TSTP Solution File: SEU387+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 0.17s 0.45s
% Output : Proof 0.17s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU387+1 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.32 % Computer : n018.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Sat Sep 3 13:04:44 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.33 Usage: tptp [options] [-file:]file
% 0.11/0.33 -h, -? prints this message.
% 0.11/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.33 -m, -model generate model.
% 0.11/0.33 -p, -proof generate proof.
% 0.11/0.33 -c, -core generate unsat core of named formulas.
% 0.11/0.33 -st, -statistics display statistics.
% 0.11/0.33 -t:timeout set timeout (in second).
% 0.11/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.33 -<param>:<value> configuration parameter and value.
% 0.11/0.33 -o:<output-file> file to place output in.
% 0.17/0.45 % SZS status Theorem
% 0.17/0.45 % SZS output start Proof
% 0.17/0.45 tff(in_type, type, (
% 0.17/0.45 in: ( $i * $i ) > $o)).
% 0.17/0.45 tff(tptp_fun_B_27_type, type, (
% 0.17/0.45 tptp_fun_B_27: $i)).
% 0.17/0.45 tff(bottom_of_relstr_type, type, (
% 0.17/0.45 bottom_of_relstr: $i > $i)).
% 0.17/0.45 tff(boole_POSet_type, type, (
% 0.17/0.45 boole_POSet: $i > $i)).
% 0.17/0.45 tff(tptp_fun_A_26_type, type, (
% 0.17/0.45 tptp_fun_A_26: $i)).
% 0.17/0.45 tff(tptp_fun_C_28_type, type, (
% 0.17/0.45 tptp_fun_C_28: $i)).
% 0.17/0.45 tff(empty_set_type, type, (
% 0.17/0.45 empty_set: $i)).
% 0.17/0.45 tff(empty_type, type, (
% 0.17/0.45 empty: $i > $o)).
% 0.17/0.45 tff(element_type, type, (
% 0.17/0.45 element: ( $i * $i ) > $o)).
% 0.17/0.45 tff(powerset_type, type, (
% 0.17/0.45 powerset: $i > $i)).
% 0.17/0.45 tff(the_carrier_type, type, (
% 0.17/0.45 the_carrier: $i > $i)).
% 0.17/0.45 tff(proper_element_type, type, (
% 0.17/0.45 proper_element: ( $i * $i ) > $o)).
% 0.17/0.45 tff(upper_relstr_subset_type, type, (
% 0.17/0.45 upper_relstr_subset: ( $i * $i ) > $o)).
% 0.17/0.45 tff(filtered_subset_type, type, (
% 0.17/0.45 filtered_subset: ( $i * $i ) > $o)).
% 0.17/0.45 tff(relation_type, type, (
% 0.17/0.45 relation: $i > $o)).
% 0.17/0.45 tff(relation_empty_yielding_type, type, (
% 0.17/0.45 relation_empty_yielding: $i > $o)).
% 0.17/0.45 tff(empty_carrier_type, type, (
% 0.17/0.45 empty_carrier: $i > $o)).
% 0.17/0.45 tff(complete_relstr_type, type, (
% 0.17/0.45 complete_relstr: $i > $o)).
% 0.17/0.45 tff(with_infima_relstr_type, type, (
% 0.17/0.45 with_infima_relstr: $i > $o)).
% 0.17/0.45 tff(with_suprema_relstr_type, type, (
% 0.17/0.45 with_suprema_relstr: $i > $o)).
% 0.17/0.45 tff(boolean_relstr_type, type, (
% 0.17/0.45 boolean_relstr: $i > $o)).
% 0.17/0.45 tff(complemented_relstr_type, type, (
% 0.17/0.45 complemented_relstr: $i > $o)).
% 0.17/0.45 tff(heyting_relstr_type, type, (
% 0.17/0.45 heyting_relstr: $i > $o)).
% 0.17/0.45 tff(distributive_relstr_type, type, (
% 0.17/0.45 distributive_relstr: $i > $o)).
% 0.17/0.45 tff(join_complete_relstr_type, type, (
% 0.17/0.45 join_complete_relstr: $i > $o)).
% 0.17/0.45 tff(up_complete_relstr_type, type, (
% 0.17/0.45 up_complete_relstr: $i > $o)).
% 0.17/0.45 tff(bounded_relstr_type, type, (
% 0.17/0.45 bounded_relstr: $i > $o)).
% 0.17/0.45 tff(v1_yellow_3_type, type, (
% 0.17/0.45 v1_yellow_3: $i > $o)).
% 0.17/0.45 tff(strict_rel_str_type, type, (
% 0.17/0.45 strict_rel_str: $i > $o)).
% 0.17/0.45 tff(upper_bounded_relstr_type, type, (
% 0.17/0.45 upper_bounded_relstr: $i > $o)).
% 0.17/0.45 tff(trivial_carrier_type, type, (
% 0.17/0.45 trivial_carrier: $i > $o)).
% 0.17/0.45 tff(antisymmetric_relstr_type, type, (
% 0.17/0.45 antisymmetric_relstr: $i > $o)).
% 0.17/0.45 tff(transitive_relstr_type, type, (
% 0.17/0.45 transitive_relstr: $i > $o)).
% 0.17/0.45 tff(lower_bounded_relstr_type, type, (
% 0.17/0.45 lower_bounded_relstr: $i > $o)).
% 0.17/0.45 tff(reflexive_relstr_type, type, (
% 0.17/0.45 reflexive_relstr: $i > $o)).
% 0.17/0.45 tff(rel_str_type, type, (
% 0.17/0.45 rel_str: $i > $o)).
% 0.17/0.45 tff(1,plain,
% 0.17/0.45 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(2,plain,
% 0.17/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[1])).
% 0.17/0.45 tff(3,plain,
% 0.17/0.45 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(4,plain,
% 0.17/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[3])).
% 0.17/0.45 tff(5,plain,
% 0.17/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(6,plain,
% 0.17/0.45 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.17/0.45 inference(bind,[status(th)],[])).
% 0.17/0.45 tff(7,plain,
% 0.17/0.45 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.17/0.45 inference(quant_intro,[status(thm)],[6])).
% 0.17/0.45 tff(8,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.17/0.45 tff(9,plain,
% 0.17/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.17/0.45 tff(10,plain,
% 0.17/0.45 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.17/0.45 tff(11,plain,(
% 0.17/0.45 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.17/0.45 inference(skolemize,[status(sab)],[10])).
% 0.17/0.45 tff(12,plain,
% 0.17/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.17/0.45 tff(13,plain,
% 0.17/0.45 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.17/0.45 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.17/0.45 tff(14,plain,
% 0.17/0.45 (((~empty(A!26)) & ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))) <=> ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(15,plain,
% 0.17/0.45 ((((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))) & (in(C!28, B!27) & empty(C!28))) <=> ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(16,plain,
% 0.17/0.45 ((~(~(in(C!28, B!27) & empty(C!28)))) <=> (in(C!28, B!27) & empty(C!28))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(17,plain,
% 0.17/0.45 ((~(~((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) <=> ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))))),
% 0.17/0.45 inference(rewrite,[status(thm)],[])).
% 0.17/0.45 tff(18,plain,
% 0.17/0.45 (((~(~((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) & (~(~(in(C!28, B!27) & empty(C!28))))) <=> (((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))) & (in(C!28, B!27) & empty(C!28)))),
% 0.17/0.45 inference(monotonicity,[status(thm)],[17, 16])).
% 0.17/0.45 tff(19,plain,
% 0.17/0.45 (((~(~((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) & (~(~(in(C!28, B!27) & empty(C!28))))) <=> ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.17/0.45 inference(transitivity,[status(thm)],[18, 15])).
% 0.17/0.45 tff(20,plain,
% 0.17/0.45 (((~empty(A!26)) & ((~(~((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) & (~(~(in(C!28, B!27) & empty(C!28)))))) <=> ((~empty(A!26)) & ((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28)))),
% 0.17/0.46 inference(monotonicity,[status(thm)],[19])).
% 0.17/0.46 tff(21,plain,
% 0.17/0.46 (((~empty(A!26)) & ((~(~((~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) & (~(~(in(C!28, B!27) & empty(C!28)))))) <=> ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28))),
% 0.17/0.46 inference(transitivity,[status(thm)],[20, 14])).
% 0.17/0.46 tff(22,plain,
% 0.17/0.46 ((~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))) <=> (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(23,plain,
% 0.17/0.46 ((~![A: $i] : ((~empty(A)) => ![B: $i] : ((((((~empty(B)) & filtered_subset(B, boole_POSet(A))) & upper_relstr_subset(B, boole_POSet(A))) & proper_element(B, powerset(the_carrier(boole_POSet(A))))) & element(B, powerset(the_carrier(boole_POSet(A))))) => ![C: $i] : (~(in(C, B) & empty(C)))))) <=> (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C))))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 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')).
% 0.17/0.46 tff(25,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.17/0.46 tff(26,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.17/0.46 tff(27,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.17/0.46 tff(28,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.17/0.46 tff(29,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[28, 22])).
% 0.17/0.46 tff(30,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[29, 22])).
% 0.17/0.46 tff(31,plain,
% 0.17/0.46 (~![A: $i] : (empty(A) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, boole_POSet(A)) & upper_relstr_subset(B, boole_POSet(A)) & proper_element(B, powerset(the_carrier(boole_POSet(A)))) & element(B, powerset(the_carrier(boole_POSet(A)))))) | ![C: $i] : (~(in(C, B) & empty(C)))))),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[30, 22])).
% 0.17/0.46 tff(32,plain,
% 0.17/0.46 ((~empty(A!26)) & (~empty(B!27)) & filtered_subset(B!27, boole_POSet(A!26)) & upper_relstr_subset(B!27, boole_POSet(A!26)) & proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & element(B!27, powerset(the_carrier(boole_POSet(A!26)))) & in(C!28, B!27) & empty(C!28)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[31, 21])).
% 0.17/0.46 tff(33,plain,
% 0.17/0.46 (empty(C!28)),
% 0.17/0.46 inference(and_elim,[status(thm)],[32])).
% 0.17/0.46 tff(34,plain,
% 0.17/0.46 (empty(empty_set) <=> empty(empty_set)),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(35,axiom,((empty(empty_set) & relation(empty_set)) & relation_empty_yielding(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc12_relat_1')).
% 0.17/0.46 tff(36,plain,
% 0.17/0.46 (empty(empty_set) & relation(empty_set)),
% 0.17/0.46 inference(and_elim,[status(thm)],[35])).
% 0.17/0.46 tff(37,plain,
% 0.17/0.46 (empty(empty_set)),
% 0.17/0.46 inference(and_elim,[status(thm)],[36])).
% 0.17/0.46 tff(38,plain,
% 0.17/0.46 (empty(empty_set)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[37, 34])).
% 0.17/0.46 tff(39,plain,
% 0.17/0.46 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(40,plain,
% 0.17/0.46 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28))),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(41,plain,
% 0.17/0.46 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(C!28)) | (empty_set = C!28)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.17/0.46 tff(42,plain,
% 0.17/0.46 (empty_set = C!28),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[41, 38, 33, 13])).
% 0.17/0.46 tff(43,plain,
% 0.17/0.46 (^[A: $i] : refl((bottom_of_relstr(boole_POSet(A)) = empty_set) <=> (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 0.17/0.46 inference(bind,[status(th)],[])).
% 0.17/0.46 tff(44,plain,
% 0.17/0.46 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.17/0.46 inference(quant_intro,[status(thm)],[43])).
% 0.17/0.46 tff(45,plain,
% 0.17/0.46 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set) <=> ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(46,axiom,(![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_yellow_1')).
% 0.17/0.46 tff(47,plain,
% 0.17/0.46 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[46, 45])).
% 0.17/0.46 tff(48,plain,(
% 0.17/0.46 ![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.17/0.46 inference(skolemize,[status(sab)],[47])).
% 0.17/0.46 tff(49,plain,
% 0.17/0.46 (![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.17/0.46 tff(50,plain,
% 0.17/0.46 ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) | (bottom_of_relstr(boole_POSet(A!26)) = empty_set)),
% 0.17/0.46 inference(quant_inst,[status(thm)],[])).
% 0.17/0.46 tff(51,plain,
% 0.17/0.46 (bottom_of_relstr(boole_POSet(A!26)) = empty_set),
% 0.17/0.46 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.17/0.46 tff(52,plain,
% 0.17/0.46 (bottom_of_relstr(boole_POSet(A!26)) = C!28),
% 0.17/0.46 inference(transitivity,[status(thm)],[51, 42])).
% 0.17/0.46 tff(53,plain,
% 0.17/0.46 (in(bottom_of_relstr(boole_POSet(A!26)), B!27) <=> in(C!28, B!27)),
% 0.17/0.46 inference(monotonicity,[status(thm)],[52])).
% 0.17/0.46 tff(54,plain,
% 0.17/0.46 (in(C!28, B!27) <=> in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.17/0.46 inference(symmetry,[status(thm)],[53])).
% 0.17/0.46 tff(55,plain,
% 0.17/0.46 (in(C!28, B!27)),
% 0.17/0.46 inference(and_elim,[status(thm)],[32])).
% 0.17/0.46 tff(56,plain,
% 0.17/0.46 (in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.17/0.46 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.17/0.46 tff(57,plain,
% 0.17/0.46 (~empty(A!26)),
% 0.17/0.46 inference(and_elim,[status(thm)],[32])).
% 0.17/0.46 tff(58,plain,
% 0.17/0.46 (^[A: $i] : refl((empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) <=> (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))))),
% 0.17/0.46 inference(bind,[status(th)],[])).
% 0.17/0.46 tff(59,plain,
% 0.17/0.46 (![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) <=> ![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 0.17/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.17/0.46 tff(60,plain,
% 0.17/0.46 (^[A: $i] : rewrite((empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))))),
% 0.17/0.46 inference(bind,[status(th)],[])).
% 0.17/0.46 tff(61,plain,
% 0.17/0.46 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 0.17/0.46 inference(quant_intro,[status(thm)],[60])).
% 0.17/0.46 tff(62,plain,
% 0.17/0.46 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 0.17/0.46 inference(rewrite,[status(thm)],[])).
% 0.17/0.46 tff(63,plain,
% 0.17/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))))), ((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)))), ((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))))), (((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))), (((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))))), ((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)))), ((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))))), (((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)))), (((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))))), ((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)))), ((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))))), (((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)))), (((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))))), ((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)))), ((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))))), (((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))))), (((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))))), ((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)))), ((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))))), (((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)))), (((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)))), ((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))))), (((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)))), (((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))))), ((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)))), ((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))))), (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)))), (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))))), ((((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))), ((((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))), (((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> ((~empty(A)) => ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))))), rewrite(((~empty(A)) => ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))), (((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))))),
% 0.17/0.47 inference(bind,[status(th)],[])).
% 0.17/0.47 tff(64,plain,
% 0.17/0.47 (![A: $i] : ((~empty(A)) => (((((((((((((((((((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A)))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & up_complete_relstr(boole_POSet(A))) & join_complete_relstr(boole_POSet(A))) & (~v1_yellow_3(boole_POSet(A)))) & distributive_relstr(boole_POSet(A))) & heyting_relstr(boole_POSet(A))) & complemented_relstr(boole_POSet(A))) & boolean_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))) <=> ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 0.17/0.47 inference(quant_intro,[status(thm)],[63])).
% 0.17/0.47 tff(65,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')).
% 0.17/0.47 tff(66,plain,
% 0.17/0.47 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.17/0.47 tff(67,plain,
% 0.17/0.47 (![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.17/0.47 tff(68,plain,(
% 0.17/0.47 ![A: $i] : (empty(A) | ((~empty_carrier(boole_POSet(A))) & (~trivial_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & up_complete_relstr(boole_POSet(A)) & join_complete_relstr(boole_POSet(A)) & (~v1_yellow_3(boole_POSet(A))) & distributive_relstr(boole_POSet(A)) & heyting_relstr(boole_POSet(A)) & complemented_relstr(boole_POSet(A)) & boolean_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))))),
% 0.17/0.47 inference(skolemize,[status(sab)],[67])).
% 0.17/0.47 tff(69,plain,
% 0.17/0.47 (![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.17/0.47 tff(70,plain,
% 0.17/0.47 (![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 0.17/0.47 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.17/0.47 tff(71,plain,
% 0.17/0.47 (((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | (empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(72,plain,
% 0.17/0.47 ((empty(A!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))) <=> (empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.17/0.47 inference(rewrite,[status(thm)],[])).
% 0.17/0.47 tff(73,plain,
% 0.17/0.47 (((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | (empty(A!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | (empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))))),
% 0.17/0.47 inference(monotonicity,[status(thm)],[72])).
% 0.17/0.47 tff(74,plain,
% 0.17/0.47 (((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | (empty(A!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))) <=> ((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.17/0.47 inference(transitivity,[status(thm)],[73, 71])).
% 0.17/0.47 tff(75,plain,
% 0.17/0.47 ((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | (empty(A!26) | (~(v1_yellow_3(boole_POSet(A!26)) | empty_carrier(boole_POSet(A!26)) | trivial_carrier(boole_POSet(A!26)) | (~strict_rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))))),
% 0.17/0.47 inference(quant_inst,[status(thm)],[])).
% 0.17/0.47 tff(76,plain,
% 0.17/0.47 ((~![A: $i] : (empty(A) | (~(v1_yellow_3(boole_POSet(A)) | empty_carrier(boole_POSet(A)) | trivial_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~up_complete_relstr(boole_POSet(A))) | (~join_complete_relstr(boole_POSet(A))) | (~distributive_relstr(boole_POSet(A))) | (~heyting_relstr(boole_POSet(A))) | (~complemented_relstr(boole_POSet(A))) | (~boolean_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))) | empty(A!26) | (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.17/0.48 tff(77,plain,
% 0.17/0.48 (~(empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[76, 70, 57])).
% 0.17/0.48 tff(78,plain,
% 0.17/0.48 ((empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | (~empty_carrier(boole_POSet(A!26)))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(79,plain,
% 0.17/0.48 (~empty_carrier(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.17/0.48 tff(80,plain,
% 0.17/0.48 ((empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | antisymmetric_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(81,plain,
% 0.17/0.48 (antisymmetric_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[80, 77])).
% 0.17/0.48 tff(82,plain,
% 0.17/0.48 ((empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | transitive_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(83,plain,
% 0.17/0.48 (transitive_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.17/0.48 tff(84,plain,
% 0.17/0.48 ((empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | lower_bounded_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(85,plain,
% 0.17/0.48 (lower_bounded_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[84, 77])).
% 0.17/0.48 tff(86,plain,
% 0.17/0.48 ((empty_carrier(boole_POSet(A!26)) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | trivial_carrier(boole_POSet(A!26)) | (~upper_bounded_relstr(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))) | v1_yellow_3(boole_POSet(A!26)) | (~bounded_relstr(boole_POSet(A!26))) | (~up_complete_relstr(boole_POSet(A!26))) | (~join_complete_relstr(boole_POSet(A!26))) | (~distributive_relstr(boole_POSet(A!26))) | (~heyting_relstr(boole_POSet(A!26))) | (~complemented_relstr(boole_POSet(A!26))) | (~boolean_relstr(boole_POSet(A!26))) | (~with_suprema_relstr(boole_POSet(A!26))) | (~with_infima_relstr(boole_POSet(A!26))) | (~complete_relstr(boole_POSet(A!26)))) | reflexive_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(87,plain,
% 0.17/0.48 (reflexive_relstr(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[86, 77])).
% 0.17/0.48 tff(88,plain,
% 0.17/0.48 (^[A: $i] : refl((~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(89,plain,
% 0.17/0.48 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[88])).
% 0.17/0.48 tff(90,plain,
% 0.17/0.48 (^[A: $i] : rewrite((strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(91,plain,
% 0.17/0.48 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[90])).
% 0.17/0.48 tff(92,plain,
% 0.17/0.48 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(93,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')).
% 0.17/0.48 tff(94,plain,
% 0.17/0.48 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.17/0.48 tff(95,plain,(
% 0.17/0.48 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.17/0.48 inference(skolemize,[status(sab)],[94])).
% 0.17/0.48 tff(96,plain,
% 0.17/0.48 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.17/0.48 tff(97,plain,
% 0.17/0.48 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[96, 89])).
% 0.17/0.48 tff(98,plain,
% 0.17/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(99,plain,
% 0.17/0.48 ((~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26))))) <=> (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(100,plain,
% 0.17/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.17/0.48 inference(monotonicity,[status(thm)],[99])).
% 0.17/0.48 tff(101,plain,
% 0.17/0.48 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[100, 98])).
% 0.17/0.48 tff(102,plain,
% 0.17/0.48 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!26))) | (~rel_str(boole_POSet(A!26)))))),
% 0.17/0.48 inference(quant_inst,[status(thm)],[])).
% 0.17/0.48 tff(103,plain,
% 0.17/0.48 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[102, 101])).
% 0.17/0.48 tff(104,plain,
% 0.17/0.48 (~((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26))))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[103, 97])).
% 0.17/0.48 tff(105,plain,
% 0.17/0.48 (((~rel_str(boole_POSet(A!26))) | (~strict_rel_str(boole_POSet(A!26)))) | rel_str(boole_POSet(A!26))),
% 0.17/0.48 inference(tautology,[status(thm)],[])).
% 0.17/0.48 tff(106,plain,
% 0.17/0.48 (rel_str(boole_POSet(A!26))),
% 0.17/0.48 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.17/0.48 tff(107,plain,
% 0.17/0.48 (^[A: $i] : refl((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(108,plain,
% 0.17/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.17/0.48 tff(109,plain,
% 0.17/0.48 (^[A: $i] : rewrite((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(110,plain,
% 0.17/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[109])).
% 0.17/0.48 tff(111,plain,
% 0.17/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.48 inference(transitivity,[status(thm)],[110, 108])).
% 0.17/0.48 tff(112,plain,
% 0.17/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)) <=> (~(empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (~(~(empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))))), rewrite((~(~(empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)))), ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(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))) | (~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) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))), (![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))) <=> ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A)))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))), (((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(113,plain,
% 0.17/0.48 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[112])).
% 0.17/0.48 tff(114,plain,
% 0.17/0.48 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~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)))))),
% 0.17/0.48 inference(rewrite,[status(thm)],[])).
% 0.17/0.48 tff(115,plain,
% 0.17/0.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A)) & antisymmetric_relstr(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A))), (((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A))), ((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> (((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)))), rewrite((((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))), (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) <=> ((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A))), (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> (((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))))), rewrite((((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))), (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) <=> ((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A)))))), ((((((~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)))))))),
% 0.17/0.48 inference(bind,[status(th)],[])).
% 0.17/0.48 tff(116,plain,
% 0.17/0.48 (![A: $i] : (((((((~empty_carrier(A)) & reflexive_relstr(A)) & transitive_relstr(A)) & antisymmetric_relstr(A)) & lower_bounded_relstr(A)) & rel_str(A)) => ![B: $i] : (((((~empty(B)) & filtered_subset(B, A)) & upper_relstr_subset(B, A)) & element(B, powerset(the_carrier(A)))) => (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~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)))))),
% 0.17/0.48 inference(quant_intro,[status(thm)],[115])).
% 0.17/0.48 tff(117,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')).
% 0.17/0.48 tff(118,plain,
% 0.17/0.48 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.17/0.48 tff(119,plain,
% 0.17/0.48 (![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))),
% 0.17/0.48 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.17/0.48 tff(120,plain,(
% 0.17/0.48 ![A: $i] : ((~((~empty_carrier(A)) & reflexive_relstr(A) & transitive_relstr(A) & antisymmetric_relstr(A) & lower_bounded_relstr(A) & rel_str(A))) | ![B: $i] : ((~((~empty(B)) & filtered_subset(B, A) & upper_relstr_subset(B, A) & element(B, powerset(the_carrier(A))))) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B)))))),
% 0.17/0.48 inference(skolemize,[status(sab)],[119])).
% 0.17/0.48 tff(121,plain,
% 0.17/0.48 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.17/0.49 tff(122,plain,
% 0.17/0.49 (![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.17/0.49 tff(123,plain,
% 0.17/0.49 (((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(124,plain,
% 0.17/0.49 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26)))))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(125,plain,
% 0.17/0.49 ((~![A: $i] : (empty_carrier(A) | (~rel_str(A)) | (~reflexive_relstr(A)) | (~lower_bounded_relstr(A)) | (~transitive_relstr(A)) | (~antisymmetric_relstr(A)) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(A))) <=> (~in(bottom_of_relstr(A), B))) | (~filtered_subset(B, A)) | (~upper_relstr_subset(B, A)) | (~element(B, powerset(the_carrier(A))))))) | empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.17/0.49 tff(126,plain,
% 0.17/0.49 (empty_carrier(boole_POSet(A!26)) | (~rel_str(boole_POSet(A!26))) | (~reflexive_relstr(boole_POSet(A!26))) | (~lower_bounded_relstr(boole_POSet(A!26))) | (~transitive_relstr(boole_POSet(A!26))) | (~antisymmetric_relstr(boole_POSet(A!26))) | ![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[125, 122])).
% 0.17/0.49 tff(127,plain,
% 0.17/0.49 (![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[126, 106, 87, 85, 83, 81, 79])).
% 0.17/0.49 tff(128,plain,
% 0.17/0.49 (element(B!27, powerset(the_carrier(boole_POSet(A!26))))),
% 0.17/0.49 inference(and_elim,[status(thm)],[32])).
% 0.17/0.49 tff(129,plain,
% 0.17/0.49 (upper_relstr_subset(B!27, boole_POSet(A!26))),
% 0.17/0.49 inference(and_elim,[status(thm)],[32])).
% 0.17/0.49 tff(130,plain,
% 0.17/0.49 (filtered_subset(B!27, boole_POSet(A!26))),
% 0.17/0.49 inference(and_elim,[status(thm)],[32])).
% 0.17/0.49 tff(131,plain,
% 0.17/0.49 (~empty(B!27)),
% 0.17/0.49 inference(and_elim,[status(thm)],[32])).
% 0.17/0.49 tff(132,plain,
% 0.17/0.49 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(133,plain,
% 0.17/0.49 ((empty(B!27) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26)))))) <=> (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.17/0.49 inference(rewrite,[status(thm)],[])).
% 0.17/0.49 tff(134,plain,
% 0.17/0.49 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26)))))),
% 0.17/0.49 inference(monotonicity,[status(thm)],[133])).
% 0.17/0.49 tff(135,plain,
% 0.17/0.49 (((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))) <=> ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))))),
% 0.17/0.49 inference(transitivity,[status(thm)],[134, 132])).
% 0.17/0.49 tff(136,plain,
% 0.17/0.49 ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | (empty(B!27) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26))) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))))),
% 0.17/0.49 inference(quant_inst,[status(thm)],[])).
% 0.17/0.49 tff(137,plain,
% 0.17/0.49 ((~![B: $i] : (empty(B) | (proper_element(B, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B))) | (~filtered_subset(B, boole_POSet(A!26))) | (~upper_relstr_subset(B, boole_POSet(A!26))) | (~element(B, powerset(the_carrier(boole_POSet(A!26))))))) | empty(B!27) | (~element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))) | (~filtered_subset(B!27, boole_POSet(A!26))) | (~upper_relstr_subset(B!27, boole_POSet(A!26)))),
% 0.17/0.49 inference(modus_ponens,[status(thm)],[136, 135])).
% 0.17/0.49 tff(138,plain,
% 0.17/0.49 (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))),
% 0.17/0.49 inference(unit_resolution,[status(thm)],[137, 131, 130, 129, 128, 127])).
% 0.17/0.49 tff(139,plain,
% 0.17/0.49 (proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))),
% 0.17/0.49 inference(and_elim,[status(thm)],[32])).
% 0.17/0.49 tff(140,plain,
% 0.17/0.49 ((~(proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27)))) | (~proper_element(B!27, powerset(the_carrier(boole_POSet(A!26))))) | (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))),
% 0.17/0.49 inference(tautology,[status(thm)],[])).
% 0.17/0.49 tff(141,plain,
% 0.17/0.49 ((~(proper_element(B!27, powerset(the_carrier(boole_POSet(A!26)))) <=> (~in(bottom_of_relstr(boole_POSet(A!26)), B!27)))) | (~in(bottom_of_relstr(boole_POSet(A!26)), B!27))),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[140, 139])).
% 0.17/0.50 tff(142,plain,
% 0.17/0.50 (~in(bottom_of_relstr(boole_POSet(A!26)), B!27)),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[141, 138])).
% 0.17/0.50 tff(143,plain,
% 0.17/0.50 ($false),
% 0.17/0.50 inference(unit_resolution,[status(thm)],[142, 56])).
% 0.17/0.50 % SZS output end Proof
%------------------------------------------------------------------------------