%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU174+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:08 AM UTC 2025
% Result : Theorem 0.21s 0.43s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEU174+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n002.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:14:16 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.43 % SZS status Theorem
% 0.21/0.43 % SZS output start Proof
% 0.21/0.43 tff(in_type, type, (
% 0.21/0.43 in: ( $i * $i ) > $o)).
% 0.21/0.43 tff(empty_set_type, type, (
% 0.21/0.43 empty_set: $i)).
% 0.21/0.43 tff(subset_complement_type, type, (
% 0.21/0.43 subset_complement: ( $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_D_1_type, type, (
% 0.21/0.43 tptp_fun_D_1: ( $i * $i * $i ) > $i)).
% 0.21/0.43 tff(tptp_fun_A_8_type, type, (
% 0.21/0.43 tptp_fun_A_8: $i)).
% 0.21/0.43 tff(tptp_fun_B_5_type, type, (
% 0.21/0.43 tptp_fun_B_5: $i > $i)).
% 0.21/0.43 tff(powerset_type, type, (
% 0.21/0.43 powerset: $i > $i)).
% 0.21/0.43 tff(empty_type, type, (
% 0.21/0.43 empty: $i > $o)).
% 0.21/0.43 tff(tptp_fun_B_7_type, type, (
% 0.21/0.43 tptp_fun_B_7: $i)).
% 0.21/0.43 tff(element_type, type, (
% 0.21/0.43 element: ( $i * $i ) > $o)).
% 0.21/0.43 tff(complements_of_subsets_type, type, (
% 0.21/0.43 complements_of_subsets: ( $i * $i ) > $i)).
% 0.21/0.43 tff(1,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl(((~empty(B)) | (~in(A, B))) <=> ((~empty(B)) | (~in(A, B))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(2,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[1])).
% 0.21/0.43 tff(3,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(rewrite((in(A, B) & empty(B)) <=> (~((~empty(B)) | (~in(A, B))))), ((~(in(A, B) & empty(B))) <=> (~(~((~empty(B)) | (~in(A, B))))))), rewrite((~(~((~empty(B)) | (~in(A, B))))) <=> ((~empty(B)) | (~in(A, B)))), ((~(in(A, B) & empty(B))) <=> ((~empty(B)) | (~in(A, B)))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(4,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[3])).
% 0.21/0.43 tff(5,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B))) <=> ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(6,axiom,(![A: $i, B: $i] : (~(in(A, B) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_boole')).
% 0.21/0.43 tff(7,plain,
% 0.21/0.43 (![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.21/0.43 tff(8,plain,(
% 0.21/0.43 ![A: $i, B: $i] : (~(in(A, B) & empty(B)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[7])).
% 0.21/0.43 tff(9,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.21/0.43 tff(10,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.21/0.43 tff(11,plain,
% 0.21/0.43 (empty(empty_set) <=> empty(empty_set)),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(12,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.21/0.43 tff(13,plain,
% 0.21/0.43 (empty(empty_set)),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[12, 11])).
% 0.21/0.43 tff(14,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set)))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(15,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set)))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(16,plain,
% 0.21/0.43 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.21/0.43 tff(17,plain,
% 0.21/0.43 (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set)),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[16, 13, 10])).
% 0.21/0.43 tff(18,plain,
% 0.21/0.43 (^[A: $i] : refl((~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))) <=> (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(19,plain,
% 0.21/0.43 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[18])).
% 0.21/0.43 tff(20,plain,
% 0.21/0.43 (^[A: $i] : rewrite((element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A))) <=> (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(21,plain,
% 0.21/0.43 (![A: $i] : (element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[20])).
% 0.21/0.43 tff(22,plain,
% 0.21/0.43 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(23,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc2_subset_1')).
% 0.21/0.43 tff(24,plain,
% 0.21/0.43 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[23, 22])).
% 0.21/0.43 tff(25,plain,(
% 0.21/0.43 ![A: $i] : (element(tptp_fun_B_5(A), powerset(A)) & empty(tptp_fun_B_5(A)))),
% 0.21/0.43 inference(skolemize,[status(sab)],[24])).
% 0.21/0.43 tff(26,plain,
% 0.21/0.43 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[25, 21])).
% 0.21/0.43 tff(27,plain,
% 0.21/0.43 (![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[26, 19])).
% 0.21/0.43 tff(28,plain,
% 0.21/0.43 ((~![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))) | (~((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~empty(tptp_fun_B_5(powerset(A!8))))))),
% 0.21/0.43 inference(quant_inst,[status(thm)],[])).
% 0.21/0.43 tff(29,plain,
% 0.21/0.43 (~((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~empty(tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[28, 27])).
% 0.21/0.43 tff(30,plain,
% 0.21/0.43 (((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~empty(tptp_fun_B_5(powerset(A!8))))) | element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))),
% 0.21/0.43 inference(tautology,[status(thm)],[])).
% 0.21/0.43 tff(31,plain,
% 0.21/0.43 (element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))),
% 0.21/0.43 inference(unit_resolution,[status(thm)],[30, 29])).
% 0.21/0.43 tff(32,plain,
% 0.21/0.43 (^[A: $i, B: $i] : refl(((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))) <=> ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(33,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[32])).
% 0.21/0.43 tff(34,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite(((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))) <=> ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(35,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[34])).
% 0.21/0.43 tff(36,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(transitivity,[status(thm)],[35, 33])).
% 0.21/0.43 tff(37,plain,
% 0.21/0.43 (^[A: $i, B: $i] : rewrite(((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))) & ((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))) <=> ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(38,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))) & ((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B)))))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[37])).
% 0.21/0.43 tff(39,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))),
% 0.21/0.43 inference(rewrite,[status(thm)],[])).
% 0.21/0.43 tff(40,plain,
% 0.21/0.43 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B)))) <=> ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))), ((element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B))))) <=> (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))), rewrite((element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) <=> ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))))), ((element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B))))) <=> ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))))))), (![C: $i] : (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B))))) <=> ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))), ((element(B, powerset(powerset(A))) => ![C: $i] : (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B)))))) <=> (element(B, powerset(powerset(A))) => ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))))))), rewrite((element(B, powerset(powerset(A))) => ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))))) <=> ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))), ((element(B, powerset(powerset(A))) => ![C: $i] : (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B)))))) <=> ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))))),
% 0.21/0.43 inference(bind,[status(th)],[])).
% 0.21/0.43 tff(41,plain,
% 0.21/0.43 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ![C: $i] : (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B)))))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))),
% 0.21/0.43 inference(quant_intro,[status(thm)],[40])).
% 0.21/0.43 tff(42,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => ![C: $i] : (element(C, powerset(powerset(A))) => ((C = complements_of_subsets(A, B)) <=> ![D: $i] : (element(D, powerset(A)) => (in(D, C) <=> in(subset_complement(A, D), B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_setfam_1')).
% 0.21/0.43 tff(43,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.21/0.43 tff(44,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | ((C = complements_of_subsets(A, B)) <=> ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[43, 39])).
% 0.21/0.43 tff(45,plain,(
% 0.21/0.43 ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B)))) & ((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))),
% 0.21/0.43 inference(skolemize,[status(sab)],[44])).
% 0.21/0.43 tff(46,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.21/0.43 tff(47,plain,
% 0.21/0.43 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))),
% 0.21/0.43 inference(modus_ponens,[status(thm)],[46, 36])).
% 0.21/0.43 tff(48,plain,
% 0.21/0.43 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(49,plain,
% 0.21/0.44 (((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) | (~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))))))))) <=> ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(50,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) | (~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[49])).
% 0.21/0.44 tff(51,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) | (~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))))))),
% 0.21/0.44 inference(transitivity,[status(thm)],[50, 48])).
% 0.21/0.44 tff(52,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) | (~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))))))))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(53,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.21/0.44 tff(54,plain,
% 0.21/0.44 (![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))),
% 0.21/0.44 inference(unit_resolution,[status(thm)],[53, 47, 31])).
% 0.21/0.44 tff(55,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A)))))) <=> (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(56,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))))) <=> (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A))))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(57,axiom,(~![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t46_setfam_1')).
% 0.21/0.44 tff(58,plain,
% 0.21/0.44 (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.21/0.44 tff(59,plain,
% 0.21/0.44 (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[58, 55])).
% 0.21/0.44 tff(60,plain,
% 0.21/0.44 (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.21/0.44 tff(61,plain,
% 0.21/0.44 (~![A: $i, B: $i] : ((~((~(B = empty_set)) & (complements_of_subsets(A, B) = empty_set))) | (~element(B, powerset(powerset(A)))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[60, 55])).
% 0.21/0.44 tff(62,plain,(
% 0.21/0.44 ~((~((~(B!7 = empty_set)) & (complements_of_subsets(A!8, B!7) = empty_set))) | (~element(B!7, powerset(powerset(A!8)))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[61])).
% 0.21/0.44 tff(63,plain,
% 0.21/0.44 ((~(B!7 = empty_set)) & (complements_of_subsets(A!8, B!7) = empty_set)),
% 0.21/0.44 inference(or_elim,[status(thm)],[62])).
% 0.21/0.44 tff(64,plain,
% 0.21/0.44 (complements_of_subsets(A!8, B!7) = empty_set),
% 0.21/0.44 inference(and_elim,[status(thm)],[63])).
% 0.21/0.44 tff(65,plain,
% 0.21/0.44 (empty_set = complements_of_subsets(A!8, B!7)),
% 0.21/0.44 inference(symmetry,[status(thm)],[64])).
% 0.21/0.44 tff(66,plain,
% 0.21/0.44 (element(empty_set, powerset(powerset(A!8))) <=> element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8)))),
% 0.21/0.44 inference(monotonicity,[status(thm)],[65])).
% 0.21/0.44 tff(67,plain,
% 0.21/0.44 (element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8))) <=> element(empty_set, powerset(powerset(A!8)))),
% 0.21/0.44 inference(symmetry,[status(thm)],[66])).
% 0.21/0.44 tff(68,plain,
% 0.21/0.44 (element(B!7, powerset(powerset(A!8)))),
% 0.21/0.44 inference(or_elim,[status(thm)],[62])).
% 0.21/0.44 tff(69,plain,
% 0.21/0.44 (^[A: $i, B: $i] : refl(((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A)))) <=> ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(70,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A)))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[69])).
% 0.21/0.44 tff(71,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A)))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(72,plain,
% 0.21/0.44 (^[A: $i, B: $i] : rewrite((element(B, powerset(powerset(A))) => element(complements_of_subsets(A, B), powerset(powerset(A)))) <=> ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A)))))),
% 0.21/0.44 inference(bind,[status(th)],[])).
% 0.21/0.44 tff(73,plain,
% 0.21/0.44 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => element(complements_of_subsets(A, B), powerset(powerset(A)))) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(quant_intro,[status(thm)],[72])).
% 0.21/0.44 tff(74,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => element(complements_of_subsets(A, B), powerset(powerset(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_setfam_1')).
% 0.21/0.44 tff(75,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.21/0.44 tff(76,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[75, 71])).
% 0.21/0.44 tff(77,plain,(
% 0.21/0.44 ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(skolemize,[status(sab)],[76])).
% 0.21/0.44 tff(78,plain,
% 0.21/0.44 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))),
% 0.21/0.44 inference(modus_ponens,[status(thm)],[77, 70])).
% 0.21/0.44 tff(79,plain,
% 0.21/0.44 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))) | ((~element(B!7, powerset(powerset(A!8)))) | element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))) | (~element(B!7, powerset(powerset(A!8)))) | element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8))))),
% 0.21/0.44 inference(rewrite,[status(thm)],[])).
% 0.21/0.44 tff(80,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))) | ((~element(B!7, powerset(powerset(A!8)))) | element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8))))),
% 0.21/0.44 inference(quant_inst,[status(thm)],[])).
% 0.21/0.44 tff(81,plain,
% 0.21/0.44 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | element(complements_of_subsets(A, B), powerset(powerset(A))))) | (~element(B!7, powerset(powerset(A!8)))) | element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.21/0.45 tff(82,plain,
% 0.21/0.45 (element(complements_of_subsets(A!8, B!7), powerset(powerset(A!8)))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[81, 78, 68])).
% 0.21/0.45 tff(83,plain,
% 0.21/0.45 (element(empty_set, powerset(powerset(A!8)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[82, 67])).
% 0.21/0.45 tff(84,plain,
% 0.21/0.45 (((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))) | ((~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))) <=> ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))) | (~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(85,plain,
% 0.21/0.45 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))) | ((~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(86,plain,
% 0.21/0.45 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (C = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))))) | (~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.21/0.45 tff(87,plain,
% 0.21/0.45 (~((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[86, 83, 54])).
% 0.21/0.45 tff(88,plain,
% 0.21/0.45 (((~((~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), tptp_fun_B_5(powerset(A!8))))))) | (~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))))) | ((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(89,plain,
% 0.21/0.45 ((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[88, 87])).
% 0.21/0.45 tff(90,plain,
% 0.21/0.45 ((empty_set = B!7) <=> (B!7 = empty_set)),
% 0.21/0.45 inference(commutativity,[status(thm)],[])).
% 0.21/0.45 tff(91,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl(((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(92,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[91])).
% 0.21/0.45 tff(93,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(94,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite((element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B)))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(95,plain,
% 0.21/0.45 (![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B)) <=> ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[94])).
% 0.21/0.45 tff(96,axiom,(![A: $i, B: $i] : (element(B, powerset(powerset(A))) => (complements_of_subsets(A, complements_of_subsets(A, B)) = B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','involutiveness_k7_setfam_1')).
% 0.21/0.45 tff(97,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.21/0.45 tff(98,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.21/0.45 tff(99,plain,(
% 0.21/0.45 ![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(skolemize,[status(sab)],[98])).
% 0.21/0.45 tff(100,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.21/0.45 tff(101,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | ((~element(B!7, powerset(powerset(A!8)))) | (complements_of_subsets(A!8, complements_of_subsets(A!8, B!7)) = B!7))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | (~element(B!7, powerset(powerset(A!8)))) | (complements_of_subsets(A!8, complements_of_subsets(A!8, B!7)) = B!7))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(102,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | ((~element(B!7, powerset(powerset(A!8)))) | (complements_of_subsets(A!8, complements_of_subsets(A!8, B!7)) = B!7))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(103,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | (complements_of_subsets(A, complements_of_subsets(A, B)) = B))) | (~element(B!7, powerset(powerset(A!8)))) | (complements_of_subsets(A!8, complements_of_subsets(A!8, B!7)) = B!7)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.21/0.45 tff(104,plain,
% 0.21/0.45 (complements_of_subsets(A!8, complements_of_subsets(A!8, B!7)) = B!7),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[103, 100, 68])).
% 0.21/0.45 tff(105,plain,
% 0.21/0.45 ((~![A: $i] : (~((~element(tptp_fun_B_5(A), powerset(A))) | (~empty(tptp_fun_B_5(A)))))) | (~((~element(tptp_fun_B_5(A!8), powerset(A!8))) | (~empty(tptp_fun_B_5(A!8)))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(106,plain,
% 0.21/0.45 (~((~element(tptp_fun_B_5(A!8), powerset(A!8))) | (~empty(tptp_fun_B_5(A!8))))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[105, 27])).
% 0.21/0.45 tff(107,plain,
% 0.21/0.45 (((~element(tptp_fun_B_5(A!8), powerset(A!8))) | (~empty(tptp_fun_B_5(A!8)))) | empty(tptp_fun_B_5(A!8))),
% 0.21/0.45 inference(tautology,[status(thm)],[])).
% 0.21/0.45 tff(108,plain,
% 0.21/0.45 (empty(tptp_fun_B_5(A!8))),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.21/0.45 tff(109,plain,
% 0.21/0.45 (^[A: $i, B: $i] : refl(((~empty(B)) | (A = B) | (~empty(A))) <=> ((~empty(B)) | (A = B) | (~empty(A))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(110,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[109])).
% 0.21/0.45 tff(111,plain,
% 0.21/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (A = B) | (~empty(A))))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (A = B) | (~empty(A))))))), rewrite((~(~((~empty(B)) | (A = B) | (~empty(A))))) <=> ((~empty(B)) | (A = B) | (~empty(A)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (A = B) | (~empty(A)))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(112,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[111])).
% 0.21/0.45 tff(113,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(114,plain,
% 0.21/0.45 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.21/0.45 inference(bind,[status(th)],[])).
% 0.21/0.45 tff(115,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(quant_intro,[status(thm)],[114])).
% 0.21/0.45 tff(116,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.21/0.45 tff(117,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.21/0.45 tff(118,plain,
% 0.21/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[117, 113])).
% 0.21/0.45 tff(119,plain,(
% 0.21/0.45 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.21/0.45 inference(skolemize,[status(sab)],[118])).
% 0.21/0.45 tff(120,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[119, 112])).
% 0.21/0.45 tff(121,plain,
% 0.21/0.45 (![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[120, 110])).
% 0.21/0.45 tff(122,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(123,plain,
% 0.21/0.45 (((~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set) | (~empty(tptp_fun_B_5(A!8)))) <=> ((~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set))),
% 0.21/0.45 inference(rewrite,[status(thm)],[])).
% 0.21/0.45 tff(124,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set) | (~empty(tptp_fun_B_5(A!8))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set)))),
% 0.21/0.45 inference(monotonicity,[status(thm)],[123])).
% 0.21/0.45 tff(125,plain,
% 0.21/0.45 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set) | (~empty(tptp_fun_B_5(A!8))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set))),
% 0.21/0.45 inference(transitivity,[status(thm)],[124, 122])).
% 0.21/0.45 tff(126,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set) | (~empty(tptp_fun_B_5(A!8))))),
% 0.21/0.45 inference(quant_inst,[status(thm)],[])).
% 0.21/0.45 tff(127,plain,
% 0.21/0.45 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(empty_set)) | (tptp_fun_B_5(A!8) = empty_set)),
% 0.21/0.45 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.21/0.45 tff(128,plain,
% 0.21/0.45 (tptp_fun_B_5(A!8) = empty_set),
% 0.21/0.45 inference(unit_resolution,[status(thm)],[127, 13, 121, 108])).
% 0.21/0.45 tff(129,plain,
% 0.21/0.46 (((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~empty(tptp_fun_B_5(powerset(A!8))))) | empty(tptp_fun_B_5(powerset(A!8)))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(130,plain,
% 0.21/0.46 (empty(tptp_fun_B_5(powerset(A!8)))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[129, 29])).
% 0.21/0.46 tff(131,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(132,plain,
% 0.21/0.46 (((~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))) | (~empty(tptp_fun_B_5(A!8)))) <=> ((~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(133,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))) | (~empty(tptp_fun_B_5(A!8))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[132])).
% 0.21/0.46 tff(134,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))) | (~empty(tptp_fun_B_5(A!8))))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[133, 131])).
% 0.21/0.46 tff(135,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | ((~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))) | (~empty(tptp_fun_B_5(A!8))))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(136,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~empty(B)) | (A = B) | (~empty(A)))) | (~empty(tptp_fun_B_5(A!8))) | (~empty(tptp_fun_B_5(powerset(A!8)))) | (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.21/0.46 tff(137,plain,
% 0.21/0.46 (tptp_fun_B_5(A!8) = tptp_fun_B_5(powerset(A!8))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[136, 121, 108, 130])).
% 0.21/0.46 tff(138,plain,
% 0.21/0.46 (tptp_fun_B_5(powerset(A!8)) = tptp_fun_B_5(A!8)),
% 0.21/0.46 inference(symmetry,[status(thm)],[137])).
% 0.21/0.46 tff(139,plain,
% 0.21/0.46 (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7)),
% 0.21/0.46 inference(transitivity,[status(thm)],[138, 128, 65])).
% 0.21/0.46 tff(140,plain,
% 0.21/0.46 (complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))) = complements_of_subsets(A!8, complements_of_subsets(A!8, B!7))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[139])).
% 0.21/0.46 tff(141,plain,
% 0.21/0.46 (complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))) = B!7),
% 0.21/0.46 inference(transitivity,[status(thm)],[140, 104])).
% 0.21/0.46 tff(142,plain,
% 0.21/0.46 ((empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) <=> (empty_set = B!7)),
% 0.21/0.46 inference(monotonicity,[status(thm)],[141])).
% 0.21/0.46 tff(143,plain,
% 0.21/0.46 ((empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))) <=> (B!7 = empty_set)),
% 0.21/0.46 inference(transitivity,[status(thm)],[142, 90])).
% 0.21/0.46 tff(144,plain,
% 0.21/0.46 ((B!7 = empty_set) <=> (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(symmetry,[status(thm)],[143])).
% 0.21/0.46 tff(145,plain,
% 0.21/0.46 ((~(B!7 = empty_set)) <=> (~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[144])).
% 0.21/0.46 tff(146,plain,
% 0.21/0.46 (~(B!7 = empty_set)),
% 0.21/0.46 inference(and_elim,[status(thm)],[63])).
% 0.21/0.46 tff(147,plain,
% 0.21/0.46 (~(empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.21/0.46 tff(148,plain,
% 0.21/0.46 ((~((~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8)))))) | (~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))) | (empty_set = complements_of_subsets(A!8, tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(149,plain,
% 0.21/0.46 (~((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[148, 147, 89])).
% 0.21/0.46 tff(150,plain,
% 0.21/0.46 (((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))) | element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))),
% 0.21/0.46 inference(tautology,[status(thm)],[])).
% 0.21/0.46 tff(151,plain,
% 0.21/0.46 (element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[150, 149])).
% 0.21/0.46 tff(152,plain,
% 0.21/0.46 (^[A: $i, B: $i] : refl(((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(153,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[152])).
% 0.21/0.46 tff(154,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(155,plain,
% 0.21/0.46 (^[A: $i, B: $i] : rewrite((element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A))))),
% 0.21/0.46 inference(bind,[status(th)],[])).
% 0.21/0.46 tff(156,plain,
% 0.21/0.46 (![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A))) <=> ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(quant_intro,[status(thm)],[155])).
% 0.21/0.46 tff(157,axiom,(![A: $i, B: $i] : (element(B, powerset(A)) => element(subset_complement(A, B), powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_subset_1')).
% 0.21/0.46 tff(158,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.21/0.46 tff(159,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.21/0.46 tff(160,plain,(
% 0.21/0.46 ![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(skolemize,[status(sab)],[159])).
% 0.21/0.46 tff(161,plain,
% 0.21/0.46 (![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.21/0.46 tff(162,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8)))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8)))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(163,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | ((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8)))),
% 0.21/0.46 inference(quant_inst,[status(thm)],[])).
% 0.21/0.46 tff(164,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~element(B, powerset(A))) | element(subset_complement(A, B), powerset(A)))) | (~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))),
% 0.21/0.46 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.21/0.46 tff(165,plain,
% 0.21/0.46 (element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))),
% 0.21/0.46 inference(unit_resolution,[status(thm)],[164, 161, 151])).
% 0.21/0.46 tff(166,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(167,plain,
% 0.21/0.46 (((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((C = complements_of_subsets(A!8, B!7)) | (~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))))))))) <=> ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7))))))))),
% 0.21/0.46 inference(rewrite,[status(thm)],[])).
% 0.21/0.46 tff(168,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((C = complements_of_subsets(A!8, B!7)) | (~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7))))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))))),
% 0.21/0.46 inference(monotonicity,[status(thm)],[167])).
% 0.21/0.46 tff(169,plain,
% 0.21/0.46 (((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((C = complements_of_subsets(A!8, B!7)) | (~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7))))))))))) <=> ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7))))))))),
% 0.21/0.46 inference(transitivity,[status(thm)],[168, 166])).
% 0.21/0.46 tff(170,plain,
% 0.21/0.46 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | ((~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((C = complements_of_subsets(A!8, B!7)) | (~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7))))))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(171,plain,
% 0.21/0.47 ((~![A: $i, B: $i] : ((~element(B, powerset(powerset(A)))) | ![C: $i] : ((~element(C, powerset(powerset(A)))) | (~((~((~(C = complements_of_subsets(A, B))) | ![D: $i] : ((~element(D, powerset(A))) | (in(D, C) <=> in(subset_complement(A, D), B))))) | (~((C = complements_of_subsets(A, B)) | (~((~element(tptp_fun_D_1(C, B, A), powerset(A))) | (in(tptp_fun_D_1(C, B, A), C) <=> in(subset_complement(A, tptp_fun_D_1(C, B, A)), B))))))))))) | (~element(B!7, powerset(powerset(A!8)))) | ![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.21/0.47 tff(172,plain,
% 0.21/0.47 (![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[171, 47, 68])).
% 0.21/0.47 tff(173,plain,
% 0.21/0.47 (((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | ((~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7)))))))) <=> ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | (~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(174,plain,
% 0.21/0.47 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | ((~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(175,plain,
% 0.21/0.47 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | (~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7))))))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.21/0.47 tff(176,plain,
% 0.21/0.47 ((~element(empty_set, powerset(powerset(A!8)))) | (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7))))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[175, 172])).
% 0.21/0.47 tff(177,plain,
% 0.21/0.47 (~((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7)))))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[176, 83])).
% 0.21/0.47 tff(178,plain,
% 0.21/0.47 (((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(empty_set, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, B!7, A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, B!7, A!8)), B!7)))) | (empty_set = complements_of_subsets(A!8, B!7))))) | ((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(179,plain,
% 0.21/0.47 ((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.21/0.47 tff(180,plain,
% 0.21/0.47 ((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | (~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.47 inference(tautology,[status(thm)],[])).
% 0.21/0.47 tff(181,plain,
% 0.21/0.47 ((~((~(empty_set = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7))))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[180, 65])).
% 0.21/0.47 tff(182,plain,
% 0.21/0.47 (![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[181, 179])).
% 0.21/0.47 tff(183,plain,
% 0.21/0.47 (((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))) | ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))) <=> ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))) | (~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))),
% 0.21/0.47 inference(rewrite,[status(thm)],[])).
% 0.21/0.47 tff(184,plain,
% 0.21/0.47 ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))) | ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))),
% 0.21/0.47 inference(quant_inst,[status(thm)],[])).
% 0.21/0.47 tff(185,plain,
% 0.21/0.47 ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, empty_set) <=> in(subset_complement(A!8, D), B!7)))) | (~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))),
% 0.21/0.47 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.21/0.47 tff(186,plain,
% 0.21/0.47 ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[185, 182])).
% 0.21/0.47 tff(187,plain,
% 0.21/0.47 (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)),
% 0.21/0.47 inference(unit_resolution,[status(thm)],[186, 165])).
% 0.21/0.47 tff(188,plain,
% 0.21/0.47 (((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7)))))))) <=> ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | (~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(189,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | ((~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7)))))))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(190,plain,
% 0.21/0.48 ((~![C: $i] : ((~element(C, powerset(powerset(A!8)))) | (~((~((~(C = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, C) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(C, B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(C, B!7, A!8), C) <=> in(subset_complement(A!8, tptp_fun_D_1(C, B!7, A!8)), B!7)))) | (C = complements_of_subsets(A!8, B!7)))))))) | (~element(tptp_fun_B_5(powerset(A!8)), powerset(powerset(A!8)))) | (~((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))))))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.21/0.48 tff(191,plain,
% 0.21/0.48 (~((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7)))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[190, 172, 31])).
% 0.21/0.48 tff(192,plain,
% 0.21/0.48 (((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~((~((~element(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), powerset(A!8))) | (in(tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, tptp_fun_D_1(tptp_fun_B_5(powerset(A!8)), B!7, A!8)), B!7)))) | (tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))))) | ((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(193,plain,
% 0.21/0.48 ((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.21/0.48 tff(194,plain,
% 0.21/0.48 ((~((~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7))))) | (~(tptp_fun_B_5(powerset(A!8)) = complements_of_subsets(A!8, B!7))) | ![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(195,plain,
% 0.21/0.48 (![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[194, 139, 193])).
% 0.21/0.48 tff(196,plain,
% 0.21/0.48 (((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))) | ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))) <=> ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))) | (~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(197,plain,
% 0.21/0.48 ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))) | ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(198,plain,
% 0.21/0.48 ((~![D: $i] : ((~element(D, powerset(A!8))) | (in(D, tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, D), B!7)))) | (~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.21/0.48 tff(199,plain,
% 0.21/0.48 ((~element(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), powerset(A!8))) | (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[198, 195])).
% 0.21/0.48 tff(200,plain,
% 0.21/0.48 (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[199, 165])).
% 0.21/0.48 tff(201,plain,
% 0.21/0.48 (((~element(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), powerset(A!8))) | (in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))) | (~(in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(202,plain,
% 0.21/0.48 (~(in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[201, 149])).
% 0.21/0.48 tff(203,plain,
% 0.21/0.48 (((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set)))),
% 0.21/0.48 inference(rewrite,[status(thm)],[])).
% 0.21/0.48 tff(204,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | ((~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set)))),
% 0.21/0.48 inference(quant_inst,[status(thm)],[])).
% 0.21/0.48 tff(205,plain,
% 0.21/0.48 ((~![A: $i, B: $i] : ((~empty(B)) | (~in(A, B)))) | (~empty(empty_set)) | (~in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set))),
% 0.21/0.48 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.21/0.48 tff(206,plain,
% 0.21/0.48 (~in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[205, 13, 10])).
% 0.21/0.48 tff(207,plain,
% 0.21/0.48 ((in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) <=> in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))) | in(tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8), empty_set) | in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(208,plain,
% 0.21/0.48 (in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[207, 206, 202])).
% 0.21/0.48 tff(209,plain,
% 0.21/0.48 ((~(in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8))) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))) | (~in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), tptp_fun_B_5(powerset(A!8)))) | in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(210,plain,
% 0.21/0.48 (in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7)),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[209, 208, 200])).
% 0.21/0.48 tff(211,plain,
% 0.21/0.48 ((~(in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) <=> in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))) | in(subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8)), empty_set) | (~in(subset_complement(A!8, subset_complement(A!8, tptp_fun_D_1(empty_set, tptp_fun_B_5(powerset(A!8)), A!8))), B!7))),
% 0.21/0.48 inference(tautology,[status(thm)],[])).
% 0.21/0.48 tff(212,plain,
% 0.21/0.48 ($false),
% 0.21/0.48 inference(unit_resolution,[status(thm)],[211, 210, 187, 17])).
% 0.21/0.48 % SZS output end Proof
% 0.21/0.48 % E exiting
%------------------------------------------------------------------------------