%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU371+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:27:44 AM UTC 2025
% Result : Theorem 0.20s 0.46s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13 % Problem : SEU371+1 : TPTP v9.0.0. Released v3.3.0.
% 0.06/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 06:56:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.46 % SZS status Theorem
% 0.20/0.46 % SZS output start Proof
% 0.20/0.46 tff(empty_set_type, type, (
% 0.20/0.46 empty_set: $i)).
% 0.20/0.46 tff(bottom_of_relstr_type, type, (
% 0.20/0.46 bottom_of_relstr: $i > $i)).
% 0.20/0.46 tff(boole_POSet_type, type, (
% 0.20/0.46 boole_POSet: $i > $i)).
% 0.20/0.46 tff(tptp_fun_A_27_type, type, (
% 0.20/0.46 tptp_fun_A_27: $i)).
% 0.20/0.46 tff(bottom_of_semilattstr_type, type, (
% 0.20/0.46 bottom_of_semilattstr: $i > $i)).
% 0.20/0.46 tff(boole_lattice_type, type, (
% 0.20/0.46 boole_lattice: $i > $i)).
% 0.20/0.46 tff(lower_bounded_semilattstr_type, type, (
% 0.20/0.46 lower_bounded_semilattstr: $i > $o)).
% 0.20/0.46 tff(join_of_latt_set_type, type, (
% 0.20/0.46 join_of_latt_set: ( $i * $i ) > $i)).
% 0.20/0.46 tff(lattice_type, type, (
% 0.20/0.46 lattice: $i > $o)).
% 0.20/0.46 tff(latt_str_type, type, (
% 0.20/0.46 latt_str: $i > $o)).
% 0.20/0.46 tff(empty_carrier_type, type, (
% 0.20/0.46 empty_carrier: $i > $o)).
% 0.20/0.46 tff(boolean_lattstr_type, type, (
% 0.20/0.46 boolean_lattstr: $i > $o)).
% 0.20/0.46 tff(complemented_lattstr_type, type, (
% 0.20/0.46 complemented_lattstr: $i > $o)).
% 0.20/0.46 tff(bounded_lattstr_type, type, (
% 0.20/0.46 bounded_lattstr: $i > $o)).
% 0.20/0.46 tff(upper_bounded_semilattstr_type, type, (
% 0.20/0.46 upper_bounded_semilattstr: $i > $o)).
% 0.20/0.46 tff(modular_lattstr_type, type, (
% 0.20/0.46 modular_lattstr: $i > $o)).
% 0.20/0.46 tff(distributive_lattstr_type, type, (
% 0.20/0.46 distributive_lattstr: $i > $o)).
% 0.20/0.46 tff(join_absorbing_type, type, (
% 0.20/0.46 join_absorbing: $i > $o)).
% 0.20/0.46 tff(meet_absorbing_type, type, (
% 0.20/0.46 meet_absorbing: $i > $o)).
% 0.20/0.46 tff(meet_associative_type, type, (
% 0.20/0.46 meet_associative: $i > $o)).
% 0.20/0.46 tff(meet_commutative_type, type, (
% 0.20/0.46 meet_commutative: $i > $o)).
% 0.20/0.46 tff(join_associative_type, type, (
% 0.20/0.46 join_associative: $i > $o)).
% 0.20/0.46 tff(join_commutative_type, type, (
% 0.20/0.46 join_commutative: $i > $o)).
% 0.20/0.46 tff(strict_latt_str_type, type, (
% 0.20/0.46 strict_latt_str: $i > $o)).
% 0.20/0.46 tff(complete_latt_str_type, type, (
% 0.20/0.46 complete_latt_str: $i > $o)).
% 0.20/0.46 tff(tptp_fun_A_15_type, type, (
% 0.20/0.46 tptp_fun_A_15: $i)).
% 0.20/0.46 tff(empty_type, type, (
% 0.20/0.46 empty: $i > $o)).
% 0.20/0.46 tff(join_on_relstr_type, type, (
% 0.20/0.46 join_on_relstr: ( $i * $i ) > $i)).
% 0.20/0.46 tff(poset_of_lattice_type, type, (
% 0.20/0.46 poset_of_lattice: $i > $i)).
% 0.20/0.46 tff(meet_on_relstr_type, type, (
% 0.20/0.46 meet_on_relstr: ( $i * $i ) > $i)).
% 0.20/0.46 tff(meet_of_latt_set_type, type, (
% 0.20/0.46 meet_of_latt_set: ( $i * $i ) > $i)).
% 0.20/0.46 tff(rel_str_type, type, (
% 0.20/0.46 rel_str: $i > $o)).
% 0.20/0.46 tff(strict_rel_str_type, type, (
% 0.20/0.46 strict_rel_str: $i > $o)).
% 0.20/0.46 tff(1,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(2,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.46 tff(3,plain,
% 0.20/0.46 (^[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)))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(4,plain,
% 0.20/0.46 (![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))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[3])).
% 0.20/0.46 tff(5,plain,
% 0.20/0.46 (![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))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 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')).
% 0.20/0.46 tff(7,plain,
% 0.20/0.46 (![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.20/0.46 tff(8,plain,(
% 0.20/0.46 ![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 0.20/0.46 inference(skolemize,[status(sab)],[7])).
% 0.20/0.46 tff(9,plain,
% 0.20/0.46 (![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.20/0.46 tff(10,plain,
% 0.20/0.46 (![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))),
% 0.20/0.46 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.20/0.46 tff(11,plain,
% 0.20/0.46 ((~![A: $i] : (~((~lower_bounded_semilattstr(boole_lattice(A))) | (~(bottom_of_semilattstr(boole_lattice(A)) = empty_set))))) | (~((~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = empty_set))))),
% 0.20/0.46 inference(quant_inst,[status(thm)],[])).
% 0.20/0.46 tff(12,plain,
% 0.20/0.46 (~((~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = empty_set)))),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.20/0.46 tff(13,plain,
% 0.20/0.46 (((~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = empty_set))) | (bottom_of_semilattstr(boole_lattice(A!27)) = empty_set)),
% 0.20/0.46 inference(tautology,[status(thm)],[])).
% 0.20/0.46 tff(14,plain,
% 0.20/0.46 (bottom_of_semilattstr(boole_lattice(A!27)) = empty_set),
% 0.20/0.46 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.20/0.46 tff(15,plain,
% 0.20/0.46 (^[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))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(16,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[15])).
% 0.20/0.46 tff(17,plain,
% 0.20/0.46 (^[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))))))),
% 0.20/0.46 inference(bind,[status(th)],[])).
% 0.20/0.46 tff(18,plain,
% 0.20/0.46 (![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)))))),
% 0.20/0.46 inference(quant_intro,[status(thm)],[17])).
% 0.20/0.46 tff(19,plain,
% 0.20/0.46 (![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)))),
% 0.20/0.46 inference(rewrite,[status(thm)],[])).
% 0.20/0.46 tff(20,plain,
% 0.20/0.46 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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)))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[20])).
% 0.20/0.47 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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_lattice3')).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.20/0.47 tff(25,plain,(
% 0.20/0.47 ![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)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[26, 16])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (((~![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)))))) | (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 ((~(empty_carrier(boole_lattice(A!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))) <=> (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[29])).
% 0.20/0.47 tff(31,plain,
% 0.20/0.47 (((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[30, 28])).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 ((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 ((~![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)))))) | (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (~((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[33, 27])).
% 0.20/0.47 tff(35,plain,
% 0.20/0.47 (((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))) | (~empty_carrier(boole_lattice(A!27)))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (~empty_carrier(boole_lattice(A!27))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[35, 34])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[37])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[39])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(42,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.20/0.47 tff(44,plain,(
% 0.20/0.47 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.20/0.47 inference(skolemize,[status(sab)],[43])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[44, 40])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[45, 38])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 ((~((~strict_latt_str(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))))) <=> (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27)))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))))))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[48])).
% 0.20/0.47 tff(50,plain,
% 0.20/0.47 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))))))),
% 0.20/0.47 inference(transitivity,[status(thm)],[49, 47])).
% 0.20/0.47 tff(51,plain,
% 0.20/0.47 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27)))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(52,plain,
% 0.20/0.47 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27)))))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.20/0.47 tff(53,plain,
% 0.20/0.47 (~((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[52, 46])).
% 0.20/0.47 tff(54,plain,
% 0.20/0.47 (((~latt_str(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27)))) | latt_str(boole_lattice(A!27))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(55,plain,
% 0.20/0.47 (latt_str(boole_lattice(A!27))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.20/0.47 tff(56,plain,
% 0.20/0.47 (((~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))) | lattice(boole_lattice(A!27))),
% 0.20/0.47 inference(tautology,[status(thm)],[])).
% 0.20/0.47 tff(57,plain,
% 0.20/0.47 (lattice(boole_lattice(A!27))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[56, 34])).
% 0.20/0.47 tff(58,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(59,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.47 tff(60,plain,
% 0.20/0.47 (^[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))))))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(61,plain,
% 0.20/0.47 (![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)))))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[60])).
% 0.20/0.47 tff(62,plain,
% 0.20/0.47 (![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)))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(63,plain,
% 0.20/0.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(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)))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[63])).
% 0.20/0.48 tff(65,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')).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 (![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)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[66, 62])).
% 0.20/0.48 tff(68,plain,(
% 0.20/0.48 ![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)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[67])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[68, 61])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (![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)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[69, 59])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (((~![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)))))) | (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 ((~(empty_carrier(boole_lattice(A!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))))) <=> (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(73,plain,
% 0.20/0.48 (((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[72])).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27)))))) <=> ((~![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)))))) | (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[73, 71])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 ((~![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!27)) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 ((~![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)))))) | (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[75, 74])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (~((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 (((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~strict_latt_str(boole_lattice(A!27))) | (~join_commutative(boole_lattice(A!27))) | (~join_associative(boole_lattice(A!27))) | (~meet_commutative(boole_lattice(A!27))) | (~meet_associative(boole_lattice(A!27))) | (~meet_absorbing(boole_lattice(A!27))) | (~join_absorbing(boole_lattice(A!27))) | (~distributive_lattstr(boole_lattice(A!27))) | (~modular_lattstr(boole_lattice(A!27))) | (~upper_bounded_semilattstr(boole_lattice(A!27))) | (~bounded_lattstr(boole_lattice(A!27))) | (~complemented_lattstr(boole_lattice(A!27))) | (~boolean_lattstr(boole_lattice(A!27)))) | complete_latt_str(boole_lattice(A!27))),
% 0.20/0.48 inference(tautology,[status(thm)],[])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 (complete_latt_str(boole_lattice(A!27))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (^[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)))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (^[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))))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![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))))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (![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))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(86,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[85])).
% 0.20/0.49 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')).
% 0.20/0.49 tff(88,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[87, 86])).
% 0.20/0.49 tff(89,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[88, 84])).
% 0.20/0.49 tff(90,plain,(
% 0.20/0.49 ![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))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[89])).
% 0.20/0.49 tff(91,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.49 tff(92,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[91, 81])).
% 0.20/0.49 tff(93,plain,
% 0.20/0.49 (((~![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))))))) | ((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), 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))))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(94,plain,
% 0.20/0.49 ((empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set)))))) <=> ((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(95,plain,
% 0.20/0.49 (((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), 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))))))) | ((~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set)))))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[94])).
% 0.20/0.49 tff(96,plain,
% 0.20/0.49 (((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), 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))))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[95, 93])).
% 0.20/0.49 tff(97,plain,
% 0.20/0.49 ((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(98,plain,
% 0.20/0.49 ((~![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))))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)) | (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[97, 96])).
% 0.20/0.49 tff(99,plain,
% 0.20/0.49 (~(empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[98, 92, 79, 57, 55, 36])).
% 0.20/0.49 tff(100,plain,
% 0.20/0.49 ((empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~lower_bounded_semilattstr(boole_lattice(A!27))) | (~(bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set)))) | (bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(101,plain,
% 0.20/0.49 (bottom_of_semilattstr(boole_lattice(A!27)) = join_of_latt_set(boole_lattice(A!27), empty_set)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.49 tff(102,plain,
% 0.20/0.49 (join_of_latt_set(boole_lattice(A!27), empty_set) = bottom_of_semilattstr(boole_lattice(A!27))),
% 0.20/0.49 inference(symmetry,[status(thm)],[101])).
% 0.20/0.49 tff(103,plain,
% 0.20/0.49 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(104,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[103])).
% 0.20/0.49 tff(105,plain,
% 0.20/0.49 (^[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))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(106,plain,
% 0.20/0.49 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[105])).
% 0.20/0.49 tff(107,plain,
% 0.20/0.49 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(108,plain,
% 0.20/0.49 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(109,plain,
% 0.20/0.49 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[108])).
% 0.20/0.49 tff(110,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 0.20/0.49 tff(111,plain,
% 0.20/0.49 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[110, 109])).
% 0.20/0.49 tff(112,plain,
% 0.20/0.49 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[111, 107])).
% 0.20/0.49 tff(113,plain,(
% 0.20/0.49 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[112])).
% 0.20/0.49 tff(114,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[113, 106])).
% 0.20/0.49 tff(115,plain,
% 0.20/0.49 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[114, 104])).
% 0.20/0.49 tff(116,plain,
% 0.20/0.49 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(117,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 0.20/0.49 tff(118,plain,
% 0.20/0.49 (?[A: $i] : empty(A)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.20/0.49 tff(119,plain,(
% 0.20/0.49 empty(A!15)),
% 0.20/0.49 inference(skolemize,[status(sab)],[118])).
% 0.20/0.49 tff(120,plain,
% 0.20/0.49 (empty(empty_set) <=> empty(empty_set)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(121,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 0.20/0.49 tff(122,plain,
% 0.20/0.49 (empty(empty_set)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.49 tff(123,plain,
% 0.20/0.49 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!15)) | (empty_set = A!15))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!15)) | (empty_set = A!15))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(124,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!15)) | (empty_set = A!15))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(125,plain,
% 0.20/0.49 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!15)) | (empty_set = A!15)),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.20/0.49 tff(126,plain,
% 0.20/0.49 (empty_set = A!15),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[125, 122, 119, 115])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 (A!15 = empty_set),
% 0.20/0.49 inference(symmetry,[status(thm)],[126])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 (join_of_latt_set(boole_lattice(A!27), A!15) = join_of_latt_set(boole_lattice(A!27), empty_set)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[129])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (^[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)))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[131])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[132, 130])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (^[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))))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[134])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[137])).
% 0.20/0.49 tff(139,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')).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.49 tff(141,plain,
% 0.20/0.49 (![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))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.20/0.49 tff(142,plain,(
% 0.20/0.49 ![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))))),
% 0.20/0.49 inference(skolemize,[status(sab)],[141])).
% 0.20/0.49 tff(143,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.20/0.49 tff(144,plain,
% 0.20/0.49 (![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))))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.20/0.49 tff(145,plain,
% 0.20/0.49 (((~![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))))))) | (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)))) <=> ((~![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))))))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(146,plain,
% 0.20/0.49 ((empty_carrier(boole_lattice(A!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B)))))) <=> (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(147,plain,
% 0.20/0.49 (((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), 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))))))) | (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[146])).
% 0.20/0.49 tff(148,plain,
% 0.20/0.49 (((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), 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))))))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[147, 145])).
% 0.20/0.49 tff(149,plain,
% 0.20/0.49 ((~![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!27)) | (~latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~complete_latt_str(boole_lattice(A!27))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(150,plain,
% 0.20/0.49 ((~![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))))))) | ![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.20/0.49 tff(151,plain,
% 0.20/0.49 (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))))) | (~complete_latt_str(boole_lattice(A!27))) | (~lattice(boole_lattice(A!27))) | (~latt_str(boole_lattice(A!27))) | empty_carrier(boole_lattice(A!27))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[150, 144])).
% 0.20/0.49 tff(152,plain,
% 0.20/0.49 (![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B)))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[151, 79, 57, 55, 36])).
% 0.20/0.49 tff(153,plain,
% 0.20/0.49 ((~![B: $i] : (~((~(join_of_latt_set(boole_lattice(A!27), B) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), B))) | (~(meet_of_latt_set(boole_lattice(A!27), B) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), B)))))) | (~((~(join_of_latt_set(boole_lattice(A!27), A!15) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15))) | (~(meet_of_latt_set(boole_lattice(A!27), A!15) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15)))))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(154,plain,
% 0.20/0.49 (~((~(join_of_latt_set(boole_lattice(A!27), A!15) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15))) | (~(meet_of_latt_set(boole_lattice(A!27), A!15) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15))))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.20/0.49 tff(155,plain,
% 0.20/0.49 (((~(join_of_latt_set(boole_lattice(A!27), A!15) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15))) | (~(meet_of_latt_set(boole_lattice(A!27), A!15) = meet_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15)))) | (join_of_latt_set(boole_lattice(A!27), A!15) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15))),
% 0.20/0.49 inference(tautology,[status(thm)],[])).
% 0.20/0.49 tff(156,plain,
% 0.20/0.49 (join_of_latt_set(boole_lattice(A!27), A!15) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15)),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[155, 154])).
% 0.20/0.49 tff(157,plain,
% 0.20/0.49 (join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15) = join_of_latt_set(boole_lattice(A!27), A!15)),
% 0.20/0.49 inference(symmetry,[status(thm)],[156])).
% 0.20/0.49 tff(158,plain,
% 0.20/0.49 (^[A: $i] : refl((boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> (boole_POSet(A) = poset_of_lattice(boole_lattice(A))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(159,plain,
% 0.20/0.49 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[158])).
% 0.20/0.49 tff(160,plain,
% 0.20/0.49 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(161,axiom,(![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_yellow_1')).
% 0.20/0.49 tff(162,plain,
% 0.20/0.49 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.20/0.49 tff(163,plain,(
% 0.20/0.49 ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[162])).
% 0.20/0.49 tff(164,plain,
% 0.20/0.49 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.20/0.49 tff(165,plain,
% 0.20/0.49 ((~![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))) | (boole_POSet(A!27) = poset_of_lattice(boole_lattice(A!27)))),
% 0.20/0.49 inference(quant_inst,[status(thm)],[])).
% 0.20/0.49 tff(166,plain,
% 0.20/0.49 (boole_POSet(A!27) = poset_of_lattice(boole_lattice(A!27))),
% 0.20/0.49 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.20/0.49 tff(167,plain,
% 0.20/0.49 (join_on_relstr(boole_POSet(A!27), empty_set) = join_on_relstr(poset_of_lattice(boole_lattice(A!27)), A!15)),
% 0.20/0.49 inference(monotonicity,[status(thm)],[166, 126])).
% 0.20/0.49 tff(168,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(169,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[168])).
% 0.20/0.49 tff(170,plain,
% 0.20/0.49 (^[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))))))),
% 0.20/0.49 inference(bind,[status(th)],[])).
% 0.20/0.49 tff(171,plain,
% 0.20/0.49 (![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)))))),
% 0.20/0.49 inference(quant_intro,[status(thm)],[170])).
% 0.20/0.49 tff(172,plain,
% 0.20/0.49 (![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)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(173,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')).
% 0.20/0.49 tff(174,plain,
% 0.20/0.49 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.20/0.49 tff(175,plain,(
% 0.20/0.49 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 0.20/0.49 inference(skolemize,[status(sab)],[174])).
% 0.20/0.49 tff(176,plain,
% 0.20/0.49 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.20/0.49 tff(177,plain,
% 0.20/0.49 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 0.20/0.49 inference(modus_ponens,[status(thm)],[176, 169])).
% 0.20/0.49 tff(178,plain,
% 0.20/0.49 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 ((~((~strict_rel_str(boole_POSet(A!27))) | (~rel_str(boole_POSet(A!27))))) <=> (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27)))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!27))) | (~rel_str(boole_POSet(A!27)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27))))))),
% 0.20/0.50 inference(monotonicity,[status(thm)],[179])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!27))) | (~rel_str(boole_POSet(A!27)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27))))))),
% 0.20/0.50 inference(transitivity,[status(thm)],[180, 178])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!27))) | (~rel_str(boole_POSet(A!27)))))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 (~((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27))))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[183, 177])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 (((~rel_str(boole_POSet(A!27))) | (~strict_rel_str(boole_POSet(A!27)))) | rel_str(boole_POSet(A!27))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (rel_str(boole_POSet(A!27))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[185, 184])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[187])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 (^[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))))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 (![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)))),
% 0.20/0.50 inference(quant_intro,[status(thm)],[190])).
% 0.20/0.50 tff(192,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')).
% 0.20/0.50 tff(193,plain,
% 0.20/0.50 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[192, 191])).
% 0.20/0.50 tff(194,plain,
% 0.20/0.50 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[193, 189])).
% 0.20/0.50 tff(195,plain,(
% 0.20/0.50 ![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.50 inference(skolemize,[status(sab)],[194])).
% 0.20/0.50 tff(196,plain,
% 0.20/0.50 (![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[195, 188])).
% 0.20/0.50 tff(197,plain,
% 0.20/0.50 (((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(boole_POSet(A!27))) | (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set)))) <=> ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(boole_POSet(A!27))) | (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set)))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(198,plain,
% 0.20/0.50 ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | ((~rel_str(boole_POSet(A!27))) | (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set)))),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(199,plain,
% 0.20/0.50 ((~![A: $i] : ((~rel_str(A)) | (bottom_of_relstr(A) = join_on_relstr(A, empty_set)))) | (~rel_str(boole_POSet(A!27))) | (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[198, 197])).
% 0.20/0.50 tff(200,plain,
% 0.20/0.50 ((~rel_str(boole_POSet(A!27))) | (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[199, 196])).
% 0.20/0.50 tff(201,plain,
% 0.20/0.50 (bottom_of_relstr(boole_POSet(A!27)) = join_on_relstr(boole_POSet(A!27), empty_set)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[200, 186])).
% 0.20/0.50 tff(202,plain,
% 0.20/0.50 (bottom_of_relstr(boole_POSet(A!27)) = empty_set),
% 0.20/0.50 inference(transitivity,[status(thm)],[201, 167, 157, 128, 102, 14])).
% 0.20/0.50 tff(203,plain,
% 0.20/0.50 ((~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)) <=> (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(204,axiom,(~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_yellow_1')).
% 0.20/0.50 tff(205,plain,
% 0.20/0.50 (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.20/0.50 tff(206,plain,
% 0.20/0.50 (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[205, 203])).
% 0.20/0.50 tff(207,plain,
% 0.20/0.50 (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[206, 203])).
% 0.20/0.50 tff(208,plain,
% 0.20/0.50 (~![A: $i] : (bottom_of_relstr(boole_POSet(A)) = empty_set)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.20/0.50 tff(209,plain,(
% 0.20/0.50 ~(bottom_of_relstr(boole_POSet(A!27)) = empty_set)),
% 0.20/0.50 inference(skolemize,[status(sab)],[208])).
% 0.20/0.50 tff(210,plain,
% 0.20/0.50 ($false),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[209, 202])).
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 % E exiting
%------------------------------------------------------------------------------