%------------------------------------------------------------------------------
% File     : Z3---4.8.9.0
% Problem  : SEU371+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : z3_tptp -proof -model -t:%d -file:%s

% Computer : n021.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 07:29:11 EDT 2022

% Result   : Theorem 0.20s 0.49s
% Output   : Proof 0.20s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU371+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command  : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Sat Sep  3 12:42:45 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35  Usage: tptp [options] [-file:]file
% 0.13/0.35    -h, -?       prints this message.
% 0.13/0.35    -smt2        print SMT-LIB2 benchmark.
% 0.13/0.35    -m, -model   generate model.
% 0.13/0.35    -p, -proof   generate proof.
% 0.13/0.35    -c, -core    generate unsat core of named formulas.
% 0.13/0.35    -st, -statistics display statistics.
% 0.13/0.35    -t:timeout   set timeout (in second).
% 0.13/0.35    -smt2status  display status in smt2 format instead of SZS.
% 0.13/0.35    -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35    -<param>:<value> configuration parameter and value.
% 0.13/0.35    -o:<output-file> file to place output in.
% 0.20/0.49  % SZS status Theorem
% 0.20/0.49  % SZS output start Proof
% 0.20/0.49  tff(empty_set_type, type, (
% 0.20/0.49     empty_set: $i)).
% 0.20/0.49  tff(bottom_of_relstr_type, type, (
% 0.20/0.49     bottom_of_relstr: $i > $i)).
% 0.20/0.49  tff(boole_POSet_type, type, (
% 0.20/0.49     boole_POSet: $i > $i)).
% 0.20/0.49  tff(tptp_fun_A_28_type, type, (
% 0.20/0.49     tptp_fun_A_28: $i)).
% 0.20/0.49  tff(bottom_of_semilattstr_type, type, (
% 0.20/0.49     bottom_of_semilattstr: $i > $i)).
% 0.20/0.49  tff(boole_lattice_type, type, (
% 0.20/0.49     boole_lattice: $i > $i)).
% 0.20/0.49  tff(lower_bounded_semilattstr_type, type, (
% 0.20/0.49     lower_bounded_semilattstr: $i > $o)).
% 0.20/0.49  tff(join_of_latt_set_type, type, (
% 0.20/0.49     join_of_latt_set: ( $i * $i ) > $i)).
% 0.20/0.49  tff(lattice_type, type, (
% 0.20/0.49     lattice: $i > $o)).
% 0.20/0.49  tff(latt_str_type, type, (
% 0.20/0.49     latt_str: $i > $o)).
% 0.20/0.49  tff(empty_carrier_type, type, (
% 0.20/0.49     empty_carrier: $i > $o)).
% 0.20/0.49  tff(complete_latt_str_type, type, (
% 0.20/0.49     complete_latt_str: $i > $o)).
% 0.20/0.49  tff(boolean_lattstr_type, type, (
% 0.20/0.49     boolean_lattstr: $i > $o)).
% 0.20/0.49  tff(complemented_lattstr_type, type, (
% 0.20/0.49     complemented_lattstr: $i > $o)).
% 0.20/0.49  tff(bounded_lattstr_type, type, (
% 0.20/0.49     bounded_lattstr: $i > $o)).
% 0.20/0.49  tff(upper_bounded_semilattstr_type, type, (
% 0.20/0.49     upper_bounded_semilattstr: $i > $o)).
% 0.20/0.49  tff(modular_lattstr_type, type, (
% 0.20/0.49     modular_lattstr: $i > $o)).
% 0.20/0.49  tff(distributive_lattstr_type, type, (
% 0.20/0.49     distributive_lattstr: $i > $o)).
% 0.20/0.49  tff(join_absorbing_type, type, (
% 0.20/0.49     join_absorbing: $i > $o)).
% 0.20/0.49  tff(meet_absorbing_type, type, (
% 0.20/0.49     meet_absorbing: $i > $o)).
% 0.20/0.49  tff(meet_associative_type, type, (
% 0.20/0.49     meet_associative: $i > $o)).
% 0.20/0.49  tff(meet_commutative_type, type, (
% 0.20/0.49     meet_commutative: $i > $o)).
% 0.20/0.49  tff(join_associative_type, type, (
% 0.20/0.49     join_associative: $i > $o)).
% 0.20/0.49  tff(join_commutative_type, type, (
% 0.20/0.49     join_commutative: $i > $o)).
% 0.20/0.49  tff(strict_latt_str_type, type, (
% 0.20/0.49     strict_latt_str: $i > $o)).
% 0.20/0.49  tff(tptp_fun_A_16_type, type, (
% 0.20/0.49     tptp_fun_A_16: $i)).
% 0.20/0.49  tff(empty_type, type, (
% 0.20/0.49     empty: $i > $o)).
% 0.20/0.49  tff(join_on_relstr_type, type, (
% 0.20/0.49     join_on_relstr: ( $i * $i ) > $i)).
% 0.20/0.49  tff(poset_of_lattice_type, type, (
% 0.20/0.49     poset_of_lattice: $i > $i)).
% 0.20/0.49  tff(meet_on_relstr_type, type, (
% 0.20/0.49     meet_on_relstr: ( $i * $i ) > $i)).
% 0.20/0.49  tff(meet_of_latt_set_type, type, (
% 0.20/0.49     meet_of_latt_set: ( $i * $i ) > $i)).
% 0.20/0.49  tff(rel_str_type, type, (
% 0.20/0.49     rel_str: $i > $o)).
% 0.20/0.49  tff(strict_rel_str_type, type, (
% 0.20/0.49     strict_rel_str: $i > $o)).
% 0.20/0.49  tff(1,plain,
% 0.20/0.49      (^[A: $i] : refl((~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set)))) <=> (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set)))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(2,plain,
% 0.20/0.49      (![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set)))) <=> ![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[1])).
% 0.20/0.49  tff(3,plain,
% 0.20/0.49      (^[A: $i] : rewrite((lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set)) <=> (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set)))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(4,plain,
% 0.20/0.49      (![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set)) <=> ![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[3])).
% 0.20/0.49  tff(5,plain,
% 0.20/0.49      (![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set)) <=> ![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(6,axiom,(![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_lattice3')).
% 0.20/0.49  tff(7,plain,
% 0.20/0.49      (![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.49  tff(8,plain,(
% 0.20/0.49      ![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 0.20/0.49      inference(skolemize,[status(sab)],[7])).
% 0.20/0.49  tff(9,plain,
% 0.20/0.49      (![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.49  tff(10,plain,
% 0.20/0.49      (![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.49  tff(11,plain,
% 0.20/0.49      ((~![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))) | (~((~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = empty_set))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(12,plain,
% 0.20/0.49      (~((~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = empty_set)))),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.49  tff(13,plain,
% 0.20/0.49      (((~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = empty_set))) | (bottom_of_semilattstr(boole_lattice(A!28)) = empty_set)),
% 0.20/0.49      inference(tautology,[status(thm)],[])).
% 0.20/0.49  tff(14,plain,
% 0.20/0.49      (bottom_of_semilattstr(boole_lattice(A!28)) = empty_set),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.49  tff(15,plain,
% 0.20/0.49      (^[A: $i] : refl((~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A))))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(16,plain,
% 0.20/0.49      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A))))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[15])).
% 0.20/0.49  tff(17,plain,
% 0.20/0.49      (^[A: $i] : rewrite(((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(18,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[17])).
% 0.20/0.49  tff(19,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(20,plain,
% 0.20/0.49      (^[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(rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)))), (((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)))), (((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))))), ((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)))), ((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))))), (((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)))), (((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))))), ((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)))), ((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))))), (((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)))), (((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))))), ((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)))), ((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))))), (((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)))), (((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))))), ((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)))), ((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))))), (((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)))), (((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))))), ((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)))), ((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))))), (((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)))), (((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))))), ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)))), ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))))), (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))), (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))))), ((((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))), ((((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(21,plain,
% 0.20/0.49      (![A: $i] : (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[20])).
% 0.20/0.49  tff(22,axiom,(![A: $i] : (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) & complete_latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_knaster')).
% 0.20/0.49  tff(23,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.49  tff(24,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.49  tff(25,plain,(
% 0.20/0.49      ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)) & complete_latt_str(boole_lattice(A)))),
% 0.20/0.49      inference(skolemize,[status(sab)],[24])).
% 0.20/0.49  tff(26,plain,
% 0.20/0.49      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.49  tff(27,plain,
% 0.20/0.49      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[26, 16])).
% 0.20/0.49  tff(28,plain,
% 0.20/0.49      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(29,plain,
% 0.20/0.49      ((~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))))) <=> (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))),
% 0.20/0.49      inference(rewrite,[status(thm)],[])).
% 0.20/0.49  tff(30,plain,
% 0.20/0.49      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.49      inference(monotonicity,[status(thm)],[29])).
% 0.20/0.49  tff(31,plain,
% 0.20/0.49      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.49      inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.49  tff(32,plain,
% 0.20/0.49      ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28)))))),
% 0.20/0.49      inference(quant_inst,[status(thm)],[])).
% 0.20/0.49  tff(33,plain,
% 0.20/0.49      ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))) | (~complete_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))),
% 0.20/0.49      inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.49  tff(34,plain,
% 0.20/0.49      (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[33, 27])).
% 0.20/0.49  tff(35,plain,
% 0.20/0.49      ((empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))) | complete_latt_str(boole_lattice(A!28))),
% 0.20/0.49      inference(tautology,[status(thm)],[])).
% 0.20/0.49  tff(36,plain,
% 0.20/0.49      (complete_latt_str(boole_lattice(A!28))),
% 0.20/0.49      inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.49  tff(37,plain,
% 0.20/0.49      (^[A: $i] : refl((~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(38,plain,
% 0.20/0.49      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[37])).
% 0.20/0.49  tff(39,plain,
% 0.20/0.49      (^[A: $i] : rewrite(((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A))))))),
% 0.20/0.49      inference(bind,[status(th)],[])).
% 0.20/0.49  tff(40,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))),
% 0.20/0.49      inference(quant_intro,[status(thm)],[39])).
% 0.20/0.49  tff(41,plain,
% 0.20/0.49      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(42,plain,
% 0.20/0.50      (^[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(rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)))), (((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)))), (((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))))), ((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)))), ((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))))), (((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)))), (((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))))), ((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)))), ((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))))), (((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)))), (((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))))), ((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)))), ((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))))), (((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)))), (((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))))), ((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)))), ((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))))), (((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)))), (((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))))), ((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)))), ((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))))), (((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)))), (((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))))), ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)))), ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))))), (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> (((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))))), rewrite((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))), (((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(43,plain,
% 0.20/0.50      (![A: $i] : ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[42])).
% 0.20/0.50  tff(44,axiom,(![A: $i] : ((((((((((((((((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) & join_commutative(boole_lattice(A))) & join_associative(boole_lattice(A))) & meet_commutative(boole_lattice(A))) & meet_associative(boole_lattice(A))) & meet_absorbing(boole_lattice(A))) & join_absorbing(boole_lattice(A))) & lattice(boole_lattice(A))) & distributive_lattstr(boole_lattice(A))) & modular_lattstr(boole_lattice(A))) & lower_bounded_semilattstr(boole_lattice(A))) & upper_bounded_semilattstr(boole_lattice(A))) & bounded_lattstr(boole_lattice(A))) & complemented_lattstr(boole_lattice(A))) & boolean_lattstr(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_lattice3')).
% 0.20/0.50  tff(45,plain,
% 0.20/0.50      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[44, 43])).
% 0.20/0.50  tff(46,plain,
% 0.20/0.50      (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[45, 41])).
% 0.20/0.50  tff(47,plain,(
% 0.20/0.50      ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)) & join_commutative(boole_lattice(A)) & join_associative(boole_lattice(A)) & meet_commutative(boole_lattice(A)) & meet_associative(boole_lattice(A)) & meet_absorbing(boole_lattice(A)) & join_absorbing(boole_lattice(A)) & lattice(boole_lattice(A)) & distributive_lattstr(boole_lattice(A)) & modular_lattstr(boole_lattice(A)) & lower_bounded_semilattstr(boole_lattice(A)) & upper_bounded_semilattstr(boole_lattice(A)) & bounded_lattstr(boole_lattice(A)) & complemented_lattstr(boole_lattice(A)) & boolean_lattstr(boole_lattice(A)))),
% 0.20/0.50      inference(skolemize,[status(sab)],[46])).
% 0.20/0.50  tff(48,plain,
% 0.20/0.50      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[47, 40])).
% 0.20/0.50  tff(49,plain,
% 0.20/0.50      (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[48, 38])).
% 0.20/0.50  tff(50,plain,
% 0.20/0.50      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(51,plain,
% 0.20/0.50      ((~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))) <=> (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(52,plain,
% 0.20/0.50      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.50      inference(monotonicity,[status(thm)],[51])).
% 0.20/0.50  tff(53,plain,
% 0.20/0.50      (((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))))),
% 0.20/0.50      inference(transitivity,[status(thm)],[52, 50])).
% 0.20/0.50  tff(54,plain,
% 0.20/0.50      ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(55,plain,
% 0.20/0.50      ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))) | (~distributive_lattstr(boole_lattice(A))) | (~modular_lattstr(boole_lattice(A))) | (~lower_bounded_semilattstr(boole_lattice(A))) | (~upper_bounded_semilattstr(boole_lattice(A))) | (~bounded_lattstr(boole_lattice(A))) | (~complemented_lattstr(boole_lattice(A))) | (~boolean_lattstr(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.50  tff(56,plain,
% 0.20/0.50      (~(empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[55, 49])).
% 0.20/0.50  tff(57,plain,
% 0.20/0.50      ((empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))) | lattice(boole_lattice(A!28))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(58,plain,
% 0.20/0.50      (lattice(boole_lattice(A!28))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[57, 56])).
% 0.20/0.50  tff(59,plain,
% 0.20/0.50      (^[A: $i] : refl((~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(60,plain,
% 0.20/0.50      (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[59])).
% 0.20/0.50  tff(61,plain,
% 0.20/0.50      (^[A: $i] : rewrite((strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(62,plain,
% 0.20/0.50      (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[61])).
% 0.20/0.50  tff(63,plain,
% 0.20/0.50      (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(64,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 0.20/0.50  tff(65,plain,
% 0.20/0.50      (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[64, 63])).
% 0.20/0.50  tff(66,plain,(
% 0.20/0.50      ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.20/0.50      inference(skolemize,[status(sab)],[65])).
% 0.20/0.50  tff(67,plain,
% 0.20/0.50      (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.50  tff(68,plain,
% 0.20/0.50      (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[67, 60])).
% 0.20/0.50  tff(69,plain,
% 0.20/0.50      (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(70,plain,
% 0.20/0.50      ((~((~strict_latt_str(boole_lattice(A!28))) | (~latt_str(boole_lattice(A!28))))) <=> (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28)))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(71,plain,
% 0.20/0.50      (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!28))) | (~latt_str(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))))))),
% 0.20/0.50      inference(monotonicity,[status(thm)],[70])).
% 0.20/0.50  tff(72,plain,
% 0.20/0.50      (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!28))) | (~latt_str(boole_lattice(A!28)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))))))),
% 0.20/0.50      inference(transitivity,[status(thm)],[71, 69])).
% 0.20/0.50  tff(73,plain,
% 0.20/0.50      ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!28))) | (~latt_str(boole_lattice(A!28)))))),
% 0.20/0.50      inference(quant_inst,[status(thm)],[])).
% 0.20/0.50  tff(74,plain,
% 0.20/0.50      ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28)))))),
% 0.20/0.50      inference(modus_ponens,[status(thm)],[73, 72])).
% 0.20/0.50  tff(75,plain,
% 0.20/0.50      (~((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[74, 68])).
% 0.20/0.50  tff(76,plain,
% 0.20/0.50      (((~latt_str(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28)))) | latt_str(boole_lattice(A!28))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(77,plain,
% 0.20/0.50      (latt_str(boole_lattice(A!28))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[76, 75])).
% 0.20/0.50  tff(78,plain,
% 0.20/0.50      ((empty_carrier(boole_lattice(A!28)) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~strict_latt_str(boole_lattice(A!28))) | (~join_commutative(boole_lattice(A!28))) | (~join_associative(boole_lattice(A!28))) | (~meet_commutative(boole_lattice(A!28))) | (~meet_associative(boole_lattice(A!28))) | (~meet_absorbing(boole_lattice(A!28))) | (~join_absorbing(boole_lattice(A!28))) | (~distributive_lattstr(boole_lattice(A!28))) | (~modular_lattstr(boole_lattice(A!28))) | (~upper_bounded_semilattstr(boole_lattice(A!28))) | (~bounded_lattstr(boole_lattice(A!28))) | (~complemented_lattstr(boole_lattice(A!28))) | (~boolean_lattstr(boole_lattice(A!28)))) | (~empty_carrier(boole_lattice(A!28)))),
% 0.20/0.50      inference(tautology,[status(thm)],[])).
% 0.20/0.50  tff(79,plain,
% 0.20/0.50      (~empty_carrier(boole_lattice(A!28))),
% 0.20/0.50      inference(unit_resolution,[status(thm)],[78, 56])).
% 0.20/0.50  tff(80,plain,
% 0.20/0.50      (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(81,plain,
% 0.20/0.50      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[80])).
% 0.20/0.50  tff(82,plain,
% 0.20/0.50      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), rewrite(((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))), (((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))), (((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))))),
% 0.20/0.50      inference(bind,[status(th)],[])).
% 0.20/0.50  tff(83,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))),
% 0.20/0.50      inference(quant_intro,[status(thm)],[82])).
% 0.20/0.50  tff(84,plain,
% 0.20/0.50      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))),
% 0.20/0.50      inference(rewrite,[status(thm)],[])).
% 0.20/0.50  tff(85,plain,
% 0.20/0.50      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))), trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) <=> ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A))), (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A)))), ((((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))) <=> (((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))), rewrite((((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))) <=> ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))), ((((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))) <=> ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(86,plain,
% 0.20/0.51      (![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[85])).
% 0.20/0.51  tff(87,axiom,(![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => (((((~empty_carrier(A)) & lattice(A)) & lower_bounded_semilattstr(A)) & latt_str(A)) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t50_lattice3')).
% 0.20/0.51  tff(88,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.51  tff(89,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.51  tff(90,plain,(
% 0.20/0.51      ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ((~empty_carrier(A)) & lattice(A) & lower_bounded_semilattstr(A) & latt_str(A) & (bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))),
% 0.20/0.51      inference(skolemize,[status(sab)],[89])).
% 0.20/0.51  tff(91,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.51  tff(92,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[91, 81])).
% 0.20/0.51  tff(93,plain,
% 0.20/0.51      (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))) | (empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~(empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))) | empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~(empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(94,plain,
% 0.20/0.51      ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))) | (empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~(empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set))))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(95,plain,
% 0.20/0.51      ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~lower_bounded_semilattstr(A)) | (~(bottom_of_semilattstr(A) = join_of_latt_set(A, empty_set))))))) | empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | (~(empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[94, 93])).
% 0.20/0.51  tff(96,plain,
% 0.20/0.51      (~(empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[95, 92, 79, 77, 58, 36])).
% 0.20/0.51  tff(97,plain,
% 0.20/0.51      ((empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~lower_bounded_semilattstr(boole_lattice(A!28))) | (~(bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set)))) | (bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set))),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(98,plain,
% 0.20/0.51      (bottom_of_semilattstr(boole_lattice(A!28)) = join_of_latt_set(boole_lattice(A!28), empty_set)),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[97, 96])).
% 0.20/0.51  tff(99,plain,
% 0.20/0.51      (join_of_latt_set(boole_lattice(A!28), empty_set) = bottom_of_semilattstr(boole_lattice(A!28))),
% 0.20/0.51      inference(symmetry,[status(thm)],[98])).
% 0.20/0.51  tff(100,plain,
% 0.20/0.51      (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(101,plain,
% 0.20/0.51      (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[100])).
% 0.20/0.51  tff(102,plain,
% 0.20/0.51      (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(103,plain,
% 0.20/0.51      (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[102])).
% 0.20/0.51  tff(104,plain,
% 0.20/0.51      (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(105,plain,
% 0.20/0.51      (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(106,plain,
% 0.20/0.51      (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[105])).
% 0.20/0.51  tff(107,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.20/0.51  tff(108,plain,
% 0.20/0.51      (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[107, 106])).
% 0.20/0.51  tff(109,plain,
% 0.20/0.51      (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[108, 104])).
% 0.20/0.51  tff(110,plain,(
% 0.20/0.51      ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.51      inference(skolemize,[status(sab)],[109])).
% 0.20/0.51  tff(111,plain,
% 0.20/0.51      (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[110, 103])).
% 0.20/0.51  tff(112,plain,
% 0.20/0.51      (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[111, 101])).
% 0.20/0.51  tff(113,plain,
% 0.20/0.51      (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(114,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 0.20/0.51  tff(115,plain,
% 0.20/0.51      (?[A: $i] : empty(A)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[114, 113])).
% 0.20/0.51  tff(116,plain,(
% 0.20/0.51      empty(A!16)),
% 0.20/0.51      inference(skolemize,[status(sab)],[115])).
% 0.20/0.51  tff(117,plain,
% 0.20/0.51      (empty(empty_set) <=> empty(empty_set)),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(118,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.20/0.51  tff(119,plain,
% 0.20/0.51      (empty(empty_set)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[118, 117])).
% 0.20/0.51  tff(120,plain,
% 0.20/0.51      (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!16)) | (empty_set = A!16))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!16)) | (empty_set = A!16))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(121,plain,
% 0.20/0.51      ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!16)) | (empty_set = A!16))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(122,plain,
% 0.20/0.51      ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!16)) | (empty_set = A!16)),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.51  tff(123,plain,
% 0.20/0.51      (empty_set = A!16),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[122, 119, 116, 112])).
% 0.20/0.51  tff(124,plain,
% 0.20/0.51      (A!16 = empty_set),
% 0.20/0.51      inference(symmetry,[status(thm)],[123])).
% 0.20/0.51  tff(125,plain,
% 0.20/0.51      (join_of_latt_set(boole_lattice(A!28), A!16) = join_of_latt_set(boole_lattice(A!28), empty_set)),
% 0.20/0.51      inference(monotonicity,[status(thm)],[124])).
% 0.20/0.51  tff(126,plain,
% 0.20/0.51      (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(127,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[126])).
% 0.20/0.51  tff(128,plain,
% 0.20/0.51      (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(129,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[128])).
% 0.20/0.51  tff(130,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[129, 127])).
% 0.20/0.51  tff(131,plain,
% 0.20/0.51      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)))), ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))) <=> (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))), (![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))) <=> ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))), (((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A))) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))), (((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(132,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[131])).
% 0.20/0.51  tff(133,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(134,plain,
% 0.20/0.51      (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> (((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))))), rewrite((((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))), ((((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(135,plain,
% 0.20/0.51      (![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[134])).
% 0.20/0.51  tff(136,axiom,(![A: $i] : (((((~empty_carrier(A)) & lattice(A)) & complete_latt_str(A)) & latt_str(A)) => ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t29_yellow_0')).
% 0.20/0.51  tff(137,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[136, 135])).
% 0.20/0.51  tff(138,plain,
% 0.20/0.51      (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[137, 133])).
% 0.20/0.51  tff(139,plain,(
% 0.20/0.51      ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & complete_latt_str(A) & latt_str(A))) | ![B: $i] : ((join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B)) & (meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))),
% 0.20/0.51      inference(skolemize,[status(sab)],[138])).
% 0.20/0.51  tff(140,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[139, 132])).
% 0.20/0.51  tff(141,plain,
% 0.20/0.51      (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[140, 130])).
% 0.20/0.51  tff(142,plain,
% 0.20/0.51      (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))) | (empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))) | empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(143,plain,
% 0.20/0.51      ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))) | (empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(144,plain,
% 0.20/0.51      ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | (~complete_latt_str(A)) | ![B: $i] : (~((~(join_of_latt_set(A, B) = join_on_relstr(poset_of_lattice(A), B))) | (~(meet_of_latt_set(A, B) = meet_on_relstr(poset_of_lattice(A), B))))))) | empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[143, 142])).
% 0.20/0.51  tff(145,plain,
% 0.20/0.51      (empty_carrier(boole_lattice(A!28)) | (~latt_str(boole_lattice(A!28))) | (~lattice(boole_lattice(A!28))) | (~complete_latt_str(boole_lattice(A!28))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B)))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[144, 141])).
% 0.20/0.51  tff(146,plain,
% 0.20/0.51      (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B)))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[145, 77, 58, 36, 79])).
% 0.20/0.51  tff(147,plain,
% 0.20/0.51      ((~![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!28), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), B))) | (~(meet_of_latt_set(boole_lattice(A!28), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), B)))))) | (~((~(join_of_latt_set(boole_lattice(A!28), A!16) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16))) | (~(meet_of_latt_set(boole_lattice(A!28), A!16) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16)))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(148,plain,
% 0.20/0.51      (~((~(join_of_latt_set(boole_lattice(A!28), A!16) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16))) | (~(meet_of_latt_set(boole_lattice(A!28), A!16) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[147, 146])).
% 0.20/0.51  tff(149,plain,
% 0.20/0.51      (((~(join_of_latt_set(boole_lattice(A!28), A!16) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16))) | (~(meet_of_latt_set(boole_lattice(A!28), A!16) = meet_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16)))) | (join_of_latt_set(boole_lattice(A!28), A!16) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16))),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(150,plain,
% 0.20/0.51      (join_of_latt_set(boole_lattice(A!28), A!16) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16)),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[149, 148])).
% 0.20/0.51  tff(151,plain,
% 0.20/0.51      (join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16) = join_of_latt_set(boole_lattice(A!28), A!16)),
% 0.20/0.51      inference(symmetry,[status(thm)],[150])).
% 0.20/0.51  tff(152,plain,
% 0.20/0.51      (^[A: $i] : refl((boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> (boole_POSet(A) = poset_of_lattice(boole_lattice(A))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(153,plain,
% 0.20/0.51      (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[152])).
% 0.20/0.51  tff(154,plain,
% 0.20/0.51      (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(155,axiom,(![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_yellow_1')).
% 0.20/0.51  tff(156,plain,
% 0.20/0.51      (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[155, 154])).
% 0.20/0.51  tff(157,plain,(
% 0.20/0.51      ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.51      inference(skolemize,[status(sab)],[156])).
% 0.20/0.51  tff(158,plain,
% 0.20/0.51      (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[157, 153])).
% 0.20/0.51  tff(159,plain,
% 0.20/0.51      ((~![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))) | (boole_POSet(A!28) = poset_of_lattice(boole_lattice(A!28)))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(160,plain,
% 0.20/0.51      (boole_POSet(A!28) = poset_of_lattice(boole_lattice(A!28))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[159, 158])).
% 0.20/0.51  tff(161,plain,
% 0.20/0.51      (join_on_relstr(boole_POSet(A!28), empty_set) = join_on_relstr(poset_of_lattice(boole_lattice(A!28)), A!16)),
% 0.20/0.51      inference(monotonicity,[status(thm)],[160, 123])).
% 0.20/0.51  tff(162,plain,
% 0.20/0.51      (^[A: $i] : refl((~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(163,plain,
% 0.20/0.51      (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[162])).
% 0.20/0.51  tff(164,plain,
% 0.20/0.51      (^[A: $i] : rewrite((strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A))))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(165,plain,
% 0.20/0.51      (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[164])).
% 0.20/0.51  tff(166,plain,
% 0.20/0.51      (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A))) <=> ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(167,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')).
% 0.20/0.51  tff(168,plain,
% 0.20/0.51      (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.51  tff(169,plain,(
% 0.20/0.51      ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.51      inference(skolemize,[status(sab)],[168])).
% 0.20/0.51  tff(170,plain,
% 0.20/0.51      (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[169, 165])).
% 0.20/0.51  tff(171,plain,
% 0.20/0.51      (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[170, 163])).
% 0.20/0.51  tff(172,plain,
% 0.20/0.51      (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28))))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(173,plain,
% 0.20/0.51      ((~((~strict_rel_str(boole_POSet(A!28))) | (~rel_str(boole_POSet(A!28))))) <=> (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28)))))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(174,plain,
% 0.20/0.51      (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!28))) | (~rel_str(boole_POSet(A!28)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28))))))),
% 0.20/0.51      inference(monotonicity,[status(thm)],[173])).
% 0.20/0.51  tff(175,plain,
% 0.20/0.51      (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!28))) | (~rel_str(boole_POSet(A!28)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28))))))),
% 0.20/0.51      inference(transitivity,[status(thm)],[174, 172])).
% 0.20/0.51  tff(176,plain,
% 0.20/0.51      ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!28))) | (~rel_str(boole_POSet(A!28)))))),
% 0.20/0.51      inference(quant_inst,[status(thm)],[])).
% 0.20/0.51  tff(177,plain,
% 0.20/0.51      ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28)))))),
% 0.20/0.51      inference(modus_ponens,[status(thm)],[176, 175])).
% 0.20/0.51  tff(178,plain,
% 0.20/0.51      (~((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28))))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[177, 171])).
% 0.20/0.51  tff(179,plain,
% 0.20/0.51      (((~rel_str(boole_POSet(A!28))) | (~strict_rel_str(boole_POSet(A!28)))) | rel_str(boole_POSet(A!28))),
% 0.20/0.51      inference(tautology,[status(thm)],[])).
% 0.20/0.51  tff(180,plain,
% 0.20/0.51      (rel_str(boole_POSet(A!28))),
% 0.20/0.51      inference(unit_resolution,[status(thm)],[179, 178])).
% 0.20/0.51  tff(181,plain,
% 0.20/0.51      (^[A: $i] : refl(((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(182,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.51      inference(quant_intro,[status(thm)],[181])).
% 0.20/0.51  tff(183,plain,
% 0.20/0.51      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.51      inference(rewrite,[status(thm)],[])).
% 0.20/0.51  tff(184,plain,
% 0.20/0.51      (^[A: $i] : rewrite((rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set))))),
% 0.20/0.51      inference(bind,[status(th)],[])).
% 0.20/0.51  tff(185,plain,
% 0.20/0.51      (![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set))) <=> ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.52      inference(quant_intro,[status(thm)],[184])).
% 0.20/0.52  tff(186,axiom,(![A: $i] : (rel_str(A) => (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d11_yellow_0')).
% 0.20/0.52  tff(187,plain,
% 0.20/0.52      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.52  tff(188,plain,
% 0.20/0.52      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[187, 183])).
% 0.20/0.52  tff(189,plain,(
% 0.20/0.52      ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.52      inference(skolemize,[status(sab)],[188])).
% 0.20/0.52  tff(190,plain,
% 0.20/0.52      (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[189, 182])).
% 0.20/0.52  tff(191,plain,
% 0.20/0.52      (((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(boole_POSet(A!28))) | (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set)))) <=> ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(boole_POSet(A!28))) | (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set)))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(192,plain,
% 0.20/0.52      ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(boole_POSet(A!28))) | (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set)))),
% 0.20/0.52      inference(quant_inst,[status(thm)],[])).
% 0.20/0.52  tff(193,plain,
% 0.20/0.52      ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(boole_POSet(A!28))) | (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set))),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.52  tff(194,plain,
% 0.20/0.52      ((~rel_str(boole_POSet(A!28))) | (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set))),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[193, 190])).
% 0.20/0.52  tff(195,plain,
% 0.20/0.52      (bottom_of_relstr(boole_POSet(A!28)) = join_on_relstr(boole_POSet(A!28), empty_set)),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[194, 180])).
% 0.20/0.52  tff(196,plain,
% 0.20/0.52      (bottom_of_relstr(boole_POSet(A!28)) = empty_set),
% 0.20/0.52      inference(transitivity,[status(thm)],[195, 161, 151, 125, 99, 14])).
% 0.20/0.52  tff(197,plain,
% 0.20/0.52      ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) <=> (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 0.20/0.52      inference(rewrite,[status(thm)],[])).
% 0.20/0.52  tff(198,axiom,(~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_yellow_1')).
% 0.20/0.52  tff(199,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.52  tff(200,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[199, 197])).
% 0.20/0.52  tff(201,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[200, 197])).
% 0.20/0.52  tff(202,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[201, 197])).
% 0.20/0.52  tff(203,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[202, 197])).
% 0.20/0.52  tff(204,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[203, 197])).
% 0.20/0.52  tff(205,plain,
% 0.20/0.52      (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.52      inference(modus_ponens,[status(thm)],[204, 197])).
% 0.20/0.52  tff(206,plain,(
% 0.20/0.52      ~(bottom_of_relstr(boole_POSet(A!28)) = empty_set)),
% 0.20/0.52      inference(skolemize,[status(sab)],[205])).
% 0.20/0.52  tff(207,plain,
% 0.20/0.52      ($false),
% 0.20/0.52      inference(unit_resolution,[status(thm)],[206, 196])).
% 0.20/0.52  % SZS output end Proof
%------------------------------------------------------------------------------