%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU387+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.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 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SEU387+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 06:58:55 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(in_type, type, (
% 0.20/0.46 in: ( $i * $i ) > $o)).
% 0.20/0.46 tff(tptp_fun_B_27_type, type, (
% 0.20/0.46 tptp_fun_B_27: $i)).
% 0.20/0.46 tff(bottom_of_relstr_type, type, (
% 0.20/0.46 bottom_of_relstr: $i > $i)).
% 0.20/0.46 tff(boole_POSet_type, type, (
% 0.20/0.46 boole_POSet: $i > $i)).
% 0.20/0.46 tff(tptp_fun_A_26_type, type, (
% 0.20/0.46 tptp_fun_A_26: $i)).
% 0.20/0.46 tff(tptp_fun_C_28_type, type, (
% 0.20/0.46 tptp_fun_C_28: $i)).
% 0.20/0.46 tff(empty_set_type, type, (
% 0.20/0.46 empty_set: $i)).
% 0.20/0.46 tff(empty_type, type, (
% 0.20/0.46 empty: $i > $o)).
% 0.20/0.46 tff(element_type, type, (
% 0.20/0.46 element: ( $i * $i ) > $o)).
% 0.20/0.46 tff(powerset_type, type, (
% 0.20/0.46 powerset: $i > $i)).
% 0.20/0.46 tff(the_carrier_type, type, (
% 0.20/0.46 the_carrier: $i > $i)).
% 0.20/0.46 tff(proper_element_type, type, (
% 0.20/0.46 proper_element: ( $i * $i ) > $o)).
% 0.20/0.46 tff(upper_relstr_subset_type, type, (
% 0.20/0.46 upper_relstr_subset: ( $i * $i ) > $o)).
% 0.20/0.46 tff(filtered_subset_type, type, (
% 0.20/0.46 filtered_subset: ( $i * $i ) > $o)).
% 0.20/0.46 tff(relation_type, type, (
% 0.20/0.46 relation: $i > $o)).
% 0.20/0.46 tff(relation_empty_yielding_type, type, (
% 0.20/0.46 relation_empty_yielding: $i > $o)).
% 0.20/0.46 tff(empty_carrier_type, type, (
% 0.20/0.46 empty_carrier: $i > $o)).
% 0.20/0.46 tff(complete_relstr_type, type, (
% 0.20/0.46 complete_relstr: $i > $o)).
% 0.20/0.46 tff(with_infima_relstr_type, type, (
% 0.20/0.46 with_infima_relstr: $i > $o)).
% 0.20/0.46 tff(with_suprema_relstr_type, type, (
% 0.20/0.46 with_suprema_relstr: $i > $o)).
% 0.20/0.46 tff(boolean_relstr_type, type, (
% 0.20/0.46 boolean_relstr: $i > $o)).
% 0.20/0.46 tff(complemented_relstr_type, type, (
% 0.20/0.46 complemented_relstr: $i > $o)).
% 0.20/0.46 tff(heyting_relstr_type, type, (
% 0.20/0.46 heyting_relstr: $i > $o)).
% 0.20/0.46 tff(distributive_relstr_type, type, (
% 0.20/0.46 distributive_relstr: $i > $o)).
% 0.20/0.46 tff(join_complete_relstr_type, type, (
% 0.20/0.46 join_complete_relstr: $i > $o)).
% 0.20/0.46 tff(up_complete_relstr_type, type, (
% 0.20/0.46 up_complete_relstr: $i > $o)).
% 0.20/0.46 tff(bounded_relstr_type, type, (
% 0.20/0.46 bounded_relstr: $i > $o)).
% 0.20/0.46 tff(v1_yellow_3_type, type, (
% 0.20/0.46 v1_yellow_3: $i > $o)).
% 0.20/0.46 tff(strict_rel_str_type, type, (
% 0.20/0.46 strict_rel_str: $i > $o)).
% 0.20/0.46 tff(upper_bounded_relstr_type, type, (
% 0.20/0.46 upper_bounded_relstr: $i > $o)).
% 0.20/0.46 tff(trivial_carrier_type, type, (
% 0.20/0.46 trivial_carrier: $i > $o)).
% 0.20/0.46 tff(reflexive_relstr_type, type, (
% 0.20/0.46 reflexive_relstr: $i > $o)).
% 0.20/0.46 tff(lower_bounded_relstr_type, type, (
% 0.20/0.46 lower_bounded_relstr: $i > $o)).
% 0.20/0.46 tff(transitive_relstr_type, type, (
% 0.20/0.46 transitive_relstr: $i > $o)).
% 0.20/0.46 tff(antisymmetric_relstr_type, type, (
% 0.20/0.46 antisymmetric_relstr: $i > $o)).
% 0.20/0.46 tff(rel_str_type, type, (
% 0.20/0.46 rel_str: $i > $o)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(6,plain,
% 0.20/0.46 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[6])).
% 0.20/0.46 tff(8,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t8_boole')).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.20/0.46 tff(11,plain,(
% 0.20/0.46 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.46 inference(skolemize,[status(sab)],[10])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (((~empty(A!26)) & ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))) <=> ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 ((((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))) & (in(C!28, B!27) & empty(C!28))) <=> ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (((~empty(A!26)) & (((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))) & (in(C!28, B!27) & empty(C!28)))) <=> ((~empty(A!26)) & ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28)))),
% 0.20/0.46 inference(monotonicity,[status(thm)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (((~empty(A!26)) & (((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))) & (in(C!28, B!27) & empty(C!28)))) <=> ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.20/0.46 inference(transitivity,[status(thm)],[16, 14])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 ((~![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))))))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 ((~![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))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(20,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/sandbox/benchmark/theBenchmark.p','t2_yellow19')).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 (~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (~![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (empty(C!28)),
% 0.20/0.47 inference(and_elim,[status(thm)],[25])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (empty(empty_set) <=> empty(empty_set)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(28,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc12_relat_1')).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (empty(empty_set) & relation(empty_set)),
% 0.20/0.47 inference(and_elim,[status(thm)],[28])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (empty(empty_set)),
% 0.20/0.47 inference(and_elim,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (empty(empty_set)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[30, 27])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 32])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (empty_set = C!28),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[34, 31, 26, 13])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (^[A: $i] : refl((bottom_of_relstr(boole_POSet(A)) = empty_set) <=> (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[36])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(39,axiom,(![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t18_yellow_1')).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.20/0.47 tff(41,plain,(
% 0.20/0.47 ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.47 inference(skolemize,[status(sab)],[40])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) | (bottom_of_relstr(boole_POSet(A!26)) = empty_set)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (bottom_of_relstr(boole_POSet(A!26)) = empty_set),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (bottom_of_relstr(boole_POSet(A!26)) = C!28),
% 0.20/0.47 inference(transitivity,[status(thm)],[44, 35])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> in(C!28, B!27)),
% 0.20/0.47 inference(monotonicity,[status(thm)],[45])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (in(C!28, B!27) <=> in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.20/0.47 inference(symmetry,[status(thm)],[46])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (in(C!28, B!27)),
% 0.20/0.47 inference(and_elim,[status(thm)],[25])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (~empty(A!26)),
% 0.20/0.47 inference(and_elim,[status(thm)],[25])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 (^[A: $i] : refl((empty(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))) | (~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) | (~(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))) | (~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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 (![A: $i] : (empty(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))) | (~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) | (~(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))) | (~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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[51])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (^[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) | (~(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))) | (~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)))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (![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) | (~(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))) | (~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))))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (![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))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[56])).
% 0.20/0.47 tff(58,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/sandbox/benchmark/theBenchmark.p','fc2_waybel_7')).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.20/0.48 tff(61,plain,(
% 0.20/0.48 ![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))))),
% 0.20/0.48 inference(skolemize,[status(sab)],[60])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (![A: $i] : (empty(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))) | (~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))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[61, 54])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 (![A: $i] : (empty(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))) | (~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))))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[62, 52])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (((~![A: $i] : (empty(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))) | (~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!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(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))) | (~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!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((empty(A!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))) <=> (empty(A!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (((~![A: $i] : (empty(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))) | (~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!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(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))) | (~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!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[65])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (((~![A: $i] : (empty(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))) | (~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!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(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))) | (~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!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[66, 64])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 ((~![A: $i] : (empty(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))) | (~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!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 ((~![A: $i] : (empty(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))) | (~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!26) | (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (~((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[69, 63, 50])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | (~empty_carrier(boole_POSet(A!26)))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (~empty_carrier(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[73])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[75])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(78,axiom,(![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_yellow_1')).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.20/0.48 tff(80,plain,(
% 0.20/0.48 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[79])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[80, 76])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 ((~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))))) <=> (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[84])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[85, 83])).
% 0.20/0.48 tff(87,plain,
% 0.20/0.48 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[88, 82])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))) | rel_str(boole_POSet(A!26))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (rel_str(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[90, 89])).
% 0.20/0.48 tff(92,plain,
% 0.20/0.48 (((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | reflexive_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (reflexive_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[92, 70])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 (((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | lower_bounded_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 (lower_bounded_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[94, 70])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 (((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | transitive_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 (transitive_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[96, 70])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (((~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | antisymmetric_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (antisymmetric_relstr(boole_POSet(A!26))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[98, 70])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (^[A: $i] : rewrite((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[103, 101])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (^[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)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_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)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))))), rewrite((~(~(empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_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)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_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) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~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)))))) <=> (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(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) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~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) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~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) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (![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)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (^[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)))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(109,plain,
% 0.20/0.48 (![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)))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.48 tff(110,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/sandbox/benchmark/theBenchmark.p','t8_waybel_7')).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (![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)))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.49 tff(113,plain,(
% 0.20/0.49 ![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)))))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[112])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(117,plain,
% 0.20/0.49 ((empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) <=> (![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[117])).
% 0.20/0.49 tff(119,plain,
% 0.20/0.49 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[118, 116])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(121,plain,
% 0.20/0.49 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(A), B) <=> proper_element(B, powerset(the_carrier(A))))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | ![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))) | empty_carrier(boole_POSet(A!26))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[121, 115])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[122, 99, 97, 95, 93, 91, 72])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 (element(B!27, powerset(the_carrier(boole_POSet(A!26))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[25])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 (upper_relstr_subset(B!27, boole_POSet(A!26))),
% 0.20/0.49 inference(and_elim,[status(thm)],[25])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (filtered_subset(B!27, boole_POSet(A!26))),
% 0.20/0.49 inference(and_elim,[status(thm)],[25])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (~empty(B!27)),
% 0.20/0.49 inference(and_elim,[status(thm)],[25])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))) <=> ((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) <=> (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 ((~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) <=> (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 ((empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) <=> (empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[130])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 ((empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) <=> (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[131, 129])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) <=> ((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[132])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) <=> ((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[133, 128])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 ((~![B: $i] : (empty(B) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B) <=> proper_element(B, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (~(in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[136, 127, 126, 125, 124, 123])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))),
% 0.20/0.49 inference(and_elim,[status(thm)],[25])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~in(bottom_of_relstr(boole_POSet(A!26)), B!27)) | (~proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(140,plain,
% 0.20/0.50 ((in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 (~in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[140, 137])).
% 0.20/0.50 tff(142,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[141, 49])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------