%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU369+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:27:43 AM UTC 2025
% Result : Theorem 75.82s 75.99s
% Output : Proof 75.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU369+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.11/0.34 % Computer : n013.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Fri Jun 20 06:55:23 EDT 2025
% 0.11/0.34 % CPUTime :
% 75.82/75.99 % SZS status Theorem
% 75.82/75.99 % SZS output start Proof
% 75.82/75.99 tff(below_refl_type, type, (
% 75.82/75.99 below_refl: ( $i * $i * $i ) > $o)).
% 75.82/75.99 tff(tptp_fun_C_30_type, type, (
% 75.82/75.99 tptp_fun_C_30: $i)).
% 75.82/75.99 tff(tptp_fun_B_28_type, type, (
% 75.82/75.99 tptp_fun_B_28: $i)).
% 75.82/75.99 tff(latt_str_of_type, type, (
% 75.82/75.99 latt_str_of: ( $i * $i * $i ) > $i)).
% 75.82/75.99 tff(the_L_meet_type, type, (
% 75.82/75.99 the_L_meet: $i > $i)).
% 75.82/75.99 tff(boole_lattice_type, type, (
% 75.82/75.99 boole_lattice: $i > $i)).
% 75.82/75.99 tff(tptp_fun_A_29_type, type, (
% 75.82/75.99 tptp_fun_A_29: $i)).
% 75.82/75.99 tff(the_L_join_type, type, (
% 75.82/75.99 the_L_join: $i > $i)).
% 75.82/75.99 tff(the_carrier_type, type, (
% 75.82/75.99 the_carrier: $i > $i)).
% 75.82/75.99 tff(strict_latt_str_type, type, (
% 75.82/75.99 strict_latt_str: $i > $o)).
% 75.82/75.99 tff(boolean_lattstr_type, type, (
% 75.82/75.99 boolean_lattstr: $i > $o)).
% 75.82/75.99 tff(complemented_lattstr_type, type, (
% 75.82/75.99 complemented_lattstr: $i > $o)).
% 75.82/75.99 tff(bounded_lattstr_type, type, (
% 75.82/75.99 bounded_lattstr: $i > $o)).
% 75.82/75.99 tff(upper_bounded_semilattstr_type, type, (
% 75.82/75.99 upper_bounded_semilattstr: $i > $o)).
% 75.82/75.99 tff(lower_bounded_semilattstr_type, type, (
% 75.82/75.99 lower_bounded_semilattstr: $i > $o)).
% 75.82/75.99 tff(modular_lattstr_type, type, (
% 75.82/75.99 modular_lattstr: $i > $o)).
% 75.82/75.99 tff(distributive_lattstr_type, type, (
% 75.82/75.99 distributive_lattstr: $i > $o)).
% 75.82/75.99 tff(join_absorbing_type, type, (
% 75.82/75.99 join_absorbing: $i > $o)).
% 75.82/75.99 tff(meet_absorbing_type, type, (
% 75.82/75.99 meet_absorbing: $i > $o)).
% 75.82/75.99 tff(meet_associative_type, type, (
% 75.82/75.99 meet_associative: $i > $o)).
% 75.82/75.99 tff(meet_commutative_type, type, (
% 75.82/75.99 meet_commutative: $i > $o)).
% 75.82/75.99 tff(join_associative_type, type, (
% 75.82/75.99 join_associative: $i > $o)).
% 75.82/75.99 tff(join_commutative_type, type, (
% 75.82/75.99 join_commutative: $i > $o)).
% 75.82/75.99 tff(empty_carrier_type, type, (
% 75.82/75.99 empty_carrier: $i > $o)).
% 75.82/75.99 tff(lattice_type, type, (
% 75.82/75.99 lattice: $i > $o)).
% 75.82/75.99 tff(latt_str_type, type, (
% 75.82/75.99 latt_str: $i > $o)).
% 75.82/75.99 tff(related_reflexive_type, type, (
% 75.82/75.99 related_reflexive: ( $i * $i * $i ) > $o)).
% 75.82/75.99 tff(cast_to_el_of_LattPOSet_type, type, (
% 75.82/75.99 cast_to_el_of_LattPOSet: ( $i * $i ) > $i)).
% 75.82/75.99 tff(poset_of_lattice_type, type, (
% 75.82/75.99 poset_of_lattice: $i > $i)).
% 75.82/75.99 tff(boole_POSet_type, type, (
% 75.82/75.99 boole_POSet: $i > $i)).
% 75.82/75.99 tff(element_type, type, (
% 75.82/75.99 element: ( $i * $i ) > $o)).
% 75.82/75.99 tff(k2_lattice3_type, type, (
% 75.82/75.99 k2_lattice3: $i > $i)).
% 75.82/75.99 tff(the_InternalRel_type, type, (
% 75.82/75.99 the_InternalRel: $i > $i)).
% 75.82/75.99 tff(rel_str_of_type, type, (
% 75.82/75.99 rel_str_of: ( $i * $i ) > $i)).
% 75.82/75.99 tff(strict_rel_str_type, type, (
% 75.82/75.99 strict_rel_str: $i > $o)).
% 75.82/75.99 tff(complete_relstr_type, type, (
% 75.82/75.99 complete_relstr: $i > $o)).
% 75.82/75.99 tff(with_infima_relstr_type, type, (
% 75.82/75.99 with_infima_relstr: $i > $o)).
% 75.82/75.99 tff(with_suprema_relstr_type, type, (
% 75.82/75.99 with_suprema_relstr: $i > $o)).
% 75.82/75.99 tff(bounded_relstr_type, type, (
% 75.82/75.99 bounded_relstr: $i > $o)).
% 75.82/75.99 tff(upper_bounded_relstr_type, type, (
% 75.82/75.99 upper_bounded_relstr: $i > $o)).
% 75.82/75.99 tff(lower_bounded_relstr_type, type, (
% 75.82/75.99 lower_bounded_relstr: $i > $o)).
% 75.82/75.99 tff(antisymmetric_relstr_type, type, (
% 75.82/75.99 antisymmetric_relstr: $i > $o)).
% 75.82/75.99 tff(transitive_relstr_type, type, (
% 75.82/75.99 transitive_relstr: $i > $o)).
% 75.82/75.99 tff(reflexive_relstr_type, type, (
% 75.82/75.99 reflexive_relstr: $i > $o)).
% 75.82/75.99 tff(rel_str_type, type, (
% 75.82/75.99 rel_str: $i > $o)).
% 75.82/75.99 tff(relation_of2_type, type, (
% 75.82/75.99 relation_of2: ( $i * $i * $i ) > $o)).
% 75.82/75.99 tff(relation_of2_as_subset_type, type, (
% 75.82/75.99 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 75.82/75.99 tff(subset_type, type, (
% 75.82/75.99 subset: ( $i * $i ) > $o)).
% 75.82/75.99 tff(below_type, type, (
% 75.82/75.99 below: ( $i * $i * $i ) > $o)).
% 75.82/75.99 tff(1,plain,
% 75.82/75.99 (^[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))))))),
% 75.82/75.99 inference(bind,[status(th)],[])).
% 75.82/75.99 tff(2,plain,
% 75.82/75.99 (![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)))))),
% 75.82/75.99 inference(quant_intro,[status(thm)],[1])).
% 75.82/75.99 tff(3,plain,
% 75.82/75.99 (^[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))))))),
% 75.82/75.99 inference(bind,[status(th)],[])).
% 75.82/75.99 tff(4,plain,
% 75.82/75.99 (![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)))))),
% 75.82/75.99 inference(quant_intro,[status(thm)],[3])).
% 75.82/75.99 tff(5,plain,
% 75.82/75.99 (![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)))),
% 75.82/75.99 inference(rewrite,[status(thm)],[])).
% 75.82/75.99 tff(6,plain,
% 75.82/75.99 (^[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)))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(7,plain,
% 75.82/76.00 (![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)))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[6])).
% 75.82/76.00 tff(8,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')).
% 75.82/76.00 tff(9,plain,
% 75.82/76.00 (![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)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[8, 7])).
% 75.82/76.00 tff(10,plain,
% 75.82/76.00 (![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)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[9, 5])).
% 75.82/76.00 tff(11,plain,(
% 75.82/76.00 ![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)))),
% 75.82/76.00 inference(skolemize,[status(sab)],[10])).
% 75.82/76.00 tff(12,plain,
% 75.82/76.00 (![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)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[11, 4])).
% 75.82/76.00 tff(13,plain,
% 75.82/76.00 (![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)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[12, 2])).
% 75.82/76.00 tff(14,plain,
% 75.82/76.00 (((~![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!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))) <=> ((~![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!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29))))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(15,plain,
% 75.82/76.00 ((~(empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29))))) <=> (~((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(16,plain,
% 75.82/76.00 (((~![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!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))) <=> ((~![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!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29))))))),
% 75.82/76.00 inference(monotonicity,[status(thm)],[15])).
% 75.82/76.00 tff(17,plain,
% 75.82/76.00 (((~![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!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))) <=> ((~![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!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29))))))),
% 75.82/76.00 inference(transitivity,[status(thm)],[16, 14])).
% 75.82/76.00 tff(18,plain,
% 75.82/76.00 ((~![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!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))),
% 75.82/76.00 inference(quant_inst,[status(thm)],[])).
% 75.82/76.00 tff(19,plain,
% 75.82/76.00 ((~![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!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[18, 17])).
% 75.82/76.00 tff(20,plain,
% 75.82/76.00 (~((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29))))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[19, 13])).
% 75.82/76.00 tff(21,plain,
% 75.82/76.00 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | strict_latt_str(boole_lattice(A!29))),
% 75.82/76.00 inference(tautology,[status(thm)],[])).
% 75.82/76.00 tff(22,plain,
% 75.82/76.00 (strict_latt_str(boole_lattice(A!29))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[21, 20])).
% 75.82/76.00 tff(23,plain,
% 75.82/76.00 (^[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))))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(24,plain,
% 75.82/76.00 (![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)))))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[23])).
% 75.82/76.00 tff(25,plain,
% 75.82/76.00 (^[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))))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(26,plain,
% 75.82/76.00 (![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)))))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[25])).
% 75.82/76.00 tff(27,plain,
% 75.82/76.00 (![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)))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(28,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 75.82/76.00 tff(29,plain,
% 75.82/76.00 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[28, 27])).
% 75.82/76.00 tff(30,plain,(
% 75.82/76.00 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 75.82/76.00 inference(skolemize,[status(sab)],[29])).
% 75.82/76.00 tff(31,plain,
% 75.82/76.00 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[30, 26])).
% 75.82/76.00 tff(32,plain,
% 75.82/76.00 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[31, 24])).
% 75.82/76.00 tff(33,plain,
% 75.82/76.00 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(34,plain,
% 75.82/76.00 ((~((~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))))) <=> (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(35,plain,
% 75.82/76.00 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))))))),
% 75.82/76.00 inference(monotonicity,[status(thm)],[34])).
% 75.82/76.00 tff(36,plain,
% 75.82/76.00 (((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29)))))) <=> ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))))))),
% 75.82/76.00 inference(transitivity,[status(thm)],[35, 33])).
% 75.82/76.00 tff(37,plain,
% 75.82/76.00 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29)))))),
% 75.82/76.00 inference(quant_inst,[status(thm)],[])).
% 75.82/76.00 tff(38,plain,
% 75.82/76.00 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29)))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[37, 36])).
% 75.82/76.00 tff(39,plain,
% 75.82/76.00 (~((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[38, 32])).
% 75.82/76.00 tff(40,plain,
% 75.82/76.00 (((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29)))) | latt_str(boole_lattice(A!29))),
% 75.82/76.00 inference(tautology,[status(thm)],[])).
% 75.82/76.00 tff(41,plain,
% 75.82/76.00 (latt_str(boole_lattice(A!29))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[40, 39])).
% 75.82/76.00 tff(42,plain,
% 75.82/76.00 (^[A: $i] : refl(((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(43,plain,
% 75.82/76.00 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[42])).
% 75.82/76.00 tff(44,plain,
% 75.82/76.00 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(45,plain,
% 75.82/76.00 (^[A: $i] : trans(monotonicity(rewrite((strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A)))) <=> ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))), ((latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> (latt_str(A) => ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))))), rewrite((latt_str(A) => ((~strict_latt_str(A)) | (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))), ((latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(46,plain,
% 75.82/76.00 (![A: $i] : (latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))))) <=> ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[45])).
% 75.82/76.00 tff(47,axiom,(![A: $i] : (latt_str(A) => (strict_latt_str(A) => (A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 75.82/76.00 tff(48,plain,
% 75.82/76.00 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[47, 46])).
% 75.82/76.00 tff(49,plain,
% 75.82/76.00 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[48, 44])).
% 75.82/76.00 tff(50,plain,(
% 75.82/76.00 ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(skolemize,[status(sab)],[49])).
% 75.82/76.00 tff(51,plain,
% 75.82/76.00 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[50, 43])).
% 75.82/76.00 tff(52,plain,
% 75.82/76.00 (((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(53,plain,
% 75.82/76.00 (((boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29)))) <=> ((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(54,plain,
% 75.82/76.00 (((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))))),
% 75.82/76.00 inference(monotonicity,[status(thm)],[53])).
% 75.82/76.00 tff(55,plain,
% 75.82/76.00 (((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.00 inference(transitivity,[status(thm)],[54, 52])).
% 75.82/76.00 tff(56,plain,
% 75.82/76.00 ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~strict_latt_str(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))))),
% 75.82/76.00 inference(quant_inst,[status(thm)],[])).
% 75.82/76.00 tff(57,plain,
% 75.82/76.00 ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~latt_str(boole_lattice(A!29))) | (~strict_latt_str(boole_lattice(A!29))) | (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[56, 55])).
% 75.82/76.00 tff(58,plain,
% 75.82/76.00 (boole_lattice(A!29) = latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[57, 51, 41, 22])).
% 75.82/76.00 tff(59,plain,
% 75.82/76.00 (latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))) = boole_lattice(A!29)),
% 75.82/76.00 inference(symmetry,[status(thm)],[58])).
% 75.82/76.00 tff(60,plain,
% 75.82/76.00 (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below_refl(boole_lattice(A!29), B!28, C!30)),
% 75.82/76.00 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.00 tff(61,plain,
% 75.82/76.00 (below_refl(boole_lattice(A!29), B!28, C!30) <=> below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.00 inference(symmetry,[status(thm)],[60])).
% 75.82/76.00 tff(62,plain,
% 75.82/76.00 ((~below_refl(boole_lattice(A!29), B!28, C!30)) <=> (~below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.82/76.00 inference(monotonicity,[status(thm)],[61])).
% 75.82/76.00 tff(63,plain,
% 75.82/76.00 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | (~empty_carrier(boole_lattice(A!29)))),
% 75.82/76.00 inference(tautology,[status(thm)],[])).
% 75.82/76.00 tff(64,plain,
% 75.82/76.00 (~empty_carrier(boole_lattice(A!29))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[63, 20])).
% 75.82/76.00 tff(65,plain,
% 75.82/76.00 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | lattice(boole_lattice(A!29))),
% 75.82/76.00 inference(tautology,[status(thm)],[])).
% 75.82/76.00 tff(66,plain,
% 75.82/76.00 (lattice(boole_lattice(A!29))),
% 75.82/76.00 inference(unit_resolution,[status(thm)],[65, 20])).
% 75.82/76.00 tff(67,plain,
% 75.82/76.00 (^[A: $i] : refl((empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))) <=> (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(68,plain,
% 75.82/76.00 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[67])).
% 75.82/76.00 tff(69,plain,
% 75.82/76.00 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(70,plain,
% 75.82/76.00 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[69])).
% 75.82/76.00 tff(71,plain,
% 75.82/76.00 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(72,plain,
% 75.82/76.00 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))))),
% 75.82/76.00 inference(bind,[status(th)],[])).
% 75.82/76.00 tff(73,plain,
% 75.82/76.00 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 75.82/76.00 inference(quant_intro,[status(thm)],[72])).
% 75.82/76.00 tff(74,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice3')).
% 75.82/76.00 tff(75,plain,
% 75.82/76.00 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[74, 73])).
% 75.82/76.00 tff(76,plain,
% 75.82/76.00 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[75, 71])).
% 75.82/76.00 tff(77,plain,(
% 75.82/76.00 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))))),
% 75.82/76.00 inference(skolemize,[status(sab)],[76])).
% 75.82/76.00 tff(78,plain,
% 75.82/76.00 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[77, 70])).
% 75.82/76.00 tff(79,plain,
% 75.82/76.00 (![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))),
% 75.82/76.00 inference(modus_ponens,[status(thm)],[78, 68])).
% 75.82/76.00 tff(80,plain,
% 75.82/76.00 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | ((~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(81,plain,
% 75.82/76.00 ((empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29)))) <=> ((~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))))),
% 75.82/76.00 inference(rewrite,[status(thm)],[])).
% 75.82/76.00 tff(82,plain,
% 75.82/76.00 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | ((~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))))),
% 75.82/76.00 inference(monotonicity,[status(thm)],[81])).
% 75.82/76.00 tff(83,plain,
% 75.82/76.00 (((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))))) <=> ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))))),
% 75.82/76.01 inference(transitivity,[status(thm)],[82, 80])).
% 75.82/76.01 tff(84,plain,
% 75.82/76.01 ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(85,plain,
% 75.82/76.01 ((~![A: $i] : (empty_carrier(A) | (poset_of_lattice(A) = rel_str_of(the_carrier(A), k2_lattice3(A))) | (~latt_str(A)) | (~lattice(A)))) | (~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[84, 83])).
% 75.82/76.01 tff(86,plain,
% 75.82/76.01 ((~lattice(boole_lattice(A!29))) | (~latt_str(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[85, 79])).
% 75.82/76.01 tff(87,plain,
% 75.82/76.01 (poset_of_lattice(boole_lattice(A!29)) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[86, 41, 66, 64])).
% 75.82/76.01 tff(88,plain,
% 75.82/76.01 (^[A: $i] : refl((boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> (boole_POSet(A) = poset_of_lattice(boole_lattice(A))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(89,plain,
% 75.82/76.01 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[88])).
% 75.82/76.01 tff(90,plain,
% 75.82/76.01 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A))) <=> ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(91,axiom,(![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_yellow_1')).
% 75.82/76.01 tff(92,plain,
% 75.82/76.01 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[91, 90])).
% 75.82/76.01 tff(93,plain,(
% 75.82/76.01 ![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 75.82/76.01 inference(skolemize,[status(sab)],[92])).
% 75.82/76.01 tff(94,plain,
% 75.82/76.01 (![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[93, 89])).
% 75.82/76.01 tff(95,plain,
% 75.82/76.01 ((~![A: $i] : (boole_POSet(A) = poset_of_lattice(boole_lattice(A)))) | (boole_POSet(A!29) = poset_of_lattice(boole_lattice(A!29)))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(96,plain,
% 75.82/76.01 (boole_POSet(A!29) = poset_of_lattice(boole_lattice(A!29))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[95, 94])).
% 75.82/76.01 tff(97,plain,
% 75.82/76.01 (^[A: $i] : refl((~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))) <=> (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(98,plain,
% 75.82/76.01 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))) <=> ![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[97])).
% 75.82/76.01 tff(99,plain,
% 75.82/76.01 (^[A: $i] : rewrite(((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))) <=> (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(100,plain,
% 75.82/76.01 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))) <=> ![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[99])).
% 75.82/76.01 tff(101,plain,
% 75.82/76.01 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A))) <=> ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(102,plain,
% 75.82/76.01 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)))), (((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))))), ((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)))), ((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))))), (((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)))), (((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))))), ((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)))), ((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))))), (((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)))), (((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))))), ((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)))), ((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))))), (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)))), (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))))), ((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> (((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))))), rewrite((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))), ((((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(103,plain,
% 75.82/76.01 (![A: $i] : (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A))) <=> ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[102])).
% 75.82/76.01 tff(104,axiom,(![A: $i] : (((((((((((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A))) & reflexive_relstr(boole_POSet(A))) & transitive_relstr(boole_POSet(A))) & antisymmetric_relstr(boole_POSet(A))) & lower_bounded_relstr(boole_POSet(A))) & upper_bounded_relstr(boole_POSet(A))) & bounded_relstr(boole_POSet(A))) & with_suprema_relstr(boole_POSet(A))) & with_infima_relstr(boole_POSet(A))) & complete_relstr(boole_POSet(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc8_yellow_1')).
% 75.82/76.01 tff(105,plain,
% 75.82/76.01 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[104, 103])).
% 75.82/76.01 tff(106,plain,
% 75.82/76.01 (![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[105, 101])).
% 75.82/76.01 tff(107,plain,(
% 75.82/76.01 ![A: $i] : ((~empty_carrier(boole_POSet(A))) & strict_rel_str(boole_POSet(A)) & reflexive_relstr(boole_POSet(A)) & transitive_relstr(boole_POSet(A)) & antisymmetric_relstr(boole_POSet(A)) & lower_bounded_relstr(boole_POSet(A)) & upper_bounded_relstr(boole_POSet(A)) & bounded_relstr(boole_POSet(A)) & with_suprema_relstr(boole_POSet(A)) & with_infima_relstr(boole_POSet(A)) & complete_relstr(boole_POSet(A)))),
% 75.82/76.01 inference(skolemize,[status(sab)],[106])).
% 75.82/76.01 tff(108,plain,
% 75.82/76.01 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[107, 100])).
% 75.82/76.01 tff(109,plain,
% 75.82/76.01 (![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[108, 98])).
% 75.82/76.01 tff(110,plain,
% 75.82/76.01 (((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29))))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(111,plain,
% 75.82/76.01 ((~(empty_carrier(boole_POSet(A!29)) | (~strict_rel_str(boole_POSet(A!29))) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29))))) <=> (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(112,plain,
% 75.82/76.01 (((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~strict_rel_str(boole_POSet(A!29))) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29))))))),
% 75.82/76.01 inference(monotonicity,[status(thm)],[111])).
% 75.82/76.01 tff(113,plain,
% 75.82/76.01 (((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~strict_rel_str(boole_POSet(A!29))) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29))))))),
% 75.82/76.01 inference(transitivity,[status(thm)],[112, 110])).
% 75.82/76.01 tff(114,plain,
% 75.82/76.01 ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~strict_rel_str(boole_POSet(A!29))) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(115,plain,
% 75.82/76.01 ((~![A: $i] : (~(empty_carrier(boole_POSet(A)) | (~strict_rel_str(boole_POSet(A))) | (~reflexive_relstr(boole_POSet(A))) | (~transitive_relstr(boole_POSet(A))) | (~antisymmetric_relstr(boole_POSet(A))) | (~lower_bounded_relstr(boole_POSet(A))) | (~upper_bounded_relstr(boole_POSet(A))) | (~bounded_relstr(boole_POSet(A))) | (~with_suprema_relstr(boole_POSet(A))) | (~with_infima_relstr(boole_POSet(A))) | (~complete_relstr(boole_POSet(A)))))) | (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[114, 113])).
% 75.82/76.01 tff(116,plain,
% 75.82/76.01 (~(empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29))))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[115, 109])).
% 75.82/76.01 tff(117,plain,
% 75.82/76.01 ((empty_carrier(boole_POSet(A!29)) | (~reflexive_relstr(boole_POSet(A!29))) | (~transitive_relstr(boole_POSet(A!29))) | (~antisymmetric_relstr(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))) | (~lower_bounded_relstr(boole_POSet(A!29))) | (~upper_bounded_relstr(boole_POSet(A!29))) | (~bounded_relstr(boole_POSet(A!29))) | (~with_suprema_relstr(boole_POSet(A!29))) | (~with_infima_relstr(boole_POSet(A!29))) | (~complete_relstr(boole_POSet(A!29)))) | strict_rel_str(boole_POSet(A!29))),
% 75.82/76.01 inference(tautology,[status(thm)],[])).
% 75.82/76.01 tff(118,plain,
% 75.82/76.01 (strict_rel_str(boole_POSet(A!29))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[117, 116])).
% 75.82/76.01 tff(119,plain,
% 75.82/76.01 (^[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))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(120,plain,
% 75.82/76.01 (![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)))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[119])).
% 75.82/76.01 tff(121,plain,
% 75.82/76.01 (^[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))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(122,plain,
% 75.82/76.01 (![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)))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[121])).
% 75.82/76.01 tff(123,plain,
% 75.82/76.01 (![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)))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(124,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')).
% 75.82/76.01 tff(125,plain,
% 75.82/76.01 (![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[124, 123])).
% 75.82/76.01 tff(126,plain,(
% 75.82/76.01 ![A: $i] : (strict_rel_str(boole_POSet(A)) & rel_str(boole_POSet(A)))),
% 75.82/76.01 inference(skolemize,[status(sab)],[125])).
% 75.82/76.01 tff(127,plain,
% 75.82/76.01 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[126, 122])).
% 75.82/76.01 tff(128,plain,
% 75.82/76.01 (![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[127, 120])).
% 75.82/76.01 tff(129,plain,
% 75.82/76.01 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(130,plain,
% 75.82/76.01 ((~((~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29))))) <=> (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29)))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(131,plain,
% 75.82/76.01 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))))))),
% 75.82/76.01 inference(monotonicity,[status(thm)],[130])).
% 75.82/76.01 tff(132,plain,
% 75.82/76.01 (((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29)))))) <=> ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))))))),
% 75.82/76.01 inference(transitivity,[status(thm)],[131, 129])).
% 75.82/76.01 tff(133,plain,
% 75.82/76.01 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29)))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(134,plain,
% 75.82/76.01 ((~![A: $i] : (~((~strict_rel_str(boole_POSet(A))) | (~rel_str(boole_POSet(A)))))) | (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[133, 132])).
% 75.82/76.01 tff(135,plain,
% 75.82/76.01 (~((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29))))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[134, 128])).
% 75.82/76.01 tff(136,plain,
% 75.82/76.01 (((~rel_str(boole_POSet(A!29))) | (~strict_rel_str(boole_POSet(A!29)))) | rel_str(boole_POSet(A!29))),
% 75.82/76.01 inference(tautology,[status(thm)],[])).
% 75.82/76.01 tff(137,plain,
% 75.82/76.01 (rel_str(boole_POSet(A!29))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[136, 135])).
% 75.82/76.01 tff(138,plain,
% 75.82/76.01 (^[A: $i] : refl(((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(139,plain,
% 75.82/76.01 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[138])).
% 75.82/76.01 tff(140,plain,
% 75.82/76.01 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(141,plain,
% 75.82/76.01 (^[A: $i] : trans(monotonicity(rewrite((strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))) <=> ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> (rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))))), rewrite((rel_str(A) => ((~strict_rel_str(A)) | (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))), ((rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(142,plain,
% 75.82/76.01 (![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A))))) <=> ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[141])).
% 75.82/76.01 tff(143,axiom,(![A: $i] : (rel_str(A) => (strict_rel_str(A) => (A = rel_str_of(the_carrier(A), the_InternalRel(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v1_orders_2')).
% 75.82/76.01 tff(144,plain,
% 75.82/76.01 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[143, 142])).
% 75.82/76.01 tff(145,plain,
% 75.82/76.01 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[144, 140])).
% 75.82/76.01 tff(146,plain,(
% 75.82/76.01 ![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(skolemize,[status(sab)],[145])).
% 75.82/76.01 tff(147,plain,
% 75.82/76.01 (![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[146, 139])).
% 75.82/76.01 tff(148,plain,
% 75.82/76.01 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(149,plain,
% 75.82/76.01 (((boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29)))) <=> ((~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(150,plain,
% 75.82/76.01 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29)))))),
% 75.82/76.01 inference(monotonicity,[status(thm)],[149])).
% 75.82/76.01 tff(151,plain,
% 75.82/76.01 (((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29))))) <=> ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))))),
% 75.82/76.01 inference(transitivity,[status(thm)],[150, 148])).
% 75.82/76.01 tff(152,plain,
% 75.82/76.01 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | ((boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29))) | (~rel_str(boole_POSet(A!29))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(153,plain,
% 75.82/76.01 ((~![A: $i] : ((A = rel_str_of(the_carrier(A), the_InternalRel(A))) | (~strict_rel_str(A)) | (~rel_str(A)))) | (~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[152, 151])).
% 75.82/76.01 tff(154,plain,
% 75.82/76.01 ((~rel_str(boole_POSet(A!29))) | (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))) | (~strict_rel_str(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[153, 147])).
% 75.82/76.01 tff(155,plain,
% 75.82/76.01 (boole_POSet(A!29) = rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[154, 137, 118])).
% 75.82/76.01 tff(156,plain,
% 75.82/76.01 (rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = boole_POSet(A!29)),
% 75.82/76.01 inference(symmetry,[status(thm)],[155])).
% 75.82/76.01 tff(157,plain,
% 75.82/76.01 (rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29)))),
% 75.82/76.01 inference(transitivity,[status(thm)],[156, 96, 87])).
% 75.82/76.01 tff(158,plain,
% 75.82/76.01 (^[A: $i, B: $i, C: $i] : refl((relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(159,plain,
% 75.82/76.01 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[158])).
% 75.82/76.01 tff(160,plain,
% 75.82/76.01 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(161,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 75.82/76.01 tff(162,plain,
% 75.82/76.01 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[161, 160])).
% 75.82/76.01 tff(163,plain,(
% 75.82/76.01 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 75.82/76.01 inference(skolemize,[status(sab)],[162])).
% 75.82/76.01 tff(164,plain,
% 75.82/76.01 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[163, 159])).
% 75.82/76.01 tff(165,plain,
% 75.82/76.01 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))) <=> relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(166,plain,
% 75.82/76.01 (relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))) <=> relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[165, 164])).
% 75.82/76.01 tff(167,plain,
% 75.82/76.01 (^[A: $i] : refl(((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(168,plain,
% 75.82/76.01 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[167])).
% 75.82/76.01 tff(169,plain,
% 75.82/76.01 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(170,plain,
% 75.82/76.01 (^[A: $i] : rewrite((rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(171,plain,
% 75.82/76.01 (![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A))) <=> ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[170])).
% 75.82/76.01 tff(172,axiom,(![A: $i] : (rel_str(A) => relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_orders_2')).
% 75.82/76.01 tff(173,plain,
% 75.82/76.01 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[172, 171])).
% 75.82/76.01 tff(174,plain,
% 75.82/76.01 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[173, 169])).
% 75.82/76.01 tff(175,plain,(
% 75.82/76.01 ![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(skolemize,[status(sab)],[174])).
% 75.82/76.01 tff(176,plain,
% 75.82/76.01 (![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[175, 168])).
% 75.82/76.01 tff(177,plain,
% 75.82/76.01 (((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(boole_POSet(A!29))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))) <=> ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(boole_POSet(A!29))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(178,plain,
% 75.82/76.01 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | ((~rel_str(boole_POSet(A!29))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(179,plain,
% 75.82/76.01 ((~![A: $i] : ((~rel_str(A)) | relation_of2_as_subset(the_InternalRel(A), the_carrier(A), the_carrier(A)))) | (~rel_str(boole_POSet(A!29))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[178, 177])).
% 75.82/76.01 tff(180,plain,
% 75.82/76.01 ((~rel_str(boole_POSet(A!29))) | relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[179, 176])).
% 75.82/76.01 tff(181,plain,
% 75.82/76.01 (relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[180, 137])).
% 75.82/76.01 tff(182,plain,
% 75.82/76.01 ((~(relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))) <=> relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))) | (~relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(tautology,[status(thm)],[])).
% 75.82/76.01 tff(183,plain,
% 75.82/76.01 ((~(relation_of2_as_subset(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))) <=> relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29))))) | relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[182, 181])).
% 75.82/76.01 tff(184,plain,
% 75.82/76.01 (relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))),
% 75.82/76.01 inference(unit_resolution,[status(thm)],[183, 166])).
% 75.82/76.01 tff(185,plain,
% 75.82/76.01 (^[A: $i, B: $i] : refl(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(186,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[185])).
% 75.82/76.01 tff(187,plain,
% 75.82/76.01 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(188,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[187])).
% 75.82/76.01 tff(189,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(transitivity,[status(thm)],[188, 186])).
% 75.82/76.01 tff(190,plain,
% 75.82/76.01 (^[A: $i, B: $i] : rewrite(((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D)))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(191,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[190])).
% 75.82/76.01 tff(192,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(193,plain,
% 75.82/76.01 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i, D: $i] : rewrite(((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), (![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))) <=> ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> (relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))))), rewrite((relation_of2(B, A, A) => ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))), ((relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))))),
% 75.82/76.01 inference(bind,[status(th)],[])).
% 75.82/76.01 tff(194,plain,
% 75.82/76.01 (![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D)))) <=> ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 75.82/76.01 inference(quant_intro,[status(thm)],[193])).
% 75.82/76.01 tff(195,axiom,(![A: $i, B: $i] : (relation_of2(B, A, A) => ![C: $i, D: $i] : ((rel_str_of(A, B) = rel_str_of(C, D)) => ((A = C) & (B = D))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g1_orders_2')).
% 75.82/76.01 tff(196,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[195, 194])).
% 75.82/76.01 tff(197,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[196, 192])).
% 75.82/76.01 tff(198,plain,(
% 75.82/76.01 ![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | ((A = C) & (B = D))))),
% 75.82/76.01 inference(skolemize,[status(sab)],[197])).
% 75.82/76.01 tff(199,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[198, 191])).
% 75.82/76.01 tff(200,plain,
% 75.82/76.01 (![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[199, 189])).
% 75.82/76.01 tff(201,plain,
% 75.82/76.01 (((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D))))))) <=> ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D))))))),
% 75.82/76.01 inference(rewrite,[status(thm)],[])).
% 75.82/76.01 tff(202,plain,
% 75.82/76.01 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | ((~relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D))))))),
% 75.82/76.01 inference(quant_inst,[status(thm)],[])).
% 75.82/76.01 tff(203,plain,
% 75.82/76.01 ((~![A: $i, B: $i] : ((~relation_of2(B, A, A)) | ![C: $i, D: $i] : ((~(rel_str_of(A, B) = rel_str_of(C, D))) | (~((~(A = C)) | (~(B = D))))))) | (~relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))),
% 75.82/76.01 inference(modus_ponens,[status(thm)],[202, 201])).
% 75.82/76.01 tff(204,plain,
% 75.82/76.01 ((~relation_of2(the_InternalRel(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)), the_carrier(boole_POSet(A!29)))) | ![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[203, 200])).
% 75.82/76.02 tff(205,plain,
% 75.82/76.02 (![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[204, 184])).
% 75.82/76.02 tff(206,plain,
% 75.82/76.02 (((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))) | ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))) | (~((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29)))))))) <=> ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))) | (~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))) | (~((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29)))))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(207,plain,
% 75.82/76.02 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))) | ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))) | (~((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29)))))))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(208,plain,
% 75.82/76.02 ((~![C: $i, D: $i] : ((~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(C, D))) | (~((~(the_carrier(boole_POSet(A!29)) = C)) | (~(the_InternalRel(boole_POSet(A!29)) = D)))))) | (~(rel_str_of(the_carrier(boole_POSet(A!29)), the_InternalRel(boole_POSet(A!29))) = rel_str_of(the_carrier(boole_lattice(A!29)), k2_lattice3(boole_lattice(A!29))))) | (~((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29))))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[207, 206])).
% 75.82/76.02 tff(209,plain,
% 75.82/76.02 (~((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29)))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[208, 205, 157])).
% 75.82/76.02 tff(210,plain,
% 75.82/76.02 (((~(the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))) | (~(the_InternalRel(boole_POSet(A!29)) = k2_lattice3(boole_lattice(A!29))))) | (the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29)))),
% 75.82/76.02 inference(tautology,[status(thm)],[])).
% 75.82/76.02 tff(211,plain,
% 75.82/76.02 (the_carrier(boole_POSet(A!29)) = the_carrier(boole_lattice(A!29))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[210, 209])).
% 75.82/76.02 tff(212,plain,
% 75.82/76.02 (the_carrier(boole_lattice(A!29)) = the_carrier(boole_POSet(A!29))),
% 75.82/76.02 inference(symmetry,[status(thm)],[211])).
% 75.82/76.02 tff(213,plain,
% 75.82/76.02 (element(C!30, the_carrier(boole_lattice(A!29))) <=> element(C!30, the_carrier(boole_POSet(A!29)))),
% 75.82/76.02 inference(monotonicity,[status(thm)],[212])).
% 75.82/76.02 tff(214,plain,
% 75.82/76.02 (element(C!30, the_carrier(boole_POSet(A!29))) <=> element(C!30, the_carrier(boole_lattice(A!29)))),
% 75.82/76.02 inference(symmetry,[status(thm)],[213])).
% 75.82/76.02 tff(215,plain,
% 75.82/76.02 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))) <=> (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C)))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(216,plain,
% 75.82/76.02 ((~![A: $i, B: $i] : (element(B, the_carrier(boole_POSet(A))) => ![C: $i] : (element(C, the_carrier(boole_POSet(A))) => (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))) <=> (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C)))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(217,axiom,(~![A: $i, B: $i] : (element(B, the_carrier(boole_POSet(A))) => ![C: $i] : (element(C, the_carrier(boole_POSet(A))) => (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_yellow_1')).
% 75.82/76.02 tff(218,plain,
% 75.82/76.02 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[217, 216])).
% 75.82/76.02 tff(219,plain,
% 75.82/76.02 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[218, 215])).
% 75.82/76.02 tff(220,plain,
% 75.82/76.02 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[219, 215])).
% 75.82/76.02 tff(221,plain,
% 75.82/76.02 (~![A: $i, B: $i] : ((~element(B, the_carrier(boole_POSet(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_POSet(A)))) | (related_reflexive(boole_POSet(A), B, C) <=> subset(B, C))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[220, 215])).
% 75.82/76.02 tff(222,plain,
% 75.82/76.02 (~((~element(C!30, the_carrier(boole_POSet(A!29)))) | (related_reflexive(boole_POSet(A!29), B!28, C!30) <=> subset(B!28, C!30)))),
% 75.82/76.02 inference(and_elim,[status(thm)],[221])).
% 75.82/76.02 tff(223,plain,
% 75.82/76.02 (element(C!30, the_carrier(boole_POSet(A!29)))),
% 75.82/76.02 inference(or_elim,[status(thm)],[222])).
% 75.82/76.02 tff(224,plain,
% 75.82/76.02 (element(C!30, the_carrier(boole_lattice(A!29)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[223, 214])).
% 75.82/76.02 tff(225,plain,
% 75.82/76.02 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(226,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[225])).
% 75.82/76.02 tff(227,plain,
% 75.82/76.02 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(228,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[227])).
% 75.82/76.02 tff(229,plain,
% 75.82/76.02 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(230,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[229])).
% 75.82/76.02 tff(231,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(transitivity,[status(thm)],[230, 228])).
% 75.82/76.02 tff(232,plain,
% 75.82/76.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(233,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[232])).
% 75.82/76.02 tff(234,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(235,plain,
% 75.82/76.02 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : rewrite((element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(236,plain,
% 75.82/76.02 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[235])).
% 75.82/76.02 tff(237,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => (cast_to_el_of_LattPOSet(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_lattice3')).
% 75.82/76.02 tff(238,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[237, 236])).
% 75.82/76.02 tff(239,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[238, 234])).
% 75.82/76.02 tff(240,plain,(
% 75.82/76.02 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(skolemize,[status(sab)],[239])).
% 75.82/76.02 tff(241,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[240, 233])).
% 75.82/76.02 tff(242,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)) | (~lattice(A)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[241, 231])).
% 75.82/76.02 tff(243,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[242, 226])).
% 75.82/76.02 tff(244,plain,
% 75.82/76.02 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B)))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B)))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(245,plain,
% 75.82/76.02 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | (empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B)))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(246,plain,
% 75.82/76.02 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (cast_to_el_of_LattPOSet(A, B) = B)))) | empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[245, 244])).
% 75.82/76.02 tff(247,plain,
% 75.82/76.02 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[246, 243, 64, 41, 66])).
% 75.82/76.02 tff(248,plain,
% 75.82/76.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(249,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(250,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30)),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[249, 248])).
% 75.82/76.02 tff(251,plain,
% 75.82/76.02 ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30)),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[250, 247])).
% 75.82/76.02 tff(252,plain,
% 75.82/76.02 (cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30) = C!30),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[251, 224])).
% 75.82/76.02 tff(253,plain,
% 75.82/76.02 (element(B!28, the_carrier(boole_lattice(A!29))) <=> element(B!28, the_carrier(boole_POSet(A!29)))),
% 75.82/76.02 inference(monotonicity,[status(thm)],[212])).
% 75.82/76.02 tff(254,plain,
% 75.82/76.02 (element(B!28, the_carrier(boole_POSet(A!29))) <=> element(B!28, the_carrier(boole_lattice(A!29)))),
% 75.82/76.02 inference(symmetry,[status(thm)],[253])).
% 75.82/76.02 tff(255,plain,
% 75.82/76.02 (element(B!28, the_carrier(boole_POSet(A!29)))),
% 75.82/76.02 inference(and_elim,[status(thm)],[221])).
% 75.82/76.02 tff(256,plain,
% 75.82/76.02 (element(B!28, the_carrier(boole_lattice(A!29)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[255, 254])).
% 75.82/76.02 tff(257,plain,
% 75.82/76.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(258,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(259,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B) = B))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28)),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[258, 257])).
% 75.82/76.02 tff(260,plain,
% 75.82/76.02 ((~element(B!28, the_carrier(boole_lattice(A!29)))) | (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28)),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[259, 247])).
% 75.82/76.02 tff(261,plain,
% 75.82/76.02 (cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28) = B!28),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[260, 256])).
% 75.82/76.02 tff(262,plain,
% 75.82/76.02 (poset_of_lattice(boole_lattice(A!29)) = boole_POSet(A!29)),
% 75.82/76.02 inference(symmetry,[status(thm)],[96])).
% 75.82/76.02 tff(263,plain,
% 75.82/76.02 (related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)) <=> related_reflexive(boole_POSet(A!29), B!28, C!30)),
% 75.82/76.02 inference(monotonicity,[status(thm)],[262, 261, 252])).
% 75.82/76.02 tff(264,plain,
% 75.82/76.02 (related_reflexive(boole_POSet(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.82/76.02 inference(symmetry,[status(thm)],[263])).
% 75.82/76.02 tff(265,plain,
% 75.82/76.02 ((~related_reflexive(boole_POSet(A!29), B!28, C!30)) <=> (~related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))),
% 75.82/76.02 inference(monotonicity,[status(thm)],[264])).
% 75.82/76.02 tff(266,assumption,(~subset(B!28, C!30)), introduced(assumption)).
% 75.82/76.02 tff(267,plain,
% 75.82/76.02 (~(related_reflexive(boole_POSet(A!29), B!28, C!30) <=> subset(B!28, C!30))),
% 75.82/76.02 inference(or_elim,[status(thm)],[222])).
% 75.82/76.02 tff(268,plain,
% 75.82/76.02 ((related_reflexive(boole_POSet(A!29), B!28, C!30) <=> subset(B!28, C!30)) | related_reflexive(boole_POSet(A!29), B!28, C!30) | subset(B!28, C!30)),
% 75.82/76.02 inference(tautology,[status(thm)],[])).
% 75.82/76.02 tff(269,plain,
% 75.82/76.02 (related_reflexive(boole_POSet(A!29), B!28, C!30) | subset(B!28, C!30)),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[268, 267])).
% 75.82/76.02 tff(270,plain,
% 75.82/76.02 (related_reflexive(boole_POSet(A!29), B!28, C!30)),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[269, 266])).
% 75.82/76.02 tff(271,plain,
% 75.82/76.02 (related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[270, 264])).
% 75.82/76.02 tff(272,plain,
% 75.82/76.02 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(273,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[272])).
% 75.82/76.02 tff(274,plain,
% 75.82/76.02 (^[A: $i] : refl((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(275,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[274])).
% 75.82/76.02 tff(276,plain,
% 75.82/76.02 (^[A: $i] : rewrite((empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(277,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[276])).
% 75.82/76.02 tff(278,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(transitivity,[status(thm)],[277, 275])).
% 75.82/76.02 tff(279,plain,
% 75.82/76.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & lattice(A) & latt_str(A)) <=> (~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))))), rewrite((~(~(empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)))), ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) <=> (empty_carrier(A) | (~latt_str(A)) | (~lattice(A))))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), rewrite(((empty_carrier(A) | (~latt_str(A)) | (~lattice(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))), (((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(280,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[279])).
% 75.82/76.02 tff(281,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(282,plain,
% 75.82/76.02 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & lattice(A) & latt_str(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))) <=> ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), (![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> (((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))))), rewrite((((~empty_carrier(A)) & lattice(A) & latt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), (((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))))),
% 75.82/76.02 inference(bind,[status(th)],[])).
% 75.82/76.02 tff(283,plain,
% 75.82/76.02 (![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(quant_intro,[status(thm)],[282])).
% 75.82/76.02 tff(284,axiom,(![A: $i] : ((((~empty_carrier(A)) & lattice(A)) & latt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t7_lattice3')).
% 75.82/76.02 tff(285,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[284, 283])).
% 75.82/76.02 tff(286,plain,
% 75.82/76.02 (![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[285, 281])).
% 75.82/76.02 tff(287,plain,(
% 75.82/76.02 ![A: $i] : ((~((~empty_carrier(A)) & lattice(A) & latt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(skolemize,[status(sab)],[286])).
% 75.82/76.02 tff(288,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[287, 280])).
% 75.82/76.02 tff(289,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))) | (~lattice(A)))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[288, 278])).
% 75.82/76.02 tff(290,plain,
% 75.82/76.02 (![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[289, 273])).
% 75.82/76.02 tff(291,plain,
% 75.82/76.02 (((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | (empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(292,plain,
% 75.82/76.02 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | (empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(293,plain,
% 75.82/76.02 ((~![A: $i] : (empty_carrier(A) | (~latt_str(A)) | (~lattice(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (below_refl(A, B, C) <=> related_reflexive(poset_of_lattice(A), cast_to_el_of_LattPOSet(A, B), cast_to_el_of_LattPOSet(A, C))))))) | empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[292, 291])).
% 75.82/76.02 tff(294,plain,
% 75.82/76.02 (empty_carrier(boole_lattice(A!29)) | (~latt_str(boole_lattice(A!29))) | (~lattice(boole_lattice(A!29))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[293, 290])).
% 75.82/76.02 tff(295,plain,
% 75.82/76.02 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[294, 41, 66, 64])).
% 75.82/76.02 tff(296,plain,
% 75.82/76.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))),
% 75.82/76.02 inference(rewrite,[status(thm)],[])).
% 75.82/76.02 tff(297,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))),
% 75.82/76.02 inference(quant_inst,[status(thm)],[])).
% 75.82/76.02 tff(298,plain,
% 75.82/76.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B), cast_to_el_of_LattPOSet(boole_lattice(A!29), C)))))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))),
% 75.82/76.02 inference(modus_ponens,[status(thm)],[297, 296])).
% 75.82/76.02 tff(299,plain,
% 75.82/76.02 ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))),
% 75.82/76.02 inference(unit_resolution,[status(thm)],[298, 295])).
% 75.82/76.02 tff(300,plain,
% 75.82/76.02 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[299, 256])).
% 75.82/76.03 tff(301,plain,
% 75.82/76.03 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(302,plain,
% 75.82/76.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))))),
% 75.82/76.03 inference(quant_inst,[status(thm)],[])).
% 75.82/76.03 tff(303,plain,
% 75.82/76.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C))))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[302, 301])).
% 75.82/76.03 tff(304,plain,
% 75.82/76.03 (below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[303, 300, 224])).
% 75.82/76.03 tff(305,plain,
% 75.82/76.03 ((~(below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))) | below_refl(boole_lattice(A!29), B!28, C!30) | (~related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))),
% 75.82/76.03 inference(tautology,[status(thm)],[])).
% 75.82/76.03 tff(306,plain,
% 75.82/76.03 (below_refl(boole_lattice(A!29), B!28, C!30) | (~related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[305, 304])).
% 75.82/76.03 tff(307,plain,
% 75.82/76.03 (below_refl(boole_lattice(A!29), B!28, C!30)),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[306, 271])).
% 75.82/76.03 tff(308,plain,
% 75.82/76.03 (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[307, 61])).
% 75.82/76.03 tff(309,plain,
% 75.82/76.03 (below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(boole_lattice(A!29), B!28, C!30)),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(310,plain,
% 75.82/76.03 (below(boole_lattice(A!29), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.03 inference(symmetry,[status(thm)],[309])).
% 75.82/76.03 tff(311,plain,
% 75.82/76.03 ((~below(boole_lattice(A!29), B!28, C!30)) <=> (~below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[310])).
% 75.82/76.03 tff(312,plain,
% 75.82/76.03 (^[A: $i, B: $i] : refl(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(313,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[312])).
% 75.82/76.03 tff(314,plain,
% 75.82/76.03 (^[A: $i, B: $i] : rewrite(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(315,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[314])).
% 75.82/76.03 tff(316,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(transitivity,[status(thm)],[315, 313])).
% 75.82/76.03 tff(317,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(318,plain,
% 75.82/76.03 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C))) <=> ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))), (![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C))) <=> ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))))), rewrite((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(319,plain,
% 75.82/76.03 (![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C)))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[318])).
% 75.82/76.03 tff(320,axiom,(![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => (below(boole_lattice(A), B, C) <=> subset(B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_lattice3')).
% 75.82/76.03 tff(321,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[320, 319])).
% 75.82/76.03 tff(322,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[321, 317])).
% 75.82/76.03 tff(323,plain,(
% 75.82/76.03 ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(skolemize,[status(sab)],[322])).
% 75.82/76.03 tff(324,plain,
% 75.82/76.03 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[323, 316])).
% 75.82/76.03 tff(325,plain,
% 75.82/76.03 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C))))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(326,plain,
% 75.82/76.03 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))) | ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C))))),
% 75.82/76.03 inference(quant_inst,[status(thm)],[])).
% 75.82/76.03 tff(327,plain,
% 75.82/76.03 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (below(boole_lattice(A), B, C) <=> subset(B, C))))) | (~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[326, 325])).
% 75.82/76.03 tff(328,plain,
% 75.82/76.03 ((~element(B!28, the_carrier(boole_lattice(A!29)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[327, 324])).
% 75.82/76.03 tff(329,plain,
% 75.82/76.03 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[328, 256])).
% 75.82/76.03 tff(330,plain,
% 75.82/76.03 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30)))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30)))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(331,plain,
% 75.82/76.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))) | ((~element(C!30, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30)))),
% 75.82/76.03 inference(quant_inst,[status(thm)],[])).
% 75.82/76.03 tff(332,plain,
% 75.82/76.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C) <=> subset(B!28, C)))) | (~element(C!30, the_carrier(boole_lattice(A!29)))) | (below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[331, 330])).
% 75.82/76.03 tff(333,plain,
% 75.82/76.03 (below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30)),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[332, 224, 329])).
% 75.82/76.03 tff(334,plain,
% 75.82/76.03 ((~(below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30))) | (~below(boole_lattice(A!29), B!28, C!30)) | subset(B!28, C!30)),
% 75.82/76.03 inference(tautology,[status(thm)],[])).
% 75.82/76.03 tff(335,plain,
% 75.82/76.03 ((~below(boole_lattice(A!29), B!28, C!30)) | subset(B!28, C!30)),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[334, 333])).
% 75.82/76.03 tff(336,plain,
% 75.82/76.03 (~below(boole_lattice(A!29), B!28, C!30)),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[335, 266])).
% 75.82/76.03 tff(337,plain,
% 75.82/76.03 (~below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[336, 311])).
% 75.82/76.03 tff(338,plain,
% 75.82/76.03 (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) <=> empty_carrier(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(339,plain,
% 75.82/76.03 (empty_carrier(boole_lattice(A!29)) <=> empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[338])).
% 75.82/76.03 tff(340,plain,
% 75.82/76.03 ((~empty_carrier(boole_lattice(A!29))) <=> (~empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[339])).
% 75.82/76.03 tff(341,plain,
% 75.82/76.03 (~empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[64, 340])).
% 75.82/76.03 tff(342,plain,
% 75.82/76.03 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) = the_carrier(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(343,plain,
% 75.82/76.03 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) = the_carrier(boole_POSet(A!29))),
% 75.82/76.03 inference(transitivity,[status(thm)],[342, 212])).
% 75.82/76.03 tff(344,plain,
% 75.82/76.03 (element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) <=> element(C!30, the_carrier(boole_POSet(A!29)))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[343])).
% 75.82/76.03 tff(345,plain,
% 75.82/76.03 (element(C!30, the_carrier(boole_POSet(A!29))) <=> element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[344])).
% 75.82/76.03 tff(346,plain,
% 75.82/76.03 (element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[223, 345])).
% 75.82/76.03 tff(347,plain,
% 75.82/76.03 (latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) <=> latt_str(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(348,plain,
% 75.82/76.03 (latt_str(boole_lattice(A!29)) <=> latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[347])).
% 75.82/76.03 tff(349,plain,
% 75.82/76.03 (latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[41, 348])).
% 75.82/76.03 tff(350,plain,
% 75.82/76.03 (join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) <=> join_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(351,plain,
% 75.82/76.03 (join_absorbing(boole_lattice(A!29)) <=> join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[350])).
% 75.82/76.03 tff(352,plain,
% 75.82/76.03 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | join_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(tautology,[status(thm)],[])).
% 75.82/76.03 tff(353,plain,
% 75.82/76.03 (join_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[352, 20])).
% 75.82/76.03 tff(354,plain,
% 75.82/76.03 (join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[353, 351])).
% 75.82/76.03 tff(355,plain,
% 75.82/76.03 (meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) <=> meet_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(356,plain,
% 75.82/76.03 (meet_absorbing(boole_lattice(A!29)) <=> meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[355])).
% 75.82/76.03 tff(357,plain,
% 75.82/76.03 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | meet_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(tautology,[status(thm)],[])).
% 75.82/76.03 tff(358,plain,
% 75.82/76.03 (meet_absorbing(boole_lattice(A!29))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[357, 20])).
% 75.82/76.03 tff(359,plain,
% 75.82/76.03 (meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[358, 356])).
% 75.82/76.03 tff(360,plain,
% 75.82/76.03 (meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) <=> meet_commutative(boole_lattice(A!29))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[59])).
% 75.82/76.03 tff(361,plain,
% 75.82/76.03 (meet_commutative(boole_lattice(A!29)) <=> meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[360])).
% 75.82/76.03 tff(362,plain,
% 75.82/76.03 (((~lattice(boole_lattice(A!29))) | empty_carrier(boole_lattice(A!29)) | (~strict_latt_str(boole_lattice(A!29))) | (~join_commutative(boole_lattice(A!29))) | (~join_associative(boole_lattice(A!29))) | (~meet_commutative(boole_lattice(A!29))) | (~meet_associative(boole_lattice(A!29))) | (~meet_absorbing(boole_lattice(A!29))) | (~join_absorbing(boole_lattice(A!29))) | (~distributive_lattstr(boole_lattice(A!29))) | (~modular_lattstr(boole_lattice(A!29))) | (~lower_bounded_semilattstr(boole_lattice(A!29))) | (~upper_bounded_semilattstr(boole_lattice(A!29))) | (~bounded_lattstr(boole_lattice(A!29))) | (~complemented_lattstr(boole_lattice(A!29))) | (~boolean_lattstr(boole_lattice(A!29)))) | meet_commutative(boole_lattice(A!29))),
% 75.82/76.03 inference(tautology,[status(thm)],[])).
% 75.82/76.03 tff(363,plain,
% 75.82/76.03 (meet_commutative(boole_lattice(A!29))),
% 75.82/76.03 inference(unit_resolution,[status(thm)],[362, 20])).
% 75.82/76.03 tff(364,plain,
% 75.82/76.03 (meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[363, 361])).
% 75.82/76.03 tff(365,plain,
% 75.82/76.03 (element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) <=> element(B!28, the_carrier(boole_POSet(A!29)))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[343])).
% 75.82/76.03 tff(366,plain,
% 75.82/76.03 (element(B!28, the_carrier(boole_POSet(A!29))) <=> element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.03 inference(symmetry,[status(thm)],[365])).
% 75.82/76.03 tff(367,plain,
% 75.82/76.03 (element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[255, 366])).
% 75.82/76.03 tff(368,plain,
% 75.82/76.03 (^[A: $i, B: $i, C: $i] : refl(((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(369,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[368])).
% 75.82/76.03 tff(370,plain,
% 75.82/76.03 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) <=> (~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))))), rewrite((~(~(empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) <=> (empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))))), rewrite(((empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))), (((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(371,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[370])).
% 75.82/76.03 tff(372,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(373,plain,
% 75.82/76.03 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A))), (((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A))), ((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)))), (((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))), ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) <=> ((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> (((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))))), rewrite((((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))), (((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))))),
% 75.82/76.03 inference(bind,[status(th)],[])).
% 75.82/76.03 tff(374,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 75.82/76.03 inference(quant_intro,[status(thm)],[373])).
% 75.82/76.03 tff(375,axiom,(![A: $i, B: $i, C: $i] : ((((((((~empty_carrier(A)) & meet_commutative(A)) & meet_absorbing(A)) & join_absorbing(A)) & latt_str(A)) & element(B, the_carrier(A))) & element(C, the_carrier(A))) => (below_refl(A, B, C) <=> below(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 75.82/76.03 tff(376,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[375, 374])).
% 75.82/76.03 tff(377,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[376, 372])).
% 75.82/76.03 tff(378,plain,(
% 75.82/76.03 ![A: $i, B: $i, C: $i] : ((~((~empty_carrier(A)) & meet_commutative(A) & meet_absorbing(A) & join_absorbing(A) & latt_str(A) & element(B, the_carrier(A)) & element(C, the_carrier(A)))) | (below_refl(A, B, C) <=> below(A, B, C)))),
% 75.82/76.03 inference(skolemize,[status(sab)],[377])).
% 75.82/76.03 tff(379,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[378, 371])).
% 75.82/76.03 tff(380,plain,
% 75.82/76.03 (![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))),
% 75.82/76.03 inference(modus_ponens,[status(thm)],[379, 369])).
% 75.82/76.03 tff(381,plain,
% 75.82/76.03 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(382,plain,
% 75.82/76.03 (((below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))))) <=> (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)))),
% 75.82/76.03 inference(rewrite,[status(thm)],[])).
% 75.82/76.03 tff(383,plain,
% 75.82/76.03 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))))),
% 75.82/76.03 inference(monotonicity,[status(thm)],[382])).
% 75.82/76.03 tff(384,plain,
% 75.82/76.03 (((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)))),
% 75.82/76.04 inference(transitivity,[status(thm)],[383, 381])).
% 75.82/76.04 tff(385,plain,
% 75.82/76.04 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | ((below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))))),
% 75.82/76.04 inference(quant_inst,[status(thm)],[])).
% 75.82/76.04 tff(386,plain,
% 75.82/76.04 ((~![A: $i, B: $i, C: $i] : ((below_refl(A, B, C) <=> below(A, B, C)) | empty_carrier(A) | (~element(C, the_carrier(A))) | (~meet_commutative(A)) | (~meet_absorbing(A)) | (~join_absorbing(A)) | (~latt_str(A)) | (~element(B, the_carrier(A))))) | empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.82/76.04 inference(modus_ponens,[status(thm)],[385, 384])).
% 75.82/76.04 tff(387,plain,
% 75.82/76.04 (empty_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))) | (~element(B!28, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (~meet_commutative(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~meet_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~join_absorbing(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))))) | (~element(C!30, the_carrier(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29)))))) | (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[386, 380])).
% 75.82/76.04 tff(388,plain,
% 75.82/76.04 (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[387, 367, 364, 359, 354, 349, 346, 341])).
% 75.82/76.04 tff(389,plain,
% 75.82/76.04 ((~(below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))) | (~below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.04 inference(tautology,[status(thm)],[])).
% 75.82/76.04 tff(390,plain,
% 75.82/76.04 ((~below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)) | below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[389, 388])).
% 75.82/76.04 tff(391,plain,
% 75.82/76.04 (~below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[390, 337])).
% 75.82/76.04 tff(392,plain,
% 75.82/76.04 ($false),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[391, 308])).
% 75.82/76.04 tff(393,plain,(subset(B!28, C!30)), inference(lemma,lemma(discharge,[]))).
% 75.82/76.04 tff(394,plain,
% 75.82/76.04 ((related_reflexive(boole_POSet(A!29), B!28, C!30) <=> subset(B!28, C!30)) | (~related_reflexive(boole_POSet(A!29), B!28, C!30)) | (~subset(B!28, C!30))),
% 75.82/76.04 inference(tautology,[status(thm)],[])).
% 75.82/76.04 tff(395,plain,
% 75.82/76.04 ((~related_reflexive(boole_POSet(A!29), B!28, C!30)) | (~subset(B!28, C!30))),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[394, 267])).
% 75.82/76.04 tff(396,plain,
% 75.82/76.04 (~related_reflexive(boole_POSet(A!29), B!28, C!30)),
% 75.82/76.04 inference(unit_resolution,[status(thm)],[395, 393])).
% 75.82/76.04 tff(397,plain,
% 75.82/76.04 (~related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.82/76.04 inference(modus_ponens,[status(thm)],[396, 265])).
% 75.82/76.04 tff(398,plain,
% 75.82/76.04 ((~(below_refl(boole_lattice(A!29), B!28, C!30) <=> related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30)))) | (~below_refl(boole_lattice(A!29), B!28, C!30)) | related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.87/76.05 inference(tautology,[status(thm)],[])).
% 75.87/76.05 tff(399,plain,
% 75.87/76.05 ((~below_refl(boole_lattice(A!29), B!28, C!30)) | related_reflexive(poset_of_lattice(boole_lattice(A!29)), cast_to_el_of_LattPOSet(boole_lattice(A!29), B!28), cast_to_el_of_LattPOSet(boole_lattice(A!29), C!30))),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[398, 304])).
% 75.87/76.05 tff(400,plain,
% 75.87/76.05 (~below_refl(boole_lattice(A!29), B!28, C!30)),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[399, 397])).
% 75.87/76.05 tff(401,plain,
% 75.87/76.05 (~below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.87/76.05 inference(modus_ponens,[status(thm)],[400, 62])).
% 75.87/76.05 tff(402,plain,
% 75.87/76.05 ((~(below(boole_lattice(A!29), B!28, C!30) <=> subset(B!28, C!30))) | below(boole_lattice(A!29), B!28, C!30) | (~subset(B!28, C!30))),
% 75.87/76.05 inference(tautology,[status(thm)],[])).
% 75.87/76.05 tff(403,plain,
% 75.87/76.05 (below(boole_lattice(A!29), B!28, C!30) | (~subset(B!28, C!30))),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[402, 333])).
% 75.87/76.05 tff(404,plain,
% 75.87/76.05 (below(boole_lattice(A!29), B!28, C!30)),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[403, 393])).
% 75.87/76.05 tff(405,plain,
% 75.87/76.05 (below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.87/76.05 inference(modus_ponens,[status(thm)],[404, 310])).
% 75.87/76.05 tff(406,plain,
% 75.87/76.05 ((~(below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) <=> below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))) | below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) | (~below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.87/76.05 inference(tautology,[status(thm)],[])).
% 75.87/76.05 tff(407,plain,
% 75.87/76.05 (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30) | (~below(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30))),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[406, 388])).
% 75.87/76.05 tff(408,plain,
% 75.87/76.05 (below_refl(latt_str_of(the_carrier(boole_lattice(A!29)), the_L_join(boole_lattice(A!29)), the_L_meet(boole_lattice(A!29))), B!28, C!30)),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[407, 405])).
% 75.87/76.05 tff(409,plain,
% 75.87/76.05 ($false),
% 75.87/76.05 inference(unit_resolution,[status(thm)],[408, 401])).
% 75.87/76.05 % SZS output end Proof
% 76.13/76.34 % E exiting
%------------------------------------------------------------------------------