TSTP Solution File: SEU387+2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU387+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n026.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 : Tue Sep 20 07:29:17 EDT 2022
% Result : Theorem 33.50s 21.77s
% Output : Proof 33.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU387+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Sep 3 13:15:39 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 33.50/21.77 % SZS status Theorem
% 33.50/21.77 % SZS output start Proof
% 33.50/21.77 tff(in_type, type, (
% 33.50/21.77 in: ( $i * $i ) > $o)).
% 33.50/21.77 tff(tptp_fun_B_484_type, type, (
% 33.50/21.77 tptp_fun_B_484: $i)).
% 33.50/21.77 tff(bottom_of_relstr_type, type, (
% 33.50/21.77 bottom_of_relstr: $i > $i)).
% 33.50/21.77 tff(boole_POSet_type, type, (
% 33.50/21.77 boole_POSet: $i > $i)).
% 33.50/21.77 tff(tptp_fun_A_483_type, type, (
% 33.50/21.77 tptp_fun_A_483: $i)).
% 33.50/21.77 tff(tptp_fun_C_485_type, type, (
% 33.50/21.77 tptp_fun_C_485: $i)).
% 33.50/21.77 tff(empty_set_type, type, (
% 33.50/21.77 empty_set: $i)).
% 33.50/21.77 tff(empty_type, type, (
% 33.50/21.77 empty: $i > $o)).
% 33.50/21.77 tff(element_type, type, (
% 33.50/21.77 element: ( $i * $i ) > $o)).
% 33.50/21.77 tff(powerset_type, type, (
% 33.50/21.77 powerset: $i > $i)).
% 33.50/21.77 tff(the_carrier_type, type, (
% 33.50/21.77 the_carrier: $i > $i)).
% 33.50/21.77 tff(proper_element_type, type, (
% 33.50/21.77 proper_element: ( $i * $i ) > $o)).
% 33.50/21.77 tff(upper_relstr_subset_type, type, (
% 33.50/21.77 upper_relstr_subset: ( $i * $i ) > $o)).
% 33.50/21.77 tff(filtered_subset_type, type, (
% 33.50/21.77 filtered_subset: ( $i * $i ) > $o)).
% 33.50/21.77 tff(relation_type, type, (
% 33.50/21.77 relation: $i > $o)).
% 33.50/21.77 tff(relation_empty_yielding_type, type, (
% 33.50/21.77 relation_empty_yielding: $i > $o)).
% 33.50/21.77 tff(empty_carrier_type, type, (
% 33.50/21.77 empty_carrier: $i > $o)).
% 33.50/21.77 tff(boolean_relstr_type, type, (
% 33.50/21.77 boolean_relstr: $i > $o)).
% 33.50/21.77 tff(complemented_relstr_type, type, (
% 33.50/21.77 complemented_relstr: $i > $o)).
% 33.50/21.77 tff(heyting_relstr_type, type, (
% 33.50/21.77 heyting_relstr: $i > $o)).
% 33.50/21.77 tff(distributive_relstr_type, type, (
% 33.50/21.77 distributive_relstr: $i > $o)).
% 33.50/21.77 tff(join_complete_relstr_type, type, (
% 33.50/21.77 join_complete_relstr: $i > $o)).
% 33.50/21.77 tff(up_complete_relstr_type, type, (
% 33.50/21.77 up_complete_relstr: $i > $o)).
% 33.50/21.77 tff(bounded_relstr_type, type, (
% 33.50/21.77 bounded_relstr: $i > $o)).
% 33.50/21.77 tff(complete_relstr_type, type, (
% 33.50/21.77 complete_relstr: $i > $o)).
% 33.50/21.77 tff(with_infima_relstr_type, type, (
% 33.50/21.77 with_infima_relstr: $i > $o)).
% 33.50/21.77 tff(v1_yellow_3_type, type, (
% 33.50/21.77 v1_yellow_3: $i > $o)).
% 33.50/21.77 tff(with_suprema_relstr_type, type, (
% 33.50/21.77 with_suprema_relstr: $i > $o)).
% 33.50/21.77 tff(strict_rel_str_type, type, (
% 33.50/21.77 strict_rel_str: $i > $o)).
% 33.50/21.77 tff(upper_bounded_relstr_type, type, (
% 33.50/21.77 upper_bounded_relstr: $i > $o)).
% 33.50/21.77 tff(trivial_carrier_type, type, (
% 33.50/21.77 trivial_carrier: $i > $o)).
% 33.50/21.77 tff(reflexive_relstr_type, type, (
% 33.50/21.77 reflexive_relstr: $i > $o)).
% 33.50/21.77 tff(antisymmetric_relstr_type, type, (
% 33.50/21.77 antisymmetric_relstr: $i > $o)).
% 33.50/21.77 tff(lower_bounded_relstr_type, type, (
% 33.50/21.77 lower_bounded_relstr: $i > $o)).
% 33.50/21.77 tff(transitive_relstr_type, type, (
% 33.50/21.77 transitive_relstr: $i > $o)).
% 33.50/21.77 tff(rel_str_type, type, (
% 33.50/21.77 rel_str: $i > $o)).
% 33.50/21.77 tff(1,plain,
% 33.50/21.77 (^[A: $i, B: $i] : refl(((~empty(B)) | (~empty(A)) | (A = B)) <=> ((~empty(B)) | (~empty(A)) | (A = B)))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(2,plain,
% 33.50/21.77 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 33.50/21.77 inference(quant_intro,[status(thm)],[1])).
% 33.50/21.77 tff(3,plain,
% 33.50/21.77 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(B)) | (~empty(A)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(B)) | (~empty(A)) | (A = B)))))), rewrite((~(~((~empty(B)) | (~empty(A)) | (A = B)))) <=> ((~empty(B)) | (~empty(A)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(B)) | (~empty(A)) | (A = B))))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(4,plain,
% 33.50/21.77 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 33.50/21.77 inference(quant_intro,[status(thm)],[3])).
% 33.50/21.77 tff(5,plain,
% 33.50/21.77 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(6,plain,
% 33.50/21.77 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(7,plain,
% 33.50/21.77 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 33.50/21.77 inference(quant_intro,[status(thm)],[6])).
% 33.50/21.77 tff(8,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 33.50/21.77 tff(9,plain,
% 33.50/21.77 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[8, 7])).
% 33.50/21.77 tff(10,plain,
% 33.50/21.77 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[9, 5])).
% 33.50/21.77 tff(11,plain,(
% 33.50/21.77 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 33.50/21.77 inference(skolemize,[status(sab)],[10])).
% 33.50/21.77 tff(12,plain,
% 33.50/21.77 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[11, 4])).
% 33.50/21.77 tff(13,plain,
% 33.50/21.77 (![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[12, 2])).
% 33.50/21.77 tff(14,plain,
% 33.50/21.77 (((~empty(A!483)) & ((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485))) <=> ((~empty(A!483)) & (~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(15,plain,
% 33.50/21.77 ((((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))) & (in(C!485, B!484) & empty(C!485))) <=> ((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(16,plain,
% 33.50/21.77 ((~(~(in(C!485, B!484) & empty(C!485)))) <=> (in(C!485, B!484) & empty(C!485))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(17,plain,
% 33.50/21.77 ((~(~((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))))) <=> ((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(18,plain,
% 33.50/21.77 (((~(~((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))))) & (~(~(in(C!485, B!484) & empty(C!485))))) <=> (((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))) & (in(C!485, B!484) & empty(C!485)))),
% 33.50/21.77 inference(monotonicity,[status(thm)],[17, 16])).
% 33.50/21.77 tff(19,plain,
% 33.50/21.77 (((~(~((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))))) & (~(~(in(C!485, B!484) & empty(C!485))))) <=> ((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485))),
% 33.50/21.77 inference(transitivity,[status(thm)],[18, 15])).
% 33.50/21.77 tff(20,plain,
% 33.50/21.77 (((~empty(A!483)) & ((~(~((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))))) & (~(~(in(C!485, B!484) & empty(C!485)))))) <=> ((~empty(A!483)) & ((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485)))),
% 33.50/21.77 inference(monotonicity,[status(thm)],[19])).
% 33.50/21.77 tff(21,plain,
% 33.50/21.77 (((~empty(A!483)) & ((~(~((~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483))))))) & (~(~(in(C!485, B!484) & empty(C!485)))))) <=> ((~empty(A!483)) & (~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485))),
% 33.50/21.77 inference(transitivity,[status(thm)],[20, 14])).
% 33.50/21.77 tff(22,plain,
% 33.50/21.77 ((~![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))))))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(23,plain,
% 33.50/21.77 ((~![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))))))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(24,axiom,(~![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_yellow19')).
% 33.50/21.77 tff(25,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[24, 23])).
% 33.50/21.77 tff(26,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[25, 22])).
% 33.50/21.77 tff(27,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[26, 22])).
% 33.50/21.77 tff(28,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[27, 22])).
% 33.50/21.77 tff(29,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[28, 22])).
% 33.50/21.77 tff(30,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[29, 22])).
% 33.50/21.77 tff(31,plain,
% 33.50/21.77 (~![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)))))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[30, 22])).
% 33.50/21.77 tff(32,plain,
% 33.50/21.77 ((~empty(A!483)) & (~empty(B!484)) & filtered_subset(B!484, boole_POSet(A!483)) & upper_relstr_subset(B!484, boole_POSet(A!483)) & proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & element(B!484, powerset(the_carrier(boole_POSet(A!483)))) & in(C!485, B!484) & empty(C!485)),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[31, 21])).
% 33.50/21.77 tff(33,plain,
% 33.50/21.77 (empty(C!485)),
% 33.50/21.77 inference(and_elim,[status(thm)],[32])).
% 33.50/21.77 tff(34,plain,
% 33.50/21.77 (empty(empty_set) <=> empty(empty_set)),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(35,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 33.50/21.77 tff(36,plain,
% 33.50/21.77 (empty(empty_set) & relation(empty_set)),
% 33.50/21.77 inference(and_elim,[status(thm)],[35])).
% 33.50/21.77 tff(37,plain,
% 33.50/21.77 (empty(empty_set)),
% 33.50/21.77 inference(and_elim,[status(thm)],[36])).
% 33.50/21.77 tff(38,plain,
% 33.50/21.77 (empty(empty_set)),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[37, 34])).
% 33.50/21.77 tff(39,plain,
% 33.50/21.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485)))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485)))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(40,plain,
% 33.50/21.77 (((~empty(empty_set)) | (~empty(C!485)) | (C!485 = empty_set)) <=> ((C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485)))),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(41,plain,
% 33.50/21.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!485)) | (C!485 = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485))))),
% 33.50/21.77 inference(monotonicity,[status(thm)],[40])).
% 33.50/21.77 tff(42,plain,
% 33.50/21.77 (((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!485)) | (C!485 = empty_set))) <=> ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485)))),
% 33.50/21.77 inference(transitivity,[status(thm)],[41, 39])).
% 33.50/21.77 tff(43,plain,
% 33.50/21.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!485)) | (C!485 = empty_set))),
% 33.50/21.77 inference(quant_inst,[status(thm)],[])).
% 33.50/21.77 tff(44,plain,
% 33.50/21.77 ((~![A: $i, B: $i] : ((~empty(B)) | (~empty(A)) | (A = B))) | (C!485 = empty_set) | (~empty(empty_set)) | (~empty(C!485))),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[43, 42])).
% 33.50/21.77 tff(45,plain,
% 33.50/21.77 (C!485 = empty_set),
% 33.50/21.77 inference(unit_resolution,[status(thm)],[44, 38, 33, 13])).
% 33.50/21.77 tff(46,plain,
% 33.50/21.77 (empty_set = C!485),
% 33.50/21.77 inference(symmetry,[status(thm)],[45])).
% 33.50/21.77 tff(47,plain,
% 33.50/21.77 (^[A: $i] : refl((bottom_of_relstr(boole_POSet(A)) = empty_set) <=> (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(48,plain,
% 33.50/21.77 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 33.50/21.77 inference(quant_intro,[status(thm)],[47])).
% 33.50/21.77 tff(49,plain,
% 33.50/21.77 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 33.50/21.77 inference(rewrite,[status(thm)],[])).
% 33.50/21.77 tff(50,axiom,(![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_yellow_1')).
% 33.50/21.77 tff(51,plain,
% 33.50/21.77 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[50, 49])).
% 33.50/21.77 tff(52,plain,(
% 33.50/21.77 ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 33.50/21.77 inference(skolemize,[status(sab)],[51])).
% 33.50/21.77 tff(53,plain,
% 33.50/21.77 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[52, 48])).
% 33.50/21.77 tff(54,plain,
% 33.50/21.77 ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) | (bottom_of_relstr(boole_POSet(A!483)) = empty_set)),
% 33.50/21.77 inference(quant_inst,[status(thm)],[])).
% 33.50/21.77 tff(55,plain,
% 33.50/21.77 (bottom_of_relstr(boole_POSet(A!483)) = empty_set),
% 33.50/21.77 inference(unit_resolution,[status(thm)],[54, 53])).
% 33.50/21.77 tff(56,plain,
% 33.50/21.77 (bottom_of_relstr(boole_POSet(A!483)) = C!485),
% 33.50/21.77 inference(transitivity,[status(thm)],[55, 46])).
% 33.50/21.77 tff(57,plain,
% 33.50/21.77 (in(bottom_of_relstr(boole_POSet(A!483)), B!484) <=> in(C!485, B!484)),
% 33.50/21.77 inference(monotonicity,[status(thm)],[56])).
% 33.50/21.77 tff(58,plain,
% 33.50/21.77 (in(C!485, B!484) <=> in(bottom_of_relstr(boole_POSet(A!483)), B!484)),
% 33.50/21.77 inference(symmetry,[status(thm)],[57])).
% 33.50/21.77 tff(59,plain,
% 33.50/21.77 (in(C!485, B!484)),
% 33.50/21.77 inference(and_elim,[status(thm)],[32])).
% 33.50/21.77 tff(60,plain,
% 33.50/21.77 (in(bottom_of_relstr(boole_POSet(A!483)), B!484)),
% 33.50/21.77 inference(modus_ponens,[status(thm)],[59, 58])).
% 33.50/21.77 tff(61,plain,
% 33.50/21.77 (~empty(A!483)),
% 33.50/21.77 inference(and_elim,[status(thm)],[32])).
% 33.50/21.77 tff(62,plain,
% 33.50/21.77 (^[A: $i] : refl((empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))) <=> (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(63,plain,
% 33.50/21.77 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))) <=> ![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 33.50/21.77 inference(quant_intro,[status(thm)],[62])).
% 33.50/21.77 tff(64,plain,
% 33.50/21.77 (^[A: $i] : rewrite((empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A)))))))),
% 33.50/21.77 inference(bind,[status(th)],[])).
% 33.50/21.77 tff(65,plain,
% 33.50/21.77 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 33.50/21.77 inference(quant_intro,[status(thm)],[64])).
% 33.50/21.77 tff(66,plain,
% 33.50/21.77 (![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))))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(67,plain,
% 33.50/21.78 (^[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))))))),
% 33.50/21.78 inference(bind,[status(th)],[])).
% 33.50/21.78 tff(68,plain,
% 33.50/21.78 (![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))))),
% 33.50/21.78 inference(quant_intro,[status(thm)],[67])).
% 33.50/21.78 tff(69,axiom,(![A: $i] : ((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_waybel_7')).
% 33.50/21.78 tff(70,plain,
% 33.50/21.78 (![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))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[69, 68])).
% 33.50/21.78 tff(71,plain,
% 33.50/21.78 (![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))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[70, 66])).
% 33.50/21.78 tff(72,plain,(
% 33.50/21.78 ![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))))),
% 33.50/21.78 inference(skolemize,[status(sab)],[71])).
% 33.50/21.78 tff(73,plain,
% 33.50/21.78 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[72, 65])).
% 33.50/21.78 tff(74,plain,
% 33.50/21.78 (![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[73, 63])).
% 33.50/21.78 tff(75,plain,
% 33.50/21.78 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(76,plain,
% 33.50/21.78 ((empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | v1_yellow_3(boole_POSet(A!483)) | trivial_carrier(boole_POSet(A!483)) | (~strict_rel_str(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))))) <=> (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(77,plain,
% 33.50/21.78 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | v1_yellow_3(boole_POSet(A!483)) | trivial_carrier(boole_POSet(A!483)) | (~strict_rel_str(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))))))),
% 33.50/21.78 inference(monotonicity,[status(thm)],[76])).
% 33.50/21.78 tff(78,plain,
% 33.50/21.78 (((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | v1_yellow_3(boole_POSet(A!483)) | trivial_carrier(boole_POSet(A!483)) | (~strict_rel_str(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))) <=> ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))),
% 33.50/21.78 inference(transitivity,[status(thm)],[77, 75])).
% 33.50/21.78 tff(79,plain,
% 33.50/21.78 ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | (empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | v1_yellow_3(boole_POSet(A!483)) | trivial_carrier(boole_POSet(A!483)) | (~strict_rel_str(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))))),
% 33.50/21.78 inference(quant_inst,[status(thm)],[])).
% 33.50/21.78 tff(80,plain,
% 33.50/21.78 ((~![A: $i] : (empty(A) | (~(empty_carrier(boole_POSet(A)) | v1_yellow_3(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))))))) | empty(A!483) | (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[79, 78])).
% 33.50/21.78 tff(81,plain,
% 33.50/21.78 (~(empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483))))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[80, 74, 61])).
% 33.50/21.78 tff(82,plain,
% 33.50/21.78 ((empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))) | (~empty_carrier(boole_POSet(A!483)))),
% 33.50/21.78 inference(tautology,[status(thm)],[])).
% 33.50/21.78 tff(83,plain,
% 33.50/21.78 (~empty_carrier(boole_POSet(A!483))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[82, 81])).
% 33.50/21.78 tff(84,plain,
% 33.50/21.78 ((empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))) | reflexive_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(tautology,[status(thm)],[])).
% 33.50/21.78 tff(85,plain,
% 33.50/21.78 (reflexive_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[84, 81])).
% 33.50/21.78 tff(86,plain,
% 33.50/21.78 ((empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))) | antisymmetric_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(tautology,[status(thm)],[])).
% 33.50/21.78 tff(87,plain,
% 33.50/21.78 (antisymmetric_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[86, 81])).
% 33.50/21.78 tff(88,plain,
% 33.50/21.78 ((empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))) | lower_bounded_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(tautology,[status(thm)],[])).
% 33.50/21.78 tff(89,plain,
% 33.50/21.78 (lower_bounded_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[88, 81])).
% 33.50/21.78 tff(90,plain,
% 33.50/21.78 ((empty_carrier(boole_POSet(A!483)) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | trivial_carrier(boole_POSet(A!483)) | (~upper_bounded_relstr(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))) | (~with_suprema_relstr(boole_POSet(A!483))) | v1_yellow_3(boole_POSet(A!483)) | (~with_infima_relstr(boole_POSet(A!483))) | (~complete_relstr(boole_POSet(A!483))) | (~bounded_relstr(boole_POSet(A!483))) | (~up_complete_relstr(boole_POSet(A!483))) | (~join_complete_relstr(boole_POSet(A!483))) | (~distributive_relstr(boole_POSet(A!483))) | (~heyting_relstr(boole_POSet(A!483))) | (~complemented_relstr(boole_POSet(A!483))) | (~boolean_relstr(boole_POSet(A!483)))) | transitive_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(tautology,[status(thm)],[])).
% 33.50/21.78 tff(91,plain,
% 33.50/21.78 (transitive_relstr(boole_POSet(A!483))),
% 33.50/21.78 inference(unit_resolution,[status(thm)],[90, 81])).
% 33.50/21.78 tff(92,plain,
% 33.50/21.78 (^[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))))))),
% 33.50/21.78 inference(bind,[status(th)],[])).
% 33.50/21.78 tff(93,plain,
% 33.50/21.78 (![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)))))),
% 33.50/21.78 inference(quant_intro,[status(thm)],[92])).
% 33.50/21.78 tff(94,plain,
% 33.50/21.78 (^[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))))))),
% 33.50/21.78 inference(bind,[status(th)],[])).
% 33.50/21.78 tff(95,plain,
% 33.50/21.78 (![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)))))),
% 33.50/21.78 inference(quant_intro,[status(thm)],[94])).
% 33.50/21.78 tff(96,plain,
% 33.50/21.78 (![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)))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(97,axiom,(![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_yellow_1')).
% 33.50/21.78 tff(98,plain,
% 33.50/21.78 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[97, 96])).
% 33.50/21.78 tff(99,plain,(
% 33.50/21.78 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 33.50/21.78 inference(skolemize,[status(sab)],[98])).
% 33.50/21.78 tff(100,plain,
% 33.50/21.78 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[99, 95])).
% 33.50/21.78 tff(101,plain,
% 33.50/21.78 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 33.50/21.78 inference(modus_ponens,[status(thm)],[100, 93])).
% 33.50/21.78 tff(102,plain,
% 33.50/21.78 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))))))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(103,plain,
% 33.50/21.78 ((~((~strict_rel_str(boole_POSet(A!483))) | (~rel_str(boole_POSet(A!483))))) <=> (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483)))))),
% 33.50/21.78 inference(rewrite,[status(thm)],[])).
% 33.50/21.78 tff(104,plain,
% 33.50/21.78 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!483))) | (~rel_str(boole_POSet(A!483)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))))))),
% 33.50/21.78 inference(monotonicity,[status(thm)],[103])).
% 33.50/21.78 tff(105,plain,
% 33.50/21.78 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!483))) | (~rel_str(boole_POSet(A!483)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))))))),
% 33.50/21.78 inference(transitivity,[status(thm)],[104, 102])).
% 33.50/21.78 tff(106,plain,
% 33.50/21.78 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!483))) | (~rel_str(boole_POSet(A!483)))))),
% 33.50/21.78 inference(quant_inst,[status(thm)],[])).
% 33.50/21.79 tff(107,plain,
% 33.50/21.79 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483)))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[106, 105])).
% 33.50/21.79 tff(108,plain,
% 33.50/21.79 (~((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483))))),
% 33.50/21.79 inference(unit_resolution,[status(thm)],[107, 101])).
% 33.50/21.79 tff(109,plain,
% 33.50/21.79 (((~rel_str(boole_POSet(A!483))) | (~strict_rel_str(boole_POSet(A!483)))) | rel_str(boole_POSet(A!483))),
% 33.50/21.79 inference(tautology,[status(thm)],[])).
% 33.50/21.79 tff(110,plain,
% 33.50/21.79 (rel_str(boole_POSet(A!483))),
% 33.50/21.79 inference(unit_resolution,[status(thm)],[109, 108])).
% 33.50/21.79 tff(111,plain,
% 33.50/21.79 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))),
% 33.50/21.79 inference(bind,[status(th)],[])).
% 33.50/21.79 tff(112,plain,
% 33.50/21.79 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(quant_intro,[status(thm)],[111])).
% 33.50/21.79 tff(113,plain,
% 33.50/21.79 (^[A: $i] : rewrite((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))),
% 33.50/21.79 inference(bind,[status(th)],[])).
% 33.50/21.79 tff(114,plain,
% 33.50/21.79 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(quant_intro,[status(thm)],[113])).
% 33.50/21.79 tff(115,plain,
% 33.50/21.79 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(transitivity,[status(thm)],[114, 112])).
% 33.50/21.79 tff(116,plain,
% 33.50/21.79 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) <=> (~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))))))), rewrite((~(~(empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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))))))), (((~((~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))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))), rewrite(((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) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, 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) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, 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] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~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) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))))), rewrite(((empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A)))) <=> (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~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) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))))),
% 33.50/21.79 inference(bind,[status(th)],[])).
% 33.50/21.79 tff(117,plain,
% 33.50/21.79 (![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) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(quant_intro,[status(thm)],[116])).
% 33.50/21.79 tff(118,plain,
% 33.50/21.79 (![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] : ((~((~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)))))),
% 33.50/21.79 inference(rewrite,[status(thm)],[])).
% 33.50/21.79 tff(119,plain,
% 33.50/21.79 (^[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)))))), ((((((~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)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))), rewrite((((~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))))) | (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)))) => (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))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))))), (![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] : ((~((~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] : (((((~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] : ((~((~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))))))), rewrite((((~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] : ((~((~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] : (((((~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] : ((~((~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)))))))),
% 33.50/21.79 inference(bind,[status(th)],[])).
% 33.50/21.79 tff(120,plain,
% 33.50/21.79 (![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] : ((~((~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)))))),
% 33.50/21.79 inference(quant_intro,[status(thm)],[119])).
% 33.50/21.79 tff(121,axiom,(![A: $i] : (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_waybel_7')).
% 33.50/21.79 tff(122,plain,
% 33.50/21.79 (![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)))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[121, 120])).
% 33.50/21.79 tff(123,plain,
% 33.50/21.79 (![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)))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[122, 118])).
% 33.50/21.79 tff(124,plain,(
% 33.50/21.79 ![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)))))),
% 33.50/21.79 inference(skolemize,[status(sab)],[123])).
% 33.50/21.79 tff(125,plain,
% 33.50/21.79 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[124, 117])).
% 33.50/21.79 tff(126,plain,
% 33.50/21.79 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[125, 115])).
% 33.50/21.79 tff(127,plain,
% 33.50/21.79 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!483)) | (~rel_str(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | empty_carrier(boole_POSet(A!483)) | (~rel_str(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483)))))),
% 33.50/21.79 inference(rewrite,[status(thm)],[])).
% 33.50/21.79 tff(128,plain,
% 33.50/21.79 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | (empty_carrier(boole_POSet(A!483)) | (~rel_str(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483)))))),
% 33.50/21.79 inference(quant_inst,[status(thm)],[])).
% 33.50/21.79 tff(129,plain,
% 33.50/21.79 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~transitive_relstr(A)) | (~lower_bounded_relstr(A)) | (~antisymmetric_relstr(A)) | (~reflexive_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~element(B, powerset(the_carrier(A)))) | (~upper_relstr_subset(B, A)) | (~filtered_subset(B, A))))) | empty_carrier(boole_POSet(A!483)) | (~rel_str(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))),
% 33.50/21.79 inference(modus_ponens,[status(thm)],[128, 127])).
% 33.50/21.79 tff(130,plain,
% 33.50/21.79 (empty_carrier(boole_POSet(A!483)) | (~rel_str(boole_POSet(A!483))) | (~transitive_relstr(boole_POSet(A!483))) | (~lower_bounded_relstr(boole_POSet(A!483))) | (~antisymmetric_relstr(boole_POSet(A!483))) | (~reflexive_relstr(boole_POSet(A!483))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))),
% 33.50/21.79 inference(unit_resolution,[status(thm)],[129, 126])).
% 33.50/21.79 tff(131,plain,
% 33.50/21.79 (![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))),
% 33.50/21.79 inference(unit_resolution,[status(thm)],[130, 110, 91, 89, 87, 85, 83])).
% 33.50/21.79 tff(132,plain,
% 33.50/21.79 (element(B!484, powerset(the_carrier(boole_POSet(A!483))))),
% 33.50/21.79 inference(and_elim,[status(thm)],[32])).
% 33.50/21.79 tff(133,plain,
% 33.50/21.79 (upper_relstr_subset(B!484, boole_POSet(A!483))),
% 33.50/21.79 inference(and_elim,[status(thm)],[32])).
% 33.50/21.79 tff(134,plain,
% 33.50/21.79 (filtered_subset(B!484, boole_POSet(A!483))),
% 33.50/21.79 inference(and_elim,[status(thm)],[32])).
% 33.50/21.79 tff(135,plain,
% 33.50/21.79 (~empty(B!484)),
% 33.50/21.79 inference(and_elim,[status(thm)],[32])).
% 33.50/21.79 tff(136,plain,
% 33.50/21.79 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | (empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483))))),
% 33.50/21.79 inference(rewrite,[status(thm)],[])).
% 33.50/21.79 tff(137,plain,
% 33.50/21.79 ((empty(B!484) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (~filtered_subset(B!484, boole_POSet(A!483)))) <=> (empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483))))),
% 33.50/21.79 inference(rewrite,[status(thm)],[])).
% 33.50/21.79 tff(138,plain,
% 33.50/21.79 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | (empty(B!484) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (~filtered_subset(B!484, boole_POSet(A!483))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | (empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483)))))),
% 33.50/21.79 inference(monotonicity,[status(thm)],[137])).
% 33.50/21.79 tff(139,plain,
% 33.50/21.79 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | (empty(B!484) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (~filtered_subset(B!484, boole_POSet(A!483))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483))))),
% 33.50/21.79 inference(transitivity,[status(thm)],[138, 136])).
% 33.50/21.79 tff(140,plain,
% 33.50/21.79 ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | (empty(B!484) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (~filtered_subset(B!484, boole_POSet(A!483))))),
% 33.58/21.89 inference(quant_inst,[status(thm)],[])).
% 33.58/21.89 tff(141,plain,
% 33.58/21.89 ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B))) | (~element(B, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B, boole_POSet(A!483))) | (~filtered_subset(B, boole_POSet(A!483))))) | empty(B!484) | (~element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~upper_relstr_subset(B!484, boole_POSet(A!483))) | (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))) | (~filtered_subset(B!484, boole_POSet(A!483)))),
% 33.58/21.89 inference(modus_ponens,[status(thm)],[140, 139])).
% 33.58/21.89 tff(142,plain,
% 33.58/21.89 (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))),
% 33.58/21.89 inference(unit_resolution,[status(thm)],[141, 135, 134, 133, 132, 131])).
% 33.58/21.89 tff(143,plain,
% 33.58/21.89 (proper_element(B!484, powerset(the_carrier(boole_POSet(A!483))))),
% 33.58/21.89 inference(and_elim,[status(thm)],[32])).
% 33.58/21.89 tff(144,plain,
% 33.58/21.89 ((~(proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484)))) | (~proper_element(B!484, powerset(the_carrier(boole_POSet(A!483))))) | (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))),
% 33.58/21.89 inference(tautology,[status(thm)],[])).
% 33.58/21.89 tff(145,plain,
% 33.58/21.89 ((~(proper_element(B!484, powerset(the_carrier(boole_POSet(A!483)))) <=> (~in(bottom_of_relstr(boole_POSet(A!483)), B!484)))) | (~in(bottom_of_relstr(boole_POSet(A!483)), B!484))),
% 33.58/21.89 inference(unit_resolution,[status(thm)],[144, 143])).
% 33.58/21.89 tff(146,plain,
% 33.58/21.89 (~in(bottom_of_relstr(boole_POSet(A!483)), B!484)),
% 33.58/21.89 inference(unit_resolution,[status(thm)],[145, 142])).
% 33.58/21.89 tff(147,plain,
% 33.58/21.89 ($false),
% 33.58/21.89 inference(unit_resolution,[status(thm)],[146, 60])).
% 33.58/21.89 % SZS output end Proof
%------------------------------------------------------------------------------