1.22 tff(254,axiom,(![A: $i] : (top_str(A) => ![B: $i] : (element(B, powerset(the_carrier(A))) => ![C: $i] : (in(C, the_carrier(A)) => (in(C, topstr_closure(A, B)) <=> ![D: $i] : (element(D, powerset(the_carrier(A))) => ((closed_subset(D, A) & subset(B, D)) => in(C, D)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_pre_topc')).
% 0.99/1.22 tff(255,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.99/1.22 tff(256,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (in(C, topstr_closure(A, B)) <=> ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.99/1.22 tff(257,plain,(
% 0.99/1.22 ![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~(closed_subset(D, A) & subset(B, D))) | (~element(D, powerset(the_carrier(A)))))) & (in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~(closed_subset(tptp_fun_D_9(C, B, A), A) & subset(B, tptp_fun_D_9(C, B, A)))) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))))))))))),
% 0.99/1.22 inference(skolemize,[status(sab)],[256])).
% 0.99/1.22 tff(258,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.99/1.22 tff(259,plain,
% 0.99/1.22 (![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[258, 248])).
% 0.99/1.22 tff(260,plain,
% 0.99/1.22 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11)))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | (~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(261,plain,
% 0.99/1.22 (((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~(in(C, tptp_fun_D_9(C, B, A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~subset(B, tptp_fun_D_9(C, B, A!11)))))))))))) <=> ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(262,plain,
% 0.99/1.22 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~(in(C, tptp_fun_D_9(C, B, A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~subset(B, tptp_fun_D_9(C, B, A!11))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[261])).
% 0.99/1.22 tff(263,plain,
% 0.99/1.22 (((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~(in(C, tptp_fun_D_9(C, B, A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~subset(B, tptp_fun_D_9(C, B, A!11))))))))))))) <=> ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | (~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11)))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[262, 260])).
% 0.99/1.22 tff(264,plain,
% 0.99/1.22 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | ((~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~(in(C, tptp_fun_D_9(C, B, A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~subset(B, tptp_fun_D_9(C, B, A!11))))))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(265,plain,
% 0.99/1.22 ((~![A: $i] : ((~top_str(A)) | ![B: $i] : ((~element(B, powerset(the_carrier(A)))) | ![C: $i] : ((~in(C, the_carrier(A))) | (~((~((~in(C, topstr_closure(A, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A)))) | (~closed_subset(D, A)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A, B)) | (~(in(C, tptp_fun_D_9(C, B, A)) | (~element(tptp_fun_D_9(C, B, A), powerset(the_carrier(A)))) | (~closed_subset(tptp_fun_D_9(C, B, A), A)) | (~subset(B, tptp_fun_D_9(C, B, A))))))))))))) | (~top_str(A!11)) | ![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.99/1.22 tff(266,plain,
% 0.99/1.22 (![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[265, 259, 33])).
% 0.99/1.22 tff(267,plain,
% 0.99/1.22 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11)))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | (~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(268,plain,
% 0.99/1.22 (((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~((~subset(B!12, tptp_fun_D_9(C, B!12, A!11))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B!12, A!11)))))))))) <=> ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11)))))))))))),
% 0.99/1.22 inference(rewrite,[status(thm)],[])).
% 0.99/1.22 tff(269,plain,
% 0.99/1.22 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~((~subset(B!12, tptp_fun_D_9(C, B!12, A!11))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B!12, A!11))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))))),
% 0.99/1.22 inference(monotonicity,[status(thm)],[268])).
% 0.99/1.22 tff(270,plain,
% 0.99/1.22 (((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~((~subset(B!12, tptp_fun_D_9(C, B!12, A!11))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B!12, A!11))))))))))) <=> ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | (~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11)))))))))))),
% 0.99/1.22 inference(transitivity,[status(thm)],[269, 267])).
% 0.99/1.22 tff(271,plain,
% 0.99/1.22 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | ((~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~((~subset(B!12, tptp_fun_D_9(C, B!12, A!11))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B!12, A!11))))))))))),
% 0.99/1.22 inference(quant_inst,[status(thm)],[])).
% 0.99/1.22 tff(272,plain,
% 0.99/1.22 ((~![B: $i] : ((~element(B, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B, D))))) | (~(in(C, topstr_closure(A!11, B)) | (~((~subset(B, tptp_fun_D_9(C, B, A!11))) | (~closed_subset(tptp_fun_D_9(C, B, A!11), A!11)) | (~element(tptp_fun_D_9(C, B, A!11), powerset(the_carrier(A!11)))) | in(C, tptp_fun_D_9(C, B, A!11))))))))))) | (~element(B!12, powerset(the_carrier(A!11)))) | ![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))),
% 0.99/1.22 inference(modus_ponens,[status(thm)],[271, 270])).
% 0.99/1.22 tff(273,plain,
% 0.99/1.22 (![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))),
% 0.99/1.22 inference(unit_resolution,[status(thm)],[272, 59, 266])).
% 0.99/1.22 tff(274,plain,
% 0.99/1.22 (((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(275,plain,
% 0.99/1.23 (((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)) | (~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))))) <=> ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 0.99/1.23 tff(276,plain,
% 0.99/1.23 (((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)) | (~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))))))),
% 0.99/1.23 inference(monotonicity,[status(thm)],[275])).
% 0.99/1.23 tff(277,plain,
% 0.99/1.23 (((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)) | (~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))))))) <=> ((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))))),
% 0.99/1.23 inference(transitivity,[status(thm)],[276, 274])).
% 0.99/1.23 tff(278,plain,
% 0.99/1.23 ((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : (in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)) | (~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))))))),
% 0.99/1.23 inference(quant_inst,[status(thm)],[])).
% 0.99/1.23 tff(279,plain,
% 0.99/1.23 ((~![C: $i] : ((~in(C, the_carrier(A!11))) | (~((~((~in(C, topstr_closure(A!11, B!12))) | ![D: $i] : (in(C, D) | (~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D))))) | (~(in(C, topstr_closure(A!11, B!12)) | (~(in(C, tptp_fun_D_9(C, B!12, A!11)) | (~element(tptp_fun_D_9(C, B!12, A!11), powerset(the_carrier(A!11)))) | (~closed_subset(tptp_fun_D_9(C, B!12, A!11), A!11)) | (~subset(B!12, tptp_fun_D_9(C, B!12, A!11))))))))))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), the_carrier(A!11))) | (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))))),
% 0.99/1.23 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.99/1.23 tff(280,plain,
% 0.99/1.23 (~((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11)))))))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[279, 273, 243])).
% 0.99/1.23 tff(281,plain,
% 0.99/1.23 (((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~(in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12)) | (~((~element(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), powerset(the_carrier(A!11)))) | (~subset(B!12, tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))) | (~closed_subset(tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11), A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), tptp_fun_D_9(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12, A!11))))))) | ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))),
% 0.99/1.23 inference(tautology,[status(thm)],[])).
% 0.99/1.23 tff(282,plain,
% 0.99/1.23 ((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[281, 280])).
% 0.99/1.23 tff(283,plain,
% 0.99/1.23 ((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))),
% 0.99/1.23 inference(tautology,[status(thm)],[])).
% 0.99/1.23 tff(284,plain,
% 0.99/1.23 ((~((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D)))) | ![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[283, 200])).
% 0.99/1.23 tff(285,plain,
% 0.99/1.23 (![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[284, 282])).
% 0.99/1.23 tff(286,plain,
% 0.99/1.23 (((~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), topstr_closure(A!11, B!12))) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)) | (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))),
% 0.99/1.23 inference(tautology,[status(thm)],[])).
% 0.99/1.23 tff(287,plain,
% 0.99/1.23 (~in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[286, 198])).
% 0.99/1.23 tff(288,plain,
% 0.99/1.23 (((~closed_subset(B!12, A!11)) | (topstr_closure(A!11, B!12) = B!12)) | closed_subset(B!12, A!11)),
% 0.99/1.23 inference(tautology,[status(thm)],[])).
% 0.99/1.23 tff(289,plain,
% 0.99/1.23 (closed_subset(B!12, A!11)),
% 0.99/1.23 inference(unit_resolution,[status(thm)],[288, 146])).
% 0.99/1.23 tff(290,plain,
% 0.99/1.23 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12)))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12)))),
% 0.99/1.23 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(291,plain,
% 1.07/1.24 (((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | (~subset(B!12, B!12)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12)) <=> ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12)))),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(292,plain,
% 1.07/1.24 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | (~subset(B!12, B!12)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12))))),
% 1.07/1.24 inference(monotonicity,[status(thm)],[291])).
% 1.07/1.24 tff(293,plain,
% 1.07/1.24 (((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | (~subset(B!12, B!12)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))) <=> ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12)))),
% 1.07/1.24 inference(transitivity,[status(thm)],[292, 290])).
% 1.07/1.24 tff(294,plain,
% 1.07/1.24 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | ((~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | (~subset(B!12, B!12)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12))),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(295,plain,
% 1.07/1.24 ((~![D: $i] : ((~element(D, powerset(the_carrier(A!11)))) | (~closed_subset(D, A!11)) | (~subset(B!12, D)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), D))) | (~element(B!12, powerset(the_carrier(A!11)))) | (~closed_subset(B!12, A!11)) | in(tptp_fun_C_0(B!12, topstr_closure(A!11, B!12)), B!12) | (~subset(B!12, B!12))),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[294, 293])).
% 1.07/1.24 tff(296,plain,
% 1.07/1.24 (~subset(B!12, B!12)),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[295, 59, 289, 287, 285])).
% 1.07/1.24 tff(297,plain,
% 1.07/1.24 (^[A: $i] : refl(subset(A, A) <=> subset(A, A))),
% 1.07/1.24 inference(bind,[status(th)],[])).
% 1.07/1.24 tff(298,plain,
% 1.07/1.24 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.07/1.24 inference(quant_intro,[status(thm)],[297])).
% 1.07/1.24 tff(299,plain,
% 1.07/1.24 (![A: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.07/1.24 inference(rewrite,[status(thm)],[])).
% 1.07/1.24 tff(300,plain,
% 1.07/1.24 (![A: $i, B: $i] : subset(A, A) <=> ![A: $i] : subset(A, A)),
% 1.07/1.24 inference(elim_unused_vars,[status(thm)],[])).
% 1.07/1.24 tff(301,axiom,(![A: $i, B: $i] : subset(A, A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reflexivity_r1_tarski')).
% 1.07/1.24 tff(302,plain,
% 1.07/1.24 (![A: $i] : subset(A, A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[301, 300])).
% 1.07/1.24 tff(303,plain,
% 1.07/1.24 (![A: $i] : subset(A, A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[302, 299])).
% 1.07/1.24 tff(304,plain,(
% 1.07/1.24 ![A: $i] : subset(A, A)),
% 1.07/1.24 inference(skolemize,[status(sab)],[303])).
% 1.07/1.24 tff(305,plain,
% 1.07/1.24 (![A: $i] : subset(A, A)),
% 1.07/1.24 inference(modus_ponens,[status(thm)],[304, 298])).
% 1.07/1.24 tff(306,plain,
% 1.07/1.24 ((~![A: $i] : subset(A, A)) | subset(B!12, B!12)),
% 1.07/1.24 inference(quant_inst,[status(thm)],[])).
% 1.07/1.24 tff(307,plain,
% 1.07/1.24 ($false),
% 1.07/1.24 inference(unit_resolution,[status(thm)],[306, 305, 296])).
% 1.07/1.24 % SZS output end Proof
% 1.07/1.24 % E exiting
%------------------------------------------------------------------------------