%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU387+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:46 AM UTC 2025
% Result : Theorem 18.89s 19.08s
% Output : Proof 18.95s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU387+2 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n003.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:58:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 18.89/19.08 % SZS status Theorem
% 18.89/19.08 % SZS output start Proof
% 18.89/19.08 tff(in_type, type, (
% 18.89/19.08 in: ( $i * $i ) > $o)).
% 18.89/19.08 tff(tptp_fun_B_364_type, type, (
% 18.89/19.08 tptp_fun_B_364: $i)).
% 18.89/19.08 tff(bottom_of_relstr_type, type, (
% 18.89/19.08 bottom_of_relstr: $i > $i)).
% 18.89/19.08 tff(boole_POSet_type, type, (
% 18.89/19.08 boole_POSet: $i > $i)).
% 18.89/19.08 tff(tptp_fun_A_363_type, type, (
% 18.89/19.08 tptp_fun_A_363: $i)).
% 18.89/19.08 tff(empty_set_type, type, (
% 18.89/19.08 empty_set: $i)).
% 18.89/19.08 tff(tptp_fun_C_365_type, type, (
% 18.89/19.08 tptp_fun_C_365: $i)).
% 18.89/19.08 tff(empty_type, type, (
% 18.89/19.08 empty: $i > $o)).
% 18.89/19.08 tff(element_type, type, (
% 18.89/19.08 element: ( $i * $i ) > $o)).
% 18.89/19.08 tff(powerset_type, type, (
% 18.89/19.08 powerset: $i > $i)).
% 18.89/19.08 tff(the_carrier_type, type, (
% 18.89/19.08 the_carrier: $i > $i)).
% 18.89/19.08 tff(proper_element_type, type, (
% 18.89/19.08 proper_element: ( $i * $i ) > $o)).
% 18.89/19.08 tff(upper_relstr_subset_type, type, (
% 18.89/19.08 upper_relstr_subset: ( $i * $i ) > $o)).
% 18.89/19.08 tff(filtered_subset_type, type, (
% 18.89/19.08 filtered_subset: ( $i * $i ) > $o)).
% 18.89/19.08 tff(relation_type, type, (
% 18.89/19.08 relation: $i > $o)).
% 18.89/19.08 tff(relation_empty_yielding_type, type, (
% 18.89/19.08 relation_empty_yielding: $i > $o)).
% 18.89/19.08 tff(rel_str_type, type, (
% 18.89/19.08 rel_str: $i > $o)).
% 18.89/19.08 tff(strict_rel_str_type, type, (
% 18.89/19.08 strict_rel_str: $i > $o)).
% 18.89/19.08 tff(transitive_relstr_type, type, (
% 18.89/19.08 transitive_relstr: $i > $o)).
% 18.89/19.08 tff(boolean_relstr_type, type, (
% 18.89/19.08 boolean_relstr: $i > $o)).
% 18.89/19.08 tff(complemented_relstr_type, type, (
% 18.89/19.08 complemented_relstr: $i > $o)).
% 18.89/19.08 tff(heyting_relstr_type, type, (
% 18.89/19.08 heyting_relstr: $i > $o)).
% 18.89/19.08 tff(distributive_relstr_type, type, (
% 18.89/19.08 distributive_relstr: $i > $o)).
% 18.89/19.08 tff(join_complete_relstr_type, type, (
% 18.89/19.08 join_complete_relstr: $i > $o)).
% 18.89/19.08 tff(up_complete_relstr_type, type, (
% 18.89/19.08 up_complete_relstr: $i > $o)).
% 18.89/19.08 tff(bounded_relstr_type, type, (
% 18.89/19.08 bounded_relstr: $i > $o)).
% 18.89/19.08 tff(complete_relstr_type, type, (
% 18.89/19.08 complete_relstr: $i > $o)).
% 18.89/19.08 tff(with_infima_relstr_type, type, (
% 18.89/19.08 with_infima_relstr: $i > $o)).
% 18.89/19.08 tff(v1_yellow_3_type, type, (
% 18.89/19.08 v1_yellow_3: $i > $o)).
% 18.89/19.08 tff(with_suprema_relstr_type, type, (
% 18.89/19.08 with_suprema_relstr: $i > $o)).
% 18.89/19.08 tff(upper_bounded_relstr_type, type, (
% 18.89/19.08 upper_bounded_relstr: $i > $o)).
% 18.89/19.08 tff(trivial_carrier_type, type, (
% 18.89/19.08 trivial_carrier: $i > $o)).
% 18.89/19.08 tff(lower_bounded_relstr_type, type, (
% 18.89/19.08 lower_bounded_relstr: $i > $o)).
% 18.89/19.08 tff(reflexive_relstr_type, type, (
% 18.89/19.08 reflexive_relstr: $i > $o)).
% 18.89/19.08 tff(antisymmetric_relstr_type, type, (
% 18.89/19.08 antisymmetric_relstr: $i > $o)).
% 18.89/19.08 tff(empty_carrier_type, type, (
% 18.89/19.08 empty_carrier: $i > $o)).
% 18.89/19.08 tff(1,plain,
% 18.89/19.08 (^[A: $i] : refl((bottom_of_relstr(boole_POSet(A)) = empty_set) <=> (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 18.89/19.08 inference(bind,[status(th)],[])).
% 18.89/19.08 tff(2,plain,
% 18.89/19.08 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 18.89/19.08 inference(quant_intro,[status(thm)],[1])).
% 18.89/19.08 tff(3,plain,
% 18.89/19.08 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(4,axiom,(![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_yellow_1')).
% 18.89/19.08 tff(5,plain,
% 18.89/19.08 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[4, 3])).
% 18.89/19.08 tff(6,plain,(
% 18.89/19.08 ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 18.89/19.08 inference(skolemize,[status(sab)],[5])).
% 18.89/19.08 tff(7,plain,
% 18.89/19.08 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[6, 2])).
% 18.89/19.08 tff(8,plain,
% 18.89/19.08 ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) | (bottom_of_relstr(boole_POSet(A!363)) = empty_set)),
% 18.89/19.08 inference(quant_inst,[status(thm)],[])).
% 18.89/19.08 tff(9,plain,
% 18.89/19.08 (bottom_of_relstr(boole_POSet(A!363)) = empty_set),
% 18.89/19.08 inference(unit_resolution,[status(thm)],[8, 7])).
% 18.89/19.08 tff(10,plain,
% 18.89/19.08 (in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> in(empty_set, B!364)),
% 18.89/19.08 inference(monotonicity,[status(thm)],[9])).
% 18.89/19.08 tff(11,plain,
% 18.89/19.08 (in(empty_set, B!364) <=> in(bottom_of_relstr(boole_POSet(A!363)), B!364)),
% 18.89/19.08 inference(symmetry,[status(thm)],[10])).
% 18.89/19.08 tff(12,plain,
% 18.89/19.08 (^[A: $i, B: $i] : refl(((~empty(B)) | (~empty(A)) | (A = B)) <=> ((~empty(B)) | (~empty(A)) | (A = B)))),
% 18.89/19.08 inference(bind,[status(th)],[])).
% 18.89/19.08 tff(13,plain,
% 18.89/19.08 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 18.89/19.08 inference(quant_intro,[status(thm)],[12])).
% 18.89/19.08 tff(14,plain,
% 18.89/19.08 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (~empty(A)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (~empty(A)) | (A = B)))))), rewrite((~(~((~empty(B)) | (~empty(A)) | (A = B)))) <=> ((~empty(B)) | (~empty(A)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (~empty(A)) | (A = B))))),
% 18.89/19.08 inference(bind,[status(th)],[])).
% 18.89/19.08 tff(15,plain,
% 18.89/19.08 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 18.89/19.08 inference(quant_intro,[status(thm)],[14])).
% 18.89/19.08 tff(16,plain,
% 18.89/19.08 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(17,plain,
% 18.89/19.08 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 18.89/19.08 inference(bind,[status(th)],[])).
% 18.89/19.08 tff(18,plain,
% 18.89/19.08 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 18.89/19.08 inference(quant_intro,[status(thm)],[17])).
% 18.89/19.08 tff(19,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 18.89/19.08 tff(20,plain,
% 18.89/19.08 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[19, 18])).
% 18.89/19.08 tff(21,plain,
% 18.89/19.08 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[20, 16])).
% 18.89/19.08 tff(22,plain,(
% 18.89/19.08 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 18.89/19.08 inference(skolemize,[status(sab)],[21])).
% 18.89/19.08 tff(23,plain,
% 18.89/19.08 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[22, 15])).
% 18.89/19.08 tff(24,plain,
% 18.89/19.08 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[23, 13])).
% 18.89/19.08 tff(25,plain,
% 18.89/19.08 (((~empty(A!363)) & ((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365))) <=> ((~empty(A!363)) & (~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365))),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(26,plain,
% 18.89/19.08 ((((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363))))) & (in(C!365, B!364) & empty(C!365))) <=> ((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365))),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(27,plain,
% 18.89/19.08 (((~empty(A!363)) & (((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363))))) & (in(C!365, B!364) & empty(C!365)))) <=> ((~empty(A!363)) & ((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365)))),
% 18.89/19.08 inference(monotonicity,[status(thm)],[26])).
% 18.89/19.08 tff(28,plain,
% 18.89/19.08 (((~empty(A!363)) & (((~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363))))) & (in(C!365, B!364) & empty(C!365)))) <=> ((~empty(A!363)) & (~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365))),
% 18.89/19.08 inference(transitivity,[status(thm)],[27, 25])).
% 18.89/19.08 tff(29,plain,
% 18.89/19.08 ((~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))) <=> (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(30,plain,
% 18.89/19.08 ((~![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))) <=> (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))),
% 18.89/19.08 inference(rewrite,[status(thm)],[])).
% 18.89/19.08 tff(31,axiom,(~![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_yellow19')).
% 18.89/19.08 tff(32,plain,
% 18.89/19.08 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[31, 30])).
% 18.89/19.08 tff(33,plain,
% 18.89/19.08 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[32, 29])).
% 18.89/19.08 tff(34,plain,
% 18.89/19.08 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[33, 29])).
% 18.89/19.08 tff(35,plain,
% 18.89/19.08 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 18.89/19.08 inference(modus_ponens,[status(thm)],[34, 29])).
% 18.89/19.08 tff(36,plain,
% 18.89/19.08 ((~empty(A!363)) & (~empty(B!364)) & filtered_subset(B!364, boole_POSet(A!363)) & upper_relstr_subset(B!364, boole_POSet(A!363)) & proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & element(B!364, powerset(the_carrier(boole_POSet(A!363)))) & in(C!365, B!364) & empty(C!365)),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[35, 28])).
% 18.89/19.09 tff(37,plain,
% 18.89/19.09 (empty(C!365)),
% 18.89/19.09 inference(and_elim,[status(thm)],[36])).
% 18.89/19.09 tff(38,plain,
% 18.89/19.09 (empty(empty_set) <=> empty(empty_set)),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(39,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 18.89/19.09 tff(40,plain,
% 18.89/19.09 (empty(empty_set) & relation(empty_set)),
% 18.89/19.09 inference(and_elim,[status(thm)],[39])).
% 18.89/19.09 tff(41,plain,
% 18.89/19.09 (empty(empty_set)),
% 18.89/19.09 inference(and_elim,[status(thm)],[40])).
% 18.89/19.09 tff(42,plain,
% 18.89/19.09 (empty(empty_set)),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[41, 38])).
% 18.89/19.09 tff(43,plain,
% 18.89/19.09 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365)))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(44,plain,
% 18.89/19.09 (((~empty(empty_set)) | (~empty(C!365)) | (C!365 = empty_set)) <=> ((C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365)))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(45,plain,
% 18.89/19.09 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!365)) | (C!365 = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365))))),
% 18.89/19.09 inference(monotonicity,[status(thm)],[44])).
% 18.89/19.09 tff(46,plain,
% 18.89/19.09 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!365)) | (C!365 = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365)))),
% 18.89/19.09 inference(transitivity,[status(thm)],[45, 43])).
% 18.89/19.09 tff(47,plain,
% 18.89/19.09 ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!365)) | (C!365 = empty_set))),
% 18.89/19.09 inference(quant_inst,[status(thm)],[])).
% 18.89/19.09 tff(48,plain,
% 18.89/19.09 ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!365 = empty_set) | (~empty(empty_set)) | (~empty(C!365))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[47, 46])).
% 18.89/19.09 tff(49,plain,
% 18.89/19.09 (C!365 = empty_set),
% 18.89/19.09 inference(unit_resolution,[status(thm)],[48, 42, 37, 24])).
% 18.89/19.09 tff(50,plain,
% 18.89/19.09 (in(C!365, B!364) <=> in(empty_set, B!364)),
% 18.89/19.09 inference(monotonicity,[status(thm)],[49])).
% 18.89/19.09 tff(51,plain,
% 18.89/19.09 (in(C!365, B!364)),
% 18.89/19.09 inference(and_elim,[status(thm)],[36])).
% 18.89/19.09 tff(52,plain,
% 18.89/19.09 (in(empty_set, B!364)),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[51, 50])).
% 18.89/19.09 tff(53,plain,
% 18.89/19.09 (in(bottom_of_relstr(boole_POSet(A!363)), B!364)),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[52, 11])).
% 18.89/19.09 tff(54,plain,
% 18.89/19.09 (^[A: $i] : refl((~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 18.89/19.09 inference(bind,[status(th)],[])).
% 18.89/19.09 tff(55,plain,
% 18.89/19.09 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 18.89/19.09 inference(quant_intro,[status(thm)],[54])).
% 18.89/19.09 tff(56,plain,
% 18.89/19.09 (^[A: $i] : rewrite((strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 18.89/19.09 inference(bind,[status(th)],[])).
% 18.89/19.09 tff(57,plain,
% 18.89/19.09 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 18.89/19.09 inference(quant_intro,[status(thm)],[56])).
% 18.89/19.09 tff(58,plain,
% 18.89/19.09 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(59,axiom,(![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_1')).
% 18.89/19.09 tff(60,plain,
% 18.89/19.09 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[59, 58])).
% 18.89/19.09 tff(61,plain,(
% 18.89/19.09 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 18.89/19.09 inference(skolemize,[status(sab)],[60])).
% 18.89/19.09 tff(62,plain,
% 18.89/19.09 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[61, 57])).
% 18.89/19.09 tff(63,plain,
% 18.89/19.09 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[62, 55])).
% 18.89/19.09 tff(64,plain,
% 18.89/19.09 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))))))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(65,plain,
% 18.89/19.09 ((~((~strict_rel_str(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363))))) <=> (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363)))))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(66,plain,
% 18.89/19.09 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))))))),
% 18.89/19.09 inference(monotonicity,[status(thm)],[65])).
% 18.89/19.09 tff(67,plain,
% 18.89/19.09 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))))))),
% 18.89/19.09 inference(transitivity,[status(thm)],[66, 64])).
% 18.89/19.09 tff(68,plain,
% 18.89/19.09 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))))),
% 18.89/19.09 inference(quant_inst,[status(thm)],[])).
% 18.89/19.09 tff(69,plain,
% 18.89/19.09 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363)))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[68, 67])).
% 18.89/19.09 tff(70,plain,
% 18.89/19.09 (~((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))))),
% 18.89/19.09 inference(unit_resolution,[status(thm)],[69, 63])).
% 18.89/19.09 tff(71,plain,
% 18.89/19.09 (((~rel_str(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363)))) | rel_str(boole_POSet(A!363))),
% 18.89/19.09 inference(tautology,[status(thm)],[])).
% 18.89/19.09 tff(72,plain,
% 18.89/19.09 (rel_str(boole_POSet(A!363))),
% 18.89/19.09 inference(unit_resolution,[status(thm)],[71, 70])).
% 18.89/19.09 tff(73,plain,
% 18.89/19.09 (~empty(A!363)),
% 18.89/19.09 inference(and_elim,[status(thm)],[36])).
% 18.89/19.09 tff(74,plain,
% 18.89/19.09 (^[A: $i] : refl((empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))) <=> (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))))),
% 18.89/19.09 inference(bind,[status(th)],[])).
% 18.89/19.09 tff(75,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))) <=> ![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 18.89/19.09 inference(quant_intro,[status(thm)],[74])).
% 18.89/19.09 tff(76,plain,
% 18.89/19.09 (^[A: $i] : rewrite((empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))))),
% 18.89/19.09 inference(bind,[status(th)],[])).
% 18.89/19.09 tff(77,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 18.89/19.09 inference(quant_intro,[status(thm)],[76])).
% 18.89/19.09 tff(78,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(79,plain,
% 18.89/19.09 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))))), ((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)))), ((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))))), (((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))), (((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))))), ((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)))), ((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))))), (((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)))), (((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))))), ((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)))), ((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))))), (((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)))), (((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))))), ((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)))), ((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))))), (((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))))), (((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))))), ((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)))), ((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))))), (((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)))), (((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))))), (((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)))), (((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))))), ((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)))), ((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))))), (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)))), (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))))), ((((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))), ((((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))), (((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> ((~empty(A)) => ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))))), rewrite(((~empty(A)) => ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))), (((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))))),
% 18.89/19.09 inference(bind,[status(th)],[])).
% 18.89/19.09 tff(80,plain,
% 18.89/19.09 (![A: $i] : ((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 18.89/19.09 inference(quant_intro,[status(thm)],[79])).
% 18.89/19.09 tff(81,axiom,(![A: $i] : ((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_waybel_7')).
% 18.89/19.09 tff(82,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[81, 80])).
% 18.89/19.09 tff(83,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[82, 78])).
% 18.89/19.09 tff(84,plain,(
% 18.89/19.09 ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 18.89/19.09 inference(skolemize,[status(sab)],[83])).
% 18.89/19.09 tff(85,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[84, 77])).
% 18.89/19.09 tff(86,plain,
% 18.89/19.09 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 18.89/19.09 inference(modus_ponens,[status(thm)],[85, 75])).
% 18.89/19.09 tff(87,plain,
% 18.89/19.09 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(88,plain,
% 18.89/19.09 ((empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | v1_yellow_3(boole_POSet(A!363)) | trivial_carrier(boole_POSet(A!363)) | (~strict_rel_str(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))))) <=> (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))),
% 18.89/19.09 inference(rewrite,[status(thm)],[])).
% 18.89/19.09 tff(89,plain,
% 18.89/19.09 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | v1_yellow_3(boole_POSet(A!363)) | trivial_carrier(boole_POSet(A!363)) | (~strict_rel_str(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))))))),
% 18.89/19.09 inference(monotonicity,[status(thm)],[88])).
% 18.89/19.09 tff(90,plain,
% 18.89/19.09 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | v1_yellow_3(boole_POSet(A!363)) | trivial_carrier(boole_POSet(A!363)) | (~strict_rel_str(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))),
% 18.89/19.10 inference(transitivity,[status(thm)],[89, 87])).
% 18.89/19.10 tff(91,plain,
% 18.89/19.10 ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | v1_yellow_3(boole_POSet(A!363)) | trivial_carrier(boole_POSet(A!363)) | (~strict_rel_str(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))))),
% 18.89/19.10 inference(quant_inst,[status(thm)],[])).
% 18.89/19.10 tff(92,plain,
% 18.89/19.10 ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!363) | (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[91, 90])).
% 18.89/19.10 tff(93,plain,
% 18.89/19.10 (~(empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363))))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[92, 86, 73])).
% 18.89/19.10 tff(94,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))) | transitive_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(tautology,[status(thm)],[])).
% 18.89/19.10 tff(95,plain,
% 18.89/19.10 (transitive_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[94, 93])).
% 18.89/19.10 tff(96,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))) | lower_bounded_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(tautology,[status(thm)],[])).
% 18.89/19.10 tff(97,plain,
% 18.89/19.10 (lower_bounded_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[96, 93])).
% 18.89/19.10 tff(98,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))) | reflexive_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(tautology,[status(thm)],[])).
% 18.89/19.10 tff(99,plain,
% 18.89/19.10 (reflexive_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[98, 93])).
% 18.89/19.10 tff(100,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))) | antisymmetric_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(tautology,[status(thm)],[])).
% 18.89/19.10 tff(101,plain,
% 18.89/19.10 (antisymmetric_relstr(boole_POSet(A!363))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[100, 93])).
% 18.89/19.10 tff(102,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | trivial_carrier(boole_POSet(A!363)) | (~upper_bounded_relstr(boole_POSet(A!363))) | (~strict_rel_str(boole_POSet(A!363))) | (~with_suprema_relstr(boole_POSet(A!363))) | v1_yellow_3(boole_POSet(A!363)) | (~with_infima_relstr(boole_POSet(A!363))) | (~complete_relstr(boole_POSet(A!363))) | (~bounded_relstr(boole_POSet(A!363))) | (~up_complete_relstr(boole_POSet(A!363))) | (~join_complete_relstr(boole_POSet(A!363))) | (~distributive_relstr(boole_POSet(A!363))) | (~heyting_relstr(boole_POSet(A!363))) | (~complemented_relstr(boole_POSet(A!363))) | (~boolean_relstr(boole_POSet(A!363)))) | (~empty_carrier(boole_POSet(A!363)))),
% 18.89/19.10 inference(tautology,[status(thm)],[])).
% 18.89/19.10 tff(103,plain,
% 18.89/19.10 (~empty_carrier(boole_POSet(A!363))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[102, 93])).
% 18.89/19.10 tff(104,plain,
% 18.89/19.10 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))),
% 18.89/19.10 inference(bind,[status(th)],[])).
% 18.89/19.10 tff(105,plain,
% 18.89/19.10 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(quant_intro,[status(thm)],[104])).
% 18.89/19.10 tff(106,plain,
% 18.89/19.10 (^[A: $i] : rewrite((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))),
% 18.89/19.10 inference(bind,[status(th)],[])).
% 18.89/19.10 tff(107,plain,
% 18.89/19.10 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(quant_intro,[status(thm)],[106])).
% 18.89/19.10 tff(108,plain,
% 18.89/19.10 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(transitivity,[status(thm)],[107, 105])).
% 18.89/19.10 tff(109,plain,
% 18.89/19.10 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) <=> (~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))))))), rewrite((~(~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) <=> (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A)))))), trans(monotonicity(rewrite(((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))) <=> (~(empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))), ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) <=> (~(~(empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))))), rewrite((~(~(empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) <=> (empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))), ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) <=> (empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))), (((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))) <=> ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))), rewrite(((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (empty(B) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))), (((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))) <=> (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))), (![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))) <=> ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))) <=> ((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))), rewrite(((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))))),
% 18.89/19.10 inference(bind,[status(th)],[])).
% 18.89/19.10 tff(110,plain,
% 18.89/19.10 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(quant_intro,[status(thm)],[109])).
% 18.89/19.10 tff(111,plain,
% 18.89/19.10 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(112,plain,
% 18.89/19.10 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A)) & antisymmetric_relstr(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A))), (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> (((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))))), rewrite((((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))), (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))), trans(rewrite((proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) <=> (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A)))))), rewrite((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) <=> (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A)))))), ((proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) <=> (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))))), ((((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))) <=> (((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))) => (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A)))))))), rewrite((((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))) => (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A)))))) <=> ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))), ((((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))) <=> ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))))), (![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))) <=> ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))), ((((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) => ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))))) <=> ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))), ((((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))))),
% 18.89/19.10 inference(bind,[status(th)],[])).
% 18.89/19.10 tff(113,plain,
% 18.89/19.10 (![A: $i] : (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))),
% 18.89/19.10 inference(quant_intro,[status(thm)],[112])).
% 18.89/19.10 tff(114,axiom,(![A: $i] : (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_waybel_7')).
% 18.89/19.10 tff(115,plain,
% 18.89/19.10 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[114, 113])).
% 18.89/19.10 tff(116,plain,
% 18.89/19.10 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[115, 111])).
% 18.89/19.10 tff(117,plain,(
% 18.89/19.10 ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))))),
% 18.89/19.10 inference(skolemize,[status(sab)],[116])).
% 18.89/19.10 tff(118,plain,
% 18.89/19.10 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[117, 110])).
% 18.89/19.10 tff(119,plain,
% 18.89/19.10 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[118, 108])).
% 18.89/19.10 tff(120,plain,
% 18.89/19.10 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(121,plain,
% 18.89/19.10 ((empty_carrier(boole_POSet(A!363)) | (~rel_str(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) <=> (empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(122,plain,
% 18.89/19.10 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!363)) | (~rel_str(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))))),
% 18.89/19.10 inference(monotonicity,[status(thm)],[121])).
% 18.89/19.10 tff(123,plain,
% 18.89/19.10 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!363)) | (~rel_str(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363))))),
% 18.89/19.10 inference(transitivity,[status(thm)],[122, 120])).
% 18.89/19.10 tff(124,plain,
% 18.89/19.10 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!363)) | (~rel_str(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~antisymmetric_relstr(boole_POSet(A!363))) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))))),
% 18.89/19.10 inference(quant_inst,[status(thm)],[])).
% 18.89/19.10 tff(125,plain,
% 18.89/19.10 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~reflexive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(A)))) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))),
% 18.89/19.10 inference(modus_ponens,[status(thm)],[124, 123])).
% 18.89/19.10 tff(126,plain,
% 18.89/19.10 (empty_carrier(boole_POSet(A!363)) | ![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363)))) | (~antisymmetric_relstr(boole_POSet(A!363))) | (~reflexive_relstr(boole_POSet(A!363))) | (~lower_bounded_relstr(boole_POSet(A!363))) | (~transitive_relstr(boole_POSet(A!363))) | (~rel_str(boole_POSet(A!363)))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[125, 119])).
% 18.89/19.10 tff(127,plain,
% 18.89/19.10 (![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))),
% 18.89/19.10 inference(unit_resolution,[status(thm)],[126, 103, 101, 99, 97, 95, 72])).
% 18.89/19.10 tff(128,plain,
% 18.89/19.10 (element(B!364, powerset(the_carrier(boole_POSet(A!363))))),
% 18.89/19.10 inference(and_elim,[status(thm)],[36])).
% 18.89/19.10 tff(129,plain,
% 18.89/19.10 (upper_relstr_subset(B!364, boole_POSet(A!363))),
% 18.89/19.10 inference(and_elim,[status(thm)],[36])).
% 18.89/19.10 tff(130,plain,
% 18.89/19.10 (filtered_subset(B!364, boole_POSet(A!363))),
% 18.89/19.10 inference(and_elim,[status(thm)],[36])).
% 18.89/19.10 tff(131,plain,
% 18.89/19.10 (~empty(B!364)),
% 18.89/19.10 inference(and_elim,[status(thm)],[36])).
% 18.89/19.10 tff(132,plain,
% 18.89/19.10 (((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363))))) <=> ((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(133,plain,
% 18.89/19.10 ((empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363)))) <=> (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(134,plain,
% 18.89/19.10 ((~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) <=> (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363))))))),
% 18.89/19.10 inference(rewrite,[status(thm)],[])).
% 18.89/19.10 tff(135,plain,
% 18.89/19.10 ((empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363)))) <=> (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.89/19.10 inference(monotonicity,[status(thm)],[134])).
% 18.89/19.10 tff(136,plain,
% 18.89/19.10 ((empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363)))) <=> (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.89/19.10 inference(transitivity,[status(thm)],[135, 133])).
% 18.89/19.10 tff(137,plain,
% 18.89/19.10 (((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363))))) <=> ((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363)))))),
% 18.89/19.10 inference(monotonicity,[status(thm)],[136])).
% 18.89/19.10 tff(138,plain,
% 18.89/19.10 (((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363))))) <=> ((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.89/19.10 inference(transitivity,[status(thm)],[137, 132])).
% 18.89/19.10 tff(139,plain,
% 18.89/19.10 ((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | (empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~filtered_subset(B!364, boole_POSet(A!363))))),
% 18.95/19.17 inference(quant_inst,[status(thm)],[])).
% 18.95/19.17 tff(140,plain,
% 18.95/19.17 ((~![B: $i] : (empty(B) | (~element(B, powerset(the_carrier(boole_POSet(A!363))))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!363)))))) | (~upper_relstr_subset(B, boole_POSet(A!363))) | (~filtered_subset(B, boole_POSet(A!363))))) | empty(B!364) | (~element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~upper_relstr_subset(B!364, boole_POSet(A!363))) | (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))) | (~filtered_subset(B!364, boole_POSet(A!363)))),
% 18.95/19.17 inference(modus_ponens,[status(thm)],[139, 138])).
% 18.95/19.17 tff(141,plain,
% 18.95/19.17 (~(in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))),
% 18.95/19.17 inference(unit_resolution,[status(thm)],[140, 131, 130, 129, 128, 127])).
% 18.95/19.17 tff(142,plain,
% 18.95/19.17 (proper_element(B!364, powerset(the_carrier(boole_POSet(A!363))))),
% 18.95/19.17 inference(and_elim,[status(thm)],[36])).
% 18.95/19.17 tff(143,plain,
% 18.95/19.17 ((in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~in(bottom_of_relstr(boole_POSet(A!363)), B!364)) | (~proper_element(B!364, powerset(the_carrier(boole_POSet(A!363)))))),
% 18.95/19.17 inference(tautology,[status(thm)],[])).
% 18.95/19.17 tff(144,plain,
% 18.95/19.17 ((in(bottom_of_relstr(boole_POSet(A!363)), B!364) <=> proper_element(B!364, powerset(the_carrier(boole_POSet(A!363))))) | (~in(bottom_of_relstr(boole_POSet(A!363)), B!364))),
% 18.95/19.17 inference(unit_resolution,[status(thm)],[143, 142])).
% 18.95/19.17 tff(145,plain,
% 18.95/19.17 (~in(bottom_of_relstr(boole_POSet(A!363)), B!364)),
% 18.95/19.17 inference(unit_resolution,[status(thm)],[144, 141])).
% 18.95/19.17 tff(146,plain,
% 18.95/19.17 ($false),
% 18.95/19.17 inference(unit_resolution,[status(thm)],[145, 53])).
% 18.95/19.17 % SZS output end Proof
% 19.02/19.21 % E exiting
%------------------------------------------------------------------------------