%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU345+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:27:39 AM UTC 2025
% Result : Theorem 10.77s 10.93s
% Output : Proof 10.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU345+1 : TPTP v9.0.0. Released v3.3.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.32 % Computer : n010.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri Jun 20 06:51:27 EDT 2025
% 0.11/0.33 % CPUTime :
% 10.77/10.93 % SZS status Theorem
% 10.77/10.93 % SZS output start Proof
% 10.77/10.93 tff(join_semilatt_str_type, type, (
% 10.77/10.93 join_semilatt_str: $i > $o)).
% 10.77/10.93 tff(boole_lattice_type, type, (
% 10.77/10.93 boole_lattice: $i > $i)).
% 10.77/10.93 tff(tptp_fun_A_20_type, type, (
% 10.77/10.93 tptp_fun_A_20: $i)).
% 10.77/10.93 tff(meet_semilatt_str_type, type, (
% 10.77/10.93 meet_semilatt_str: $i > $o)).
% 10.77/10.93 tff(empty_carrier_type, type, (
% 10.77/10.93 empty_carrier: $i > $o)).
% 10.77/10.93 tff(lattice_type, type, (
% 10.77/10.93 lattice: $i > $o)).
% 10.77/10.93 tff(join_absorbing_type, type, (
% 10.77/10.93 join_absorbing: $i > $o)).
% 10.77/10.93 tff(meet_absorbing_type, type, (
% 10.77/10.93 meet_absorbing: $i > $o)).
% 10.77/10.93 tff(meet_associative_type, type, (
% 10.77/10.93 meet_associative: $i > $o)).
% 10.77/10.93 tff(meet_commutative_type, type, (
% 10.77/10.93 meet_commutative: $i > $o)).
% 10.77/10.93 tff(join_associative_type, type, (
% 10.77/10.93 join_associative: $i > $o)).
% 10.77/10.93 tff(join_commutative_type, type, (
% 10.77/10.93 join_commutative: $i > $o)).
% 10.77/10.93 tff(strict_latt_str_type, type, (
% 10.77/10.93 strict_latt_str: $i > $o)).
% 10.77/10.93 tff(meet_type, type, (
% 10.77/10.93 meet: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(tptp_fun_C_1_type, type, (
% 10.77/10.93 tptp_fun_C_1: ( $i * $i ) > $i)).
% 10.77/10.93 tff(element_type, type, (
% 10.77/10.93 element: ( $i * $i ) > $o)).
% 10.77/10.93 tff(the_carrier_type, type, (
% 10.77/10.93 the_carrier: $i > $i)).
% 10.77/10.93 tff(lower_bounded_semilattstr_type, type, (
% 10.77/10.93 lower_bounded_semilattstr: $i > $o)).
% 10.77/10.93 tff(tptp_fun_B_0_type, type, (
% 10.77/10.93 tptp_fun_B_0: $i > $i)).
% 10.77/10.93 tff(set_intersection2_type, type, (
% 10.77/10.93 set_intersection2: ( $i * $i ) > $i)).
% 10.77/10.93 tff(tptp_fun_A_12_type, type, (
% 10.77/10.93 tptp_fun_A_12: $i)).
% 10.77/10.93 tff(apply_binary_as_element_type, type, (
% 10.77/10.93 apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 10.77/10.93 tff(bottom_of_semilattstr_type, type, (
% 10.77/10.93 bottom_of_semilattstr: $i > $i)).
% 10.77/10.93 tff(the_L_meet_type, type, (
% 10.77/10.93 the_L_meet: $i > $i)).
% 10.77/10.93 tff(latt_str_of_type, type, (
% 10.77/10.93 latt_str_of: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(the_L_join_type, type, (
% 10.77/10.93 the_L_join: $i > $i)).
% 10.77/10.93 tff(latt_str_type, type, (
% 10.77/10.93 latt_str: $i > $o)).
% 10.77/10.93 tff(tptp_fun_B_13_type, type, (
% 10.77/10.93 tptp_fun_B_13: $i > $i)).
% 10.77/10.93 tff(empty_type, type, (
% 10.77/10.93 empty: $i > $o)).
% 10.77/10.93 tff(powerset_type, type, (
% 10.77/10.93 powerset: $i > $i)).
% 10.77/10.93 tff(set_union2_type, type, (
% 10.77/10.93 set_union2: ( $i * $i ) > $i)).
% 10.77/10.93 tff(join_type, type, (
% 10.77/10.93 join: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(subset_intersection2_type, type, (
% 10.77/10.93 subset_intersection2: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(apply_binary_type, type, (
% 10.77/10.93 apply_binary: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(subset_union2_type, type, (
% 10.77/10.93 subset_union2: ( $i * $i * $i ) > $i)).
% 10.77/10.93 tff(tptp_fun_D_3_type, type, (
% 10.77/10.93 tptp_fun_D_3: ( $i * $i ) > $i)).
% 10.77/10.93 tff(tptp_fun_C_2_type, type, (
% 10.77/10.93 tptp_fun_C_2: ( $i * $i ) > $i)).
% 10.77/10.93 tff(quasi_total_type, type, (
% 10.77/10.93 quasi_total: ( $i * $i * $i ) > $o)).
% 10.77/10.93 tff(cartesian_product2_type, type, (
% 10.77/10.93 cartesian_product2: ( $i * $i ) > $i)).
% 10.77/10.93 tff(v2_binop_1_type, type, (
% 10.77/10.93 v2_binop_1: ( $i * $i ) > $o)).
% 10.77/10.93 tff(v1_partfun1_type, type, (
% 10.77/10.93 v1_partfun1: ( $i * $i * $i ) > $o)).
% 10.77/10.93 tff(relation_type, type, (
% 10.77/10.93 relation: $i > $o)).
% 10.77/10.93 tff(function_type, type, (
% 10.77/10.93 function: $i > $o)).
% 10.77/10.93 tff(relation_of2_type, type, (
% 10.77/10.93 relation_of2: ( $i * $i * $i ) > $o)).
% 10.77/10.93 tff(relation_of2_as_subset_type, type, (
% 10.77/10.93 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 10.77/10.93 tff(empty_set_type, type, (
% 10.77/10.93 empty_set: $i)).
% 10.77/10.93 tff(1,plain,
% 10.77/10.93 (^[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))))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(2,plain,
% 10.77/10.93 (![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))))) <=> ![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)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[1])).
% 10.77/10.93 tff(3,plain,
% 10.77/10.93 (^[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))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))) | (~join_commutative(boole_lattice(A))) | (~join_associative(boole_lattice(A))) | (~meet_commutative(boole_lattice(A))) | (~meet_associative(boole_lattice(A))) | (~meet_absorbing(boole_lattice(A))) | (~join_absorbing(boole_lattice(A))) | (~lattice(boole_lattice(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(4,plain,
% 10.77/10.93 (![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))) <=> ![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)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[3])).
% 10.77/10.93 tff(5,plain,
% 10.77/10.93 (![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))) <=> ![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)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(6,plain,
% 10.77/10.93 (^[A: $i] : 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)))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(7,plain,
% 10.77/10.93 (![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))) <=> ![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)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[6])).
% 10.77/10.93 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)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc2_lattice3')).
% 10.77/10.93 tff(9,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[8, 7])).
% 10.77/10.93 tff(10,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[9, 5])).
% 10.77/10.93 tff(11,plain,(
% 10.77/10.93 ![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)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[10])).
% 10.77/10.93 tff(12,plain,
% 10.77/10.93 (![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)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[11, 4])).
% 10.77/10.93 tff(13,plain,
% 10.77/10.93 (![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)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[12, 2])).
% 10.77/10.93 tff(14,plain,
% 10.77/10.93 ((~![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)))))) | (~(empty_carrier(boole_lattice(A!20)) | (~strict_latt_str(boole_lattice(A!20))) | (~join_commutative(boole_lattice(A!20))) | (~join_associative(boole_lattice(A!20))) | (~meet_commutative(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~meet_absorbing(boole_lattice(A!20))) | (~join_absorbing(boole_lattice(A!20))) | (~lattice(boole_lattice(A!20)))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(15,plain,
% 10.77/10.93 (~(empty_carrier(boole_lattice(A!20)) | (~strict_latt_str(boole_lattice(A!20))) | (~join_commutative(boole_lattice(A!20))) | (~join_associative(boole_lattice(A!20))) | (~meet_commutative(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~meet_absorbing(boole_lattice(A!20))) | (~join_absorbing(boole_lattice(A!20))) | (~lattice(boole_lattice(A!20))))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[14, 13])).
% 10.77/10.93 tff(16,plain,
% 10.77/10.93 ((empty_carrier(boole_lattice(A!20)) | (~strict_latt_str(boole_lattice(A!20))) | (~join_commutative(boole_lattice(A!20))) | (~join_associative(boole_lattice(A!20))) | (~meet_commutative(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~meet_absorbing(boole_lattice(A!20))) | (~join_absorbing(boole_lattice(A!20))) | (~lattice(boole_lattice(A!20)))) | (~empty_carrier(boole_lattice(A!20)))),
% 10.77/10.93 inference(tautology,[status(thm)],[])).
% 10.77/10.93 tff(17,plain,
% 10.77/10.93 (~empty_carrier(boole_lattice(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[16, 15])).
% 10.77/10.93 tff(18,plain,
% 10.77/10.93 (^[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))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(19,plain,
% 10.77/10.93 (![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)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[18])).
% 10.77/10.93 tff(20,plain,
% 10.77/10.93 (^[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))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(21,plain,
% 10.77/10.93 (![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)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[20])).
% 10.77/10.93 tff(22,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(23,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 10.77/10.93 tff(24,plain,
% 10.77/10.93 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[23, 22])).
% 10.77/10.93 tff(25,plain,(
% 10.77/10.93 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[24])).
% 10.77/10.93 tff(26,plain,
% 10.77/10.93 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[25, 21])).
% 10.77/10.93 tff(27,plain,
% 10.77/10.93 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[26, 19])).
% 10.77/10.93 tff(28,plain,
% 10.77/10.93 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20)))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(29,plain,
% 10.77/10.93 (~((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[28, 27])).
% 10.77/10.93 tff(30,plain,
% 10.77/10.93 (((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20)))) | latt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(tautology,[status(thm)],[])).
% 10.77/10.93 tff(31,plain,
% 10.77/10.93 (latt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[30, 29])).
% 10.77/10.93 tff(32,plain,
% 10.77/10.93 ((empty_carrier(boole_lattice(A!20)) | (~strict_latt_str(boole_lattice(A!20))) | (~join_commutative(boole_lattice(A!20))) | (~join_associative(boole_lattice(A!20))) | (~meet_commutative(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~meet_absorbing(boole_lattice(A!20))) | (~join_absorbing(boole_lattice(A!20))) | (~lattice(boole_lattice(A!20)))) | strict_latt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(tautology,[status(thm)],[])).
% 10.77/10.93 tff(33,plain,
% 10.77/10.93 (strict_latt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[32, 15])).
% 10.77/10.93 tff(34,plain,
% 10.77/10.93 (^[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))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(35,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[34])).
% 10.77/10.93 tff(36,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(37,plain,
% 10.77/10.93 (^[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)))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(38,plain,
% 10.77/10.93 (![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)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[37])).
% 10.77/10.93 tff(39,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')).
% 10.77/10.93 tff(40,plain,
% 10.77/10.93 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[39, 38])).
% 10.77/10.93 tff(41,plain,
% 10.77/10.93 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[40, 36])).
% 10.77/10.93 tff(42,plain,(
% 10.77/10.93 ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[41])).
% 10.77/10.93 tff(43,plain,
% 10.77/10.93 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[42, 35])).
% 10.77/10.93 tff(44,plain,
% 10.77/10.93 (((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(45,plain,
% 10.77/10.93 (((boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20)))) <=> ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(46,plain,
% 10.77/10.93 (((~![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!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))))),
% 10.77/10.93 inference(monotonicity,[status(thm)],[45])).
% 10.77/10.93 tff(47,plain,
% 10.77/10.93 (((~![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!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))))) <=> ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.93 inference(transitivity,[status(thm)],[46, 44])).
% 10.77/10.93 tff(48,plain,
% 10.77/10.93 ((~![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!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(49,plain,
% 10.77/10.93 ((~![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[48, 47])).
% 10.77/10.93 tff(50,plain,
% 10.77/10.93 (boole_lattice(A!20) = latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[49, 43, 33, 31])).
% 10.77/10.93 tff(51,plain,
% 10.77/10.93 (latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))) = boole_lattice(A!20)),
% 10.77/10.93 inference(symmetry,[status(thm)],[50])).
% 10.77/10.93 tff(52,plain,
% 10.77/10.93 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) = the_carrier(boole_lattice(A!20))),
% 10.77/10.93 inference(monotonicity,[status(thm)],[51])).
% 10.77/10.93 tff(53,plain,
% 10.77/10.93 (the_carrier(boole_lattice(A!20)) = the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.93 inference(symmetry,[status(thm)],[52])).
% 10.77/10.93 tff(54,plain,
% 10.77/10.93 (^[A: $i] : refl((~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A))))) <=> (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(55,plain,
% 10.77/10.93 (![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A))))) <=> ![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[54])).
% 10.77/10.93 tff(56,plain,
% 10.77/10.93 (^[A: $i] : rewrite((element(tptp_fun_B_13(A), powerset(A)) & empty(tptp_fun_B_13(A))) <=> (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(57,plain,
% 10.77/10.93 (![A: $i] : (element(tptp_fun_B_13(A), powerset(A)) & empty(tptp_fun_B_13(A))) <=> ![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[56])).
% 10.77/10.93 tff(58,plain,
% 10.77/10.93 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B)) <=> ![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(59,axiom,(![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc2_subset_1')).
% 10.77/10.93 tff(60,plain,
% 10.77/10.93 (![A: $i] : ?[B: $i] : (element(B, powerset(A)) & empty(B))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[59, 58])).
% 10.77/10.93 tff(61,plain,(
% 10.77/10.93 ![A: $i] : (element(tptp_fun_B_13(A), powerset(A)) & empty(tptp_fun_B_13(A)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[60])).
% 10.77/10.93 tff(62,plain,
% 10.77/10.93 (![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[61, 57])).
% 10.77/10.93 tff(63,plain,
% 10.77/10.93 (![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[62, 55])).
% 10.77/10.93 tff(64,plain,
% 10.77/10.93 ((~![A: $i] : (~((~element(tptp_fun_B_13(A), powerset(A))) | (~empty(tptp_fun_B_13(A)))))) | (~((~element(tptp_fun_B_13(A!20), powerset(A!20))) | (~empty(tptp_fun_B_13(A!20)))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(65,plain,
% 10.77/10.93 (~((~element(tptp_fun_B_13(A!20), powerset(A!20))) | (~empty(tptp_fun_B_13(A!20))))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[64, 63])).
% 10.77/10.93 tff(66,plain,
% 10.77/10.93 (((~element(tptp_fun_B_13(A!20), powerset(A!20))) | (~empty(tptp_fun_B_13(A!20)))) | empty(tptp_fun_B_13(A!20))),
% 10.77/10.93 inference(tautology,[status(thm)],[])).
% 10.77/10.93 tff(67,plain,
% 10.77/10.93 (empty(tptp_fun_B_13(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[66, 65])).
% 10.77/10.93 tff(68,plain,
% 10.77/10.93 (^[A: $i, B: $i] : refl(((~empty(A)) | (~empty(B)) | (A = B)) <=> ((~empty(A)) | (~empty(B)) | (A = B)))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(69,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B)) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[68])).
% 10.77/10.93 tff(70,plain,
% 10.77/10.93 (^[A: $i, B: $i] : trans(monotonicity(rewrite((empty(A) & (~(A = B)) & empty(B)) <=> (~((~empty(A)) | (~empty(B)) | (A = B)))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> (~(~((~empty(A)) | (~empty(B)) | (A = B)))))), rewrite((~(~((~empty(A)) | (~empty(B)) | (A = B)))) <=> ((~empty(A)) | (~empty(B)) | (A = B))), ((~(empty(A) & (~(A = B)) & empty(B))) <=> ((~empty(A)) | (~empty(B)) | (A = B))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(71,plain,
% 10.77/10.93 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[70])).
% 10.77/10.93 tff(72,plain,
% 10.77/10.93 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(73,plain,
% 10.77/10.93 (^[A: $i, B: $i] : rewrite((~((empty(A) & (~(A = B))) & empty(B))) <=> (~(empty(A) & (~(A = B)) & empty(B))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(74,plain,
% 10.77/10.93 (![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B))) <=> ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[73])).
% 10.77/10.93 tff(75,axiom,(![A: $i, B: $i] : (~((empty(A) & (~(A = B))) & empty(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t8_boole')).
% 10.77/10.93 tff(76,plain,
% 10.77/10.93 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[75, 74])).
% 10.77/10.93 tff(77,plain,
% 10.77/10.93 (![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[76, 72])).
% 10.77/10.93 tff(78,plain,(
% 10.77/10.93 ![A: $i, B: $i] : (~(empty(A) & (~(A = B)) & empty(B)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[77])).
% 10.77/10.93 tff(79,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[78, 71])).
% 10.77/10.93 tff(80,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[79, 69])).
% 10.77/10.93 tff(81,plain,
% 10.77/10.93 (?[A: $i] : empty(A) <=> ?[A: $i] : empty(A)),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(82,axiom,(?[A: $i] : empty(A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rc1_xboole_0')).
% 10.77/10.93 tff(83,plain,
% 10.77/10.93 (?[A: $i] : empty(A)),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[82, 81])).
% 10.77/10.93 tff(84,plain,(
% 10.77/10.93 empty(A!12)),
% 10.77/10.93 inference(skolemize,[status(sab)],[83])).
% 10.77/10.93 tff(85,plain,
% 10.77/10.93 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!12)) | (~empty(tptp_fun_B_13(A!20))) | (A!12 = tptp_fun_B_13(A!20)))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!12)) | (~empty(tptp_fun_B_13(A!20))) | (A!12 = tptp_fun_B_13(A!20)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(86,plain,
% 10.77/10.93 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(A!12)) | (~empty(tptp_fun_B_13(A!20))) | (A!12 = tptp_fun_B_13(A!20)))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(87,plain,
% 10.77/10.93 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(A!12)) | (~empty(tptp_fun_B_13(A!20))) | (A!12 = tptp_fun_B_13(A!20))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[86, 85])).
% 10.77/10.93 tff(88,plain,
% 10.77/10.93 (A!12 = tptp_fun_B_13(A!20)),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[87, 84, 80, 67])).
% 10.77/10.93 tff(89,plain,
% 10.77/10.93 (meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.93 inference(monotonicity,[status(thm)],[51, 88])).
% 10.77/10.93 tff(90,plain,
% 10.77/10.93 (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.93 inference(symmetry,[status(thm)],[89])).
% 10.77/10.93 tff(91,plain,
% 10.77/10.93 (^[A: $i] : refl((set_intersection2(A, A) = A) <=> (set_intersection2(A, A) = A))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(92,plain,
% 10.77/10.93 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(quant_intro,[status(thm)],[91])).
% 10.77/10.93 tff(93,plain,
% 10.77/10.93 (![A: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(94,plain,
% 10.77/10.93 (![A: $i, B: $i] : (set_intersection2(A, A) = A) <=> ![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(elim_unused_vars,[status(thm)],[])).
% 10.77/10.93 tff(95,axiom,(![A: $i, B: $i] : (set_intersection2(A, A) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','idempotence_k3_xboole_0')).
% 10.77/10.93 tff(96,plain,
% 10.77/10.93 (![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[95, 94])).
% 10.77/10.93 tff(97,plain,
% 10.77/10.93 (![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[96, 93])).
% 10.77/10.93 tff(98,plain,(
% 10.77/10.93 ![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(skolemize,[status(sab)],[97])).
% 10.77/10.93 tff(99,plain,
% 10.77/10.93 (![A: $i] : (set_intersection2(A, A) = A)),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[98, 92])).
% 10.77/10.93 tff(100,plain,
% 10.77/10.93 ((~![A: $i] : (set_intersection2(A, A) = A)) | (set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(101,plain,
% 10.77/10.93 (set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[100, 99])).
% 10.77/10.93 tff(102,plain,
% 10.77/10.93 (^[A: $i] : refl(((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(103,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[102])).
% 10.77/10.93 tff(104,plain,
% 10.77/10.93 (^[A: $i] : rewrite(((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(105,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[104])).
% 10.77/10.93 tff(106,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(107,plain,
% 10.77/10.93 (^[A: $i] : rewrite((latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(108,plain,
% 10.77/10.93 (![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A))) <=> ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[107])).
% 10.77/10.93 tff(109,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 10.77/10.93 tff(110,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[109, 108])).
% 10.77/10.93 tff(111,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[110, 106])).
% 10.77/10.93 tff(112,plain,(
% 10.77/10.93 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[111])).
% 10.77/10.93 tff(113,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[112, 105])).
% 10.77/10.93 tff(114,plain,
% 10.77/10.93 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[113, 103])).
% 10.77/10.93 tff(115,plain,
% 10.77/10.93 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(boole_lattice(A!20))) | (~((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20))))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(boole_lattice(A!20))) | (~((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20))))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(116,plain,
% 10.77/10.93 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(boole_lattice(A!20))) | (~((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20))))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(117,plain,
% 10.77/10.93 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(boole_lattice(A!20))) | (~((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20)))))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[116, 115])).
% 10.77/10.93 tff(118,plain,
% 10.77/10.93 (~((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20))))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[117, 114, 31])).
% 10.77/10.93 tff(119,plain,
% 10.77/10.93 (((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20)))) | meet_semilatt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(tautology,[status(thm)],[])).
% 10.77/10.93 tff(120,plain,
% 10.77/10.93 (meet_semilatt_str(boole_lattice(A!20))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[119, 118])).
% 10.77/10.93 tff(121,plain,
% 10.77/10.93 (^[A: $i] : refl((empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A))) <=> (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(122,plain,
% 10.77/10.93 (![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[121])).
% 10.77/10.93 tff(123,plain,
% 10.77/10.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_semilatt_str(A)) <=> (~(empty_carrier(A) | (~meet_semilatt_str(A))))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~meet_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~meet_semilatt_str(A))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_semilatt_str(A))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))) <=> ((empty_carrier(A) | (~meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))))), rewrite(((empty_carrier(A) | (~meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))) <=> (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))) <=> (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(124,plain,
% 10.77/10.93 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))) <=> ![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[123])).
% 10.77/10.93 tff(125,plain,
% 10.77/10.93 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A)))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(126,plain,
% 10.77/10.93 (^[A: $i] : rewrite((((~empty_carrier(A)) & meet_semilatt_str(A)) => element(bottom_of_semilattstr(A), the_carrier(A))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(127,plain,
% 10.77/10.93 (![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => element(bottom_of_semilattstr(A), the_carrier(A))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A)))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[126])).
% 10.77/10.93 tff(128,axiom,(![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => element(bottom_of_semilattstr(A), the_carrier(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_lattices')).
% 10.77/10.93 tff(129,plain,
% 10.77/10.93 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[128, 127])).
% 10.77/10.93 tff(130,plain,
% 10.77/10.93 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[129, 125])).
% 10.77/10.93 tff(131,plain,(
% 10.77/10.93 ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | element(bottom_of_semilattstr(A), the_carrier(A)))),
% 10.77/10.93 inference(skolemize,[status(sab)],[130])).
% 10.77/10.93 tff(132,plain,
% 10.77/10.93 (![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[131, 124])).
% 10.77/10.93 tff(133,plain,
% 10.77/10.93 (![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[132, 122])).
% 10.77/10.93 tff(134,plain,
% 10.77/10.93 (((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))) <=> ((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(135,plain,
% 10.77/10.93 ((empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20)))) <=> ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(136,plain,
% 10.77/10.93 (((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))))) <=> ((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))),
% 10.77/10.93 inference(monotonicity,[status(thm)],[135])).
% 10.77/10.93 tff(137,plain,
% 10.77/10.93 (((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))))) <=> ((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))),
% 10.77/10.93 inference(transitivity,[status(thm)],[136, 134])).
% 10.77/10.93 tff(138,plain,
% 10.77/10.93 ((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))))),
% 10.77/10.93 inference(quant_inst,[status(thm)],[])).
% 10.77/10.93 tff(139,plain,
% 10.77/10.93 ((~![A: $i] : (empty_carrier(A) | element(bottom_of_semilattstr(A), the_carrier(A)) | (~meet_semilatt_str(A)))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.93 inference(modus_ponens,[status(thm)],[138, 137])).
% 10.77/10.93 tff(140,plain,
% 10.77/10.93 ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[139, 133])).
% 10.77/10.93 tff(141,plain,
% 10.77/10.93 (element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.93 inference(unit_resolution,[status(thm)],[140, 120, 17])).
% 10.77/10.93 tff(142,plain,
% 10.77/10.93 (^[A: $i, B: $i] : refl(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(143,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[142])).
% 10.77/10.93 tff(144,plain,
% 10.77/10.93 (^[A: $i, B: $i] : rewrite(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(145,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[144])).
% 10.77/10.93 tff(146,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.93 inference(transitivity,[status(thm)],[145, 143])).
% 10.77/10.93 tff(147,plain,
% 10.77/10.93 (^[A: $i, B: $i] : rewrite(((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(148,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[147])).
% 10.77/10.93 tff(149,plain,
% 10.77/10.93 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 10.77/10.93 inference(rewrite,[status(thm)],[])).
% 10.77/10.93 tff(150,plain,
% 10.77/10.93 (^[A: $i, B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))) <=> ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), (![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))) <=> ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))))), rewrite((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), ((element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.93 inference(bind,[status(th)],[])).
% 10.77/10.93 tff(151,plain,
% 10.77/10.93 (![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C))))) <=> ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 10.77/10.93 inference(quant_intro,[status(thm)],[150])).
% 10.77/10.93 tff(152,axiom,(![A: $i, B: $i] : (element(B, the_carrier(boole_lattice(A))) => ![C: $i] : (element(C, the_carrier(boole_lattice(A))) => ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_lattice3')).
% 10.77/10.94 tff(153,plain,
% 10.77/10.94 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[152, 151])).
% 10.77/10.94 tff(154,plain,
% 10.77/10.94 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[153, 149])).
% 10.77/10.94 tff(155,plain,(
% 10.77/10.94 ![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | ((join(boole_lattice(A), B, C) = set_union2(B, C)) & (meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))),
% 10.77/10.94 inference(skolemize,[status(sab)],[154])).
% 10.77/10.94 tff(156,plain,
% 10.77/10.94 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[155, 148])).
% 10.77/10.94 tff(157,plain,
% 10.77/10.94 (![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[156, 146])).
% 10.77/10.94 tff(158,plain,
% 10.77/10.94 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C)))))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(159,plain,
% 10.77/10.94 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C)))))))),
% 10.77/10.94 inference(quant_inst,[status(thm)],[])).
% 10.77/10.94 tff(160,plain,
% 10.77/10.94 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[159, 158])).
% 10.77/10.94 tff(161,plain,
% 10.77/10.94 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[160, 157, 141])).
% 10.77/10.94 tff(162,plain,
% 10.77/10.94 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(163,plain,
% 10.77/10.94 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.77/10.94 inference(quant_inst,[status(thm)],[])).
% 10.77/10.94 tff(164,plain,
% 10.77/10.94 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), C))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[163, 162])).
% 10.77/10.94 tff(165,plain,
% 10.77/10.94 (~((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[164, 141, 161])).
% 10.77/10.94 tff(166,plain,
% 10.77/10.94 (((~(join(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_union2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))),
% 10.77/10.94 inference(tautology,[status(thm)],[])).
% 10.77/10.94 tff(167,plain,
% 10.77/10.94 (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = set_intersection2(bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[166, 165])).
% 10.77/10.94 tff(168,plain,
% 10.77/10.94 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))))),
% 10.77/10.94 inference(bind,[status(th)],[])).
% 10.77/10.94 tff(169,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(quant_intro,[status(thm)],[168])).
% 10.77/10.94 tff(170,plain,
% 10.77/10.94 (^[A: $i] : refl((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))))),
% 10.77/10.94 inference(bind,[status(th)],[])).
% 10.77/10.94 tff(171,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(quant_intro,[status(thm)],[170])).
% 10.77/10.94 tff(172,plain,
% 10.77/10.94 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))))),
% 10.77/10.94 inference(bind,[status(th)],[])).
% 10.77/10.94 tff(173,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(quant_intro,[status(thm)],[172])).
% 10.77/10.94 tff(174,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(transitivity,[status(thm)],[173, 171])).
% 10.77/10.94 tff(175,plain,
% 10.77/10.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_semilatt_str(A)) <=> (~(empty_carrier(A) | (~meet_semilatt_str(A))))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~meet_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~meet_semilatt_str(A))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_semilatt_str(A))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ((empty_carrier(A) | (~meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))))), rewrite(((empty_carrier(A) | (~meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))))),
% 10.77/10.94 inference(bind,[status(th)],[])).
% 10.77/10.94 tff(176,plain,
% 10.77/10.94 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(quant_intro,[status(thm)],[175])).
% 10.77/10.94 tff(177,plain,
% 10.77/10.94 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(178,plain,
% 10.77/10.94 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))) <=> ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))), (![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> (((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))))), rewrite((((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))))),
% 10.77/10.94 inference(bind,[status(th)],[])).
% 10.77/10.94 tff(179,plain,
% 10.77/10.94 (![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(quant_intro,[status(thm)],[178])).
% 10.77/10.94 tff(180,axiom,(![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattices')).
% 10.77/10.94 tff(181,plain,
% 10.77/10.94 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[180, 179])).
% 10.77/10.94 tff(182,plain,
% 10.77/10.94 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[181, 177])).
% 10.77/10.94 tff(183,plain,(
% 10.77/10.94 ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(skolemize,[status(sab)],[182])).
% 10.77/10.94 tff(184,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[183, 176])).
% 10.77/10.94 tff(185,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))) | (~meet_semilatt_str(A)))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[184, 174])).
% 10.77/10.94 tff(186,plain,
% 10.77/10.94 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[185, 169])).
% 10.77/10.94 tff(187,plain,
% 10.77/10.94 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))) | empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C)))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(188,plain,
% 10.77/10.94 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C)))))),
% 10.77/10.94 inference(quant_inst,[status(thm)],[])).
% 10.77/10.94 tff(189,plain,
% 10.77/10.94 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (meet(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_meet(A), B, C)))))) | empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[188, 187])).
% 10.77/10.94 tff(190,plain,
% 10.77/10.94 ((~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[189, 186, 17])).
% 10.77/10.94 tff(191,plain,
% 10.77/10.94 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[190, 120])).
% 10.77/10.94 tff(192,plain,
% 10.77/10.94 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(193,plain,
% 10.77/10.94 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C))))),
% 10.77/10.94 inference(quant_inst,[status(thm)],[])).
% 10.77/10.94 tff(194,plain,
% 10.77/10.94 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[193, 192])).
% 10.77/10.94 tff(195,plain,
% 10.77/10.94 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[194, 141, 191])).
% 10.77/10.94 tff(196,plain,
% 10.77/10.94 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))),
% 10.77/10.94 inference(rewrite,[status(thm)],[])).
% 10.77/10.94 tff(197,plain,
% 10.77/10.94 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))),
% 10.77/10.94 inference(quant_inst,[status(thm)],[])).
% 10.77/10.94 tff(198,plain,
% 10.77/10.94 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), C)))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[197, 196])).
% 10.77/10.94 tff(199,plain,
% 10.77/10.94 (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.77/10.94 inference(unit_resolution,[status(thm)],[198, 141, 195])).
% 10.77/10.94 tff(200,plain,
% 10.77/10.94 (apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.77/10.94 inference(symmetry,[status(thm)],[199])).
% 10.77/10.94 tff(201,plain,
% 10.77/10.94 (apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))),
% 10.77/10.94 inference(transitivity,[status(thm)],[200, 167, 101])).
% 10.77/10.94 tff(202,plain,
% 10.77/10.94 (element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20))) <=> element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.94 inference(monotonicity,[status(thm)],[201])).
% 10.77/10.94 tff(203,plain,
% 10.77/10.94 (element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) <=> element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))),
% 10.77/10.94 inference(symmetry,[status(thm)],[202])).
% 10.77/10.94 tff(204,plain,
% 10.77/10.94 (element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))),
% 10.77/10.94 inference(modus_ponens,[status(thm)],[141, 203])).
% 10.77/10.94 tff(205,assumption,(![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))), introduced(assumption)).
% 10.77/10.94 tff(206,plain,
% 10.77/10.94 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))))),
% 10.77/10.95 inference(rewrite,[status(thm)],[])).
% 10.77/10.95 tff(207,plain,
% 10.77/10.95 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))))),
% 10.77/10.95 inference(quant_inst,[status(thm)],[])).
% 10.77/10.95 tff(208,plain,
% 10.77/10.95 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[207, 206])).
% 10.77/10.95 tff(209,plain,
% 10.77/10.95 (~((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.77/10.95 inference(unit_resolution,[status(thm)],[208, 205, 204])).
% 10.77/10.95 tff(210,plain,
% 10.77/10.95 (((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))))))) | element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.95 inference(tautology,[status(thm)],[])).
% 10.77/10.95 tff(211,plain,
% 10.77/10.95 (element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.95 inference(unit_resolution,[status(thm)],[210, 209])).
% 10.77/10.95 tff(212,plain,
% 10.77/10.95 (^[A: $i, B: $i] : trans(monotonicity(rewrite((~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))) <=> (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))))))), (((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))))))))), rewrite(((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))), (((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(213,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[212])).
% 10.77/10.95 tff(214,plain,
% 10.77/10.95 (^[A: $i, B: $i] : refl(((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(215,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[214])).
% 10.77/10.95 tff(216,plain,
% 10.77/10.95 (^[A: $i, B: $i] : rewrite(((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(217,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[216])).
% 10.77/10.95 tff(218,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(transitivity,[status(thm)],[217, 215])).
% 10.77/10.95 tff(219,plain,
% 10.77/10.95 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((strict_latt_str(B) & latt_str(B)) <=> (~((~strict_latt_str(B)) | (~latt_str(B))))), ((~(strict_latt_str(B) & latt_str(B))) <=> (~(~((~strict_latt_str(B)) | (~latt_str(B))))))), rewrite((~(~((~strict_latt_str(B)) | (~latt_str(B))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)))), ((~(strict_latt_str(B) & latt_str(B))) <=> ((~strict_latt_str(B)) | (~latt_str(B))))), trans(monotonicity(rewrite(((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) <=> ((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))), trans(monotonicity(trans(monotonicity(rewrite((~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))) <=> (~((~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))), ((element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))) <=> (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))), rewrite((element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))) <=> (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))), ((element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))) <=> (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))), (((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))), rewrite(((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))), (((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))), ((((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))) <=> (((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))), rewrite((((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) <=> (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))), ((((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))) <=> (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))), (((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) <=> (((~strict_latt_str(B)) | (~latt_str(B))) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))))), rewrite((((~strict_latt_str(B)) | (~latt_str(B))) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))), (((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(220,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) <=> ![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[219])).
% 10.77/10.95 tff(221,plain,
% 10.77/10.95 (^[A: $i, B: $i] : rewrite(((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | ((~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))) <=> ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(222,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | ((~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))) <=> ![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[221])).
% 10.77/10.95 tff(223,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))) <=> ![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))),
% 10.77/10.95 inference(rewrite,[status(thm)],[])).
% 10.77/10.95 tff(224,plain,
% 10.77/10.95 (^[A: $i, B: $i] : trans(monotonicity(rewrite(((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : (element(C, powerset(A)) => ![D: $i] : (element(D, powerset(A)) => ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) <=> ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))), (((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : (element(C, powerset(A)) => ![D: $i] : (element(D, powerset(A)) => ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))) <=> ((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))), rewrite(((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))) <=> ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))), (((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : (element(C, powerset(A)) => ![D: $i] : (element(D, powerset(A)) => ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))) <=> ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))))),
% 10.77/10.95 inference(bind,[status(th)],[])).
% 10.77/10.95 tff(225,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : (element(C, powerset(A)) => ![D: $i] : (element(D, powerset(A)) => ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))) <=> ![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))),
% 10.77/10.95 inference(quant_intro,[status(thm)],[224])).
% 10.77/10.95 tff(226,axiom,(![A: $i, B: $i] : ((strict_latt_str(B) & latt_str(B)) => ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : (element(C, powerset(A)) => ![D: $i] : (element(D, powerset(A)) => ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_lattice3')).
% 10.77/10.95 tff(227,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[226, 225])).
% 10.77/10.95 tff(228,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | ((B = boole_lattice(A)) <=> ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[227, 223])).
% 10.77/10.95 tff(229,plain,(
% 10.77/10.95 ![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | ((~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))),
% 10.77/10.95 inference(skolemize,[status(sab)],[228])).
% 10.77/10.95 tff(230,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~(strict_latt_str(B) & latt_str(B))) | (((~(B = boole_lattice(A))) | ((the_carrier(B) = powerset(A)) & ![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | ((apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D)) & (apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D))))))) & ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_2(B, A), powerset(A)) & (~((~element(tptp_fun_D_3(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A))))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[229, 222])).
% 10.77/10.95 tff(231,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[230, 220])).
% 10.77/10.95 tff(232,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))) | (~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[231, 218])).
% 10.77/10.95 tff(233,plain,
% 10.77/10.95 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))),
% 10.77/10.95 inference(modus_ponens,[status(thm)],[232, 213])).
% 10.77/10.95 tff(234,plain,
% 10.77/10.95 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))) <=> ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))),
% 10.77/10.95 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(235,plain,
% 10.77/10.96 (((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20)))))) <=> ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))),
% 10.77/10.96 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(236,plain,
% 10.77/10.96 ((~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))))))))) <=> (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20)))))),
% 10.77/10.96 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(237,plain,
% 10.77/10.96 (((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D))))))))))))))) <=> ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))),
% 10.77/10.96 inference(monotonicity,[status(thm)],[236])).
% 10.77/10.96 tff(238,plain,
% 10.77/10.96 (((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D))))))))))))))) <=> ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))),
% 10.77/10.96 inference(transitivity,[status(thm)],[237, 235])).
% 10.77/10.96 tff(239,plain,
% 10.77/10.96 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))))))))))) <=> ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20)))))))),
% 10.77/10.96 inference(monotonicity,[status(thm)],[238])).
% 10.77/10.96 tff(240,plain,
% 10.77/10.96 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))))))))))) <=> ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))))),
% 10.77/10.96 inference(transitivity,[status(thm)],[239, 234])).
% 10.77/10.96 tff(241,plain,
% 10.77/10.96 ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | ((~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~((boole_lattice(A!20) = boole_lattice(A!20)) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~((~element(tptp_fun_C_2(boole_lattice(A!20), A!20), powerset(A!20))) | (~element(tptp_fun_D_3(boole_lattice(A!20), A!20), powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_union2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)) = subset_intersection2(A!20, tptp_fun_C_2(boole_lattice(A!20), A!20), tptp_fun_D_3(boole_lattice(A!20), A!20)))))))))) | (~((~(boole_lattice(A!20) = boole_lattice(A!20))) | (~((~(the_carrier(boole_lattice(A!20)) = powerset(A!20))) | (~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))))))))))),
% 10.77/10.96 inference(quant_inst,[status(thm)],[])).
% 10.77/10.96 tff(242,plain,
% 10.77/10.96 ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_2(B, A), powerset(A))) | (~element(tptp_fun_D_3(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_union2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)) = subset_intersection2(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)))))))))) | (~((~(B = boole_lattice(A))) | (~((~(the_carrier(B) = powerset(A))) | (~![C: $i] : ((~element(C, powerset(A))) | ![D: $i] : ((~element(D, powerset(A))) | (~((~(apply_binary(the_L_join(B), C, D) = subset_union2(A, C, D))) | (~(apply_binary(the_L_meet(B), C, D) = subset_intersection2(A, C, D)))))))))))))))) | (~strict_latt_str(boole_lattice(A!20))) | (~latt_str(boole_lattice(A!20))) | (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20)))))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[241, 240])).
% 10.77/10.96 tff(243,plain,
% 10.77/10.96 (~((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20))))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[242, 233, 33, 31])).
% 10.77/10.96 tff(244,plain,
% 10.77/10.96 (((~![C: $i] : ((~element(C, powerset(A!20))) | ![D: $i] : ((~element(D, powerset(A!20))) | (~((~(apply_binary(the_L_join(boole_lattice(A!20)), C, D) = subset_union2(A!20, C, D))) | (~(apply_binary(the_L_meet(boole_lattice(A!20)), C, D) = subset_intersection2(A!20, C, D)))))))) | (~(the_carrier(boole_lattice(A!20)) = powerset(A!20)))) | (the_carrier(boole_lattice(A!20)) = powerset(A!20))),
% 10.77/10.96 inference(tautology,[status(thm)],[])).
% 10.77/10.96 tff(245,plain,
% 10.77/10.96 (the_carrier(boole_lattice(A!20)) = powerset(A!20)),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[244, 243])).
% 10.77/10.96 tff(246,plain,
% 10.77/10.96 (element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20))) <=> element(tptp_fun_B_13(A!20), powerset(A!20))),
% 10.77/10.96 inference(monotonicity,[status(thm)],[245])).
% 10.77/10.96 tff(247,plain,
% 10.77/10.96 (element(tptp_fun_B_13(A!20), powerset(A!20)) <=> element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))),
% 10.77/10.96 inference(symmetry,[status(thm)],[246])).
% 10.77/10.96 tff(248,plain,
% 10.77/10.96 (((~element(tptp_fun_B_13(A!20), powerset(A!20))) | (~empty(tptp_fun_B_13(A!20)))) | element(tptp_fun_B_13(A!20), powerset(A!20))),
% 10.77/10.96 inference(tautology,[status(thm)],[])).
% 10.77/10.96 tff(249,plain,
% 10.77/10.96 (element(tptp_fun_B_13(A!20), powerset(A!20))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[248, 65])).
% 10.77/10.96 tff(250,plain,
% 10.77/10.96 (element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[249, 247])).
% 10.77/10.96 tff(251,plain,
% 10.77/10.96 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C)))))))),
% 10.77/10.96 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(252,plain,
% 10.77/10.96 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C)))))))),
% 10.77/10.96 inference(quant_inst,[status(thm)],[])).
% 10.77/10.96 tff(253,plain,
% 10.77/10.96 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[252, 251])).
% 10.77/10.96 tff(254,plain,
% 10.77/10.96 ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[253, 157])).
% 10.77/10.96 tff(255,plain,
% 10.77/10.96 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[254, 250])).
% 10.77/10.96 tff(256,plain,
% 10.77/10.96 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | ((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))))))),
% 10.77/10.96 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(257,plain,
% 10.77/10.96 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | ((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))))))),
% 10.77/10.96 inference(quant_inst,[status(thm)],[])).
% 10.77/10.96 tff(258,plain,
% 10.77/10.96 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))))))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[257, 256])).
% 10.77/10.96 tff(259,plain,
% 10.77/10.96 (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[258, 255, 211])).
% 10.77/10.96 tff(260,plain,
% 10.77/10.96 (((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))),
% 10.77/10.96 inference(tautology,[status(thm)],[])).
% 10.77/10.96 tff(261,plain,
% 10.77/10.96 (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.96 inference(unit_resolution,[status(thm)],[260, 259])).
% 10.77/10.96 tff(262,plain,
% 10.77/10.96 (set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.96 inference(symmetry,[status(thm)],[261])).
% 10.77/10.96 tff(263,plain,
% 10.77/10.96 (tptp_fun_B_13(A!20) = A!12),
% 10.77/10.96 inference(symmetry,[status(thm)],[88])).
% 10.77/10.96 tff(264,plain,
% 10.77/10.96 (set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.96 inference(monotonicity,[status(thm)],[263])).
% 10.77/10.96 tff(265,plain,
% 10.77/10.96 (set_intersection2(A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.96 inference(symmetry,[status(thm)],[264])).
% 10.77/10.96 tff(266,plain,
% 10.77/10.96 (^[A: $i, B: $i] : refl((set_intersection2(A, B) = set_intersection2(B, A)) <=> (set_intersection2(A, B) = set_intersection2(B, A)))),
% 10.77/10.96 inference(bind,[status(th)],[])).
% 10.77/10.96 tff(267,plain,
% 10.77/10.96 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 10.77/10.96 inference(quant_intro,[status(thm)],[266])).
% 10.77/10.96 tff(268,plain,
% 10.77/10.96 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A)) <=> ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 10.77/10.96 inference(rewrite,[status(thm)],[])).
% 10.77/10.96 tff(269,axiom,(![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_xboole_0')).
% 10.77/10.96 tff(270,plain,
% 10.77/10.96 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[269, 268])).
% 10.77/10.96 tff(271,plain,(
% 10.77/10.96 ![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 10.77/10.96 inference(skolemize,[status(sab)],[270])).
% 10.77/10.96 tff(272,plain,
% 10.77/10.96 (![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))),
% 10.77/10.96 inference(modus_ponens,[status(thm)],[271, 267])).
% 10.77/10.96 tff(273,plain,
% 10.77/10.96 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))),
% 10.77/10.97 inference(quant_inst,[status(thm)],[])).
% 10.77/10.97 tff(274,plain,
% 10.77/10.97 (set_intersection2(A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[273, 272])).
% 10.77/10.97 tff(275,plain,
% 10.77/10.97 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12) = set_intersection2(A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(symmetry,[status(thm)],[274])).
% 10.77/10.97 tff(276,plain,
% 10.77/10.97 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12) = meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(transitivity,[status(thm)],[275, 265, 262, 90])).
% 10.77/10.97 tff(277,plain,
% 10.77/10.97 (element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20))) <=> element(meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[276, 53])).
% 10.77/10.97 tff(278,plain,
% 10.77/10.97 (element(meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) <=> element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))),
% 10.77/10.97 inference(symmetry,[status(thm)],[277])).
% 10.77/10.97 tff(279,plain,
% 10.77/10.97 (powerset(A!20) = the_carrier(boole_lattice(A!20))),
% 10.77/10.97 inference(symmetry,[status(thm)],[245])).
% 10.77/10.97 tff(280,plain,
% 10.77/10.97 (powerset(A!20) = the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.97 inference(transitivity,[status(thm)],[279, 53])).
% 10.77/10.97 tff(281,plain,
% 10.77/10.97 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(282,plain,
% 10.77/10.97 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C))))),
% 10.77/10.97 inference(quant_inst,[status(thm)],[])).
% 10.77/10.97 tff(283,plain,
% 10.77/10.97 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), B, C))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[282, 281])).
% 10.77/10.97 tff(284,plain,
% 10.77/10.97 ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[283, 191])).
% 10.77/10.97 tff(285,plain,
% 10.77/10.97 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[284, 250])).
% 10.77/10.97 tff(286,plain,
% 10.77/10.97 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))) | ((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(287,plain,
% 10.77/10.97 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))) | ((~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))))),
% 10.77/10.97 inference(quant_inst,[status(thm)],[])).
% 10.77/10.97 tff(288,plain,
% 10.77/10.97 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), C)))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[287, 286])).
% 10.77/10.97 tff(289,plain,
% 10.77/10.97 (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[288, 285, 211])).
% 10.77/10.97 tff(290,plain,
% 10.77/10.97 (apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(symmetry,[status(thm)],[289])).
% 10.77/10.97 tff(291,plain,
% 10.77/10.97 (apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), tptp_fun_B_13(A!20), tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[279, 279, 279, 88])).
% 10.77/10.97 tff(292,plain,
% 10.77/10.97 (apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))) = meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)))),
% 10.77/10.97 inference(transitivity,[status(thm)],[291, 290, 90])).
% 10.77/10.97 tff(293,plain,
% 10.77/10.97 (element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)) <=> element(meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[292, 280])).
% 10.77/10.97 tff(294,plain,
% 10.77/10.97 (element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20)) <=> element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[279])).
% 10.77/10.97 tff(295,plain,
% 10.77/10.97 (element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) <=> element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))),
% 10.77/10.97 inference(symmetry,[status(thm)],[294])).
% 10.77/10.97 tff(296,plain,
% 10.77/10.97 (element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[211, 295])).
% 10.77/10.97 tff(297,plain,
% 10.77/10.97 (element(A!12, powerset(A!20)) <=> element(tptp_fun_B_13(A!20), powerset(A!20))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[88])).
% 10.77/10.97 tff(298,plain,
% 10.77/10.97 (element(tptp_fun_B_13(A!20), powerset(A!20)) <=> element(A!12, powerset(A!20))),
% 10.77/10.97 inference(symmetry,[status(thm)],[297])).
% 10.77/10.97 tff(299,plain,
% 10.77/10.97 (element(A!12, powerset(A!20))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[249, 298])).
% 10.77/10.97 tff(300,plain,
% 10.77/10.97 (^[A: $i] : refl((~empty(powerset(A))) <=> (~empty(powerset(A))))),
% 10.77/10.97 inference(bind,[status(th)],[])).
% 10.77/10.97 tff(301,plain,
% 10.77/10.97 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 10.77/10.97 inference(quant_intro,[status(thm)],[300])).
% 10.77/10.97 tff(302,plain,
% 10.77/10.97 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(303,axiom,(![A: $i] : (~empty(powerset(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_subset_1')).
% 10.77/10.97 tff(304,plain,
% 10.77/10.97 (![A: $i] : (~empty(powerset(A)))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[303, 302])).
% 10.77/10.97 tff(305,plain,(
% 10.77/10.97 ![A: $i] : (~empty(powerset(A)))),
% 10.77/10.97 inference(skolemize,[status(sab)],[304])).
% 10.77/10.97 tff(306,plain,
% 10.77/10.97 (![A: $i] : (~empty(powerset(A)))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[305, 301])).
% 10.77/10.97 tff(307,plain,
% 10.77/10.97 ((~![A: $i] : (~empty(powerset(A)))) | (~empty(powerset(A!20)))),
% 10.77/10.97 inference(quant_inst,[status(thm)],[])).
% 10.77/10.97 tff(308,plain,
% 10.77/10.97 (~empty(powerset(A!20))),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[307, 306])).
% 10.77/10.97 tff(309,plain,
% 10.77/10.97 (cartesian_product2(powerset(A!20), powerset(A!20)) = cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[279, 279])).
% 10.77/10.97 tff(310,plain,
% 10.77/10.97 (quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20)) <=> quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[309, 279])).
% 10.77/10.97 tff(311,plain,
% 10.77/10.97 (quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20))) <=> quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))),
% 10.77/10.97 inference(symmetry,[status(thm)],[310])).
% 10.77/10.97 tff(312,plain,
% 10.77/10.97 ((empty_carrier(boole_lattice(A!20)) | (~strict_latt_str(boole_lattice(A!20))) | (~join_commutative(boole_lattice(A!20))) | (~join_associative(boole_lattice(A!20))) | (~meet_commutative(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~meet_absorbing(boole_lattice(A!20))) | (~join_absorbing(boole_lattice(A!20))) | (~lattice(boole_lattice(A!20)))) | meet_associative(boole_lattice(A!20))),
% 10.77/10.97 inference(tautology,[status(thm)],[])).
% 10.77/10.97 tff(313,plain,
% 10.77/10.97 (meet_associative(boole_lattice(A!20))),
% 10.77/10.97 inference(unit_resolution,[status(thm)],[312, 15])).
% 10.77/10.97 tff(314,plain,
% 10.77/10.97 (^[A: $i] : refl((empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))))),
% 10.77/10.97 inference(bind,[status(th)],[])).
% 10.77/10.97 tff(315,plain,
% 10.77/10.97 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))),
% 10.77/10.97 inference(quant_intro,[status(thm)],[314])).
% 10.77/10.97 tff(316,plain,
% 10.77/10.97 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A)) <=> (~(empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))))), ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))))) <=> (empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A)))), ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))))), rewrite((relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))), (((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))))), rewrite(((empty_carrier(A) | (~meet_associative(A)) | (~meet_semilatt_str(A))) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A)))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))), (((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))))),
% 10.77/10.97 inference(bind,[status(th)],[])).
% 10.77/10.97 tff(317,plain,
% 10.77/10.97 (![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))),
% 10.77/10.97 inference(quant_intro,[status(thm)],[316])).
% 10.77/10.97 tff(318,plain,
% 10.77/10.97 (![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(319,plain,
% 10.77/10.97 (^[A: $i] : trans(monotonicity(rewrite((((~empty_carrier(A)) & meet_associative(A)) & meet_semilatt_str(A)) <=> ((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))), trans(monotonicity(trans(monotonicity(rewrite(((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))), ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) <=> ((relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))))), rewrite(((relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) <=> (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)))), ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) <=> (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A))))), (((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> ((relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), rewrite(((relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))), (((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), (((((~empty_carrier(A)) & meet_associative(A)) & meet_semilatt_str(A)) => ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> (((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A)) => (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))), rewrite((((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A)) => (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), (((((~empty_carrier(A)) & meet_associative(A)) & meet_semilatt_str(A)) => ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.97 inference(bind,[status(th)],[])).
% 10.77/10.97 tff(320,plain,
% 10.77/10.97 (![A: $i] : ((((~empty_carrier(A)) & meet_associative(A)) & meet_semilatt_str(A)) => ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.97 inference(quant_intro,[status(thm)],[319])).
% 10.77/10.97 tff(321,axiom,(![A: $i] : ((((~empty_carrier(A)) & meet_associative(A)) & meet_semilatt_str(A)) => ((((relation(the_L_meet(A)) & function(the_L_meet(A))) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & v2_binop_1(the_L_meet(A), the_carrier(A))) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc5_lattice2')).
% 10.77/10.97 tff(322,plain,
% 10.77/10.97 (![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[321, 320])).
% 10.77/10.97 tff(323,plain,
% 10.77/10.97 (![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[322, 318])).
% 10.77/10.97 tff(324,plain,(
% 10.77/10.97 ![A: $i] : ((~((~empty_carrier(A)) & meet_associative(A) & meet_semilatt_str(A))) | (relation(the_L_meet(A)) & function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & v2_binop_1(the_L_meet(A), the_carrier(A)) & v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.97 inference(skolemize,[status(sab)],[323])).
% 10.77/10.97 tff(325,plain,
% 10.77/10.97 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[324, 317])).
% 10.77/10.97 tff(326,plain,
% 10.77/10.97 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))),
% 10.77/10.97 inference(modus_ponens,[status(thm)],[325, 315])).
% 10.77/10.97 tff(327,plain,
% 10.77/10.97 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(328,plain,
% 10.77/10.97 ((empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))) <=> ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(329,plain,
% 10.77/10.97 ((~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))) <=> (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))),
% 10.77/10.97 inference(rewrite,[status(thm)],[])).
% 10.77/10.97 tff(330,plain,
% 10.77/10.97 ((empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))) <=> (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[329])).
% 10.77/10.97 tff(331,plain,
% 10.77/10.97 ((empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))) <=> ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.97 inference(transitivity,[status(thm)],[330, 328])).
% 10.77/10.97 tff(332,plain,
% 10.77/10.97 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | ((~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))))),
% 10.77/10.97 inference(monotonicity,[status(thm)],[331])).
% 10.77/10.97 tff(333,plain,
% 10.77/10.97 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.97 inference(transitivity,[status(thm)],[332, 327])).
% 10.77/10.97 tff(334,plain,
% 10.77/10.97 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))))),
% 10.77/10.98 inference(quant_inst,[status(thm)],[])).
% 10.77/10.98 tff(335,plain,
% 10.77/10.98 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~meet_associative(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation(the_L_meet(A))) | (~v1_partfun1(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~v2_binop_1(the_L_meet(A), the_carrier(A))))))) | (~meet_semilatt_str(boole_lattice(A!20))) | empty_carrier(boole_lattice(A!20)) | (~meet_associative(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[334, 333])).
% 10.77/10.98 tff(336,plain,
% 10.77/10.98 ((~meet_semilatt_str(boole_lattice(A!20))) | (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))))),
% 10.77/10.98 inference(unit_resolution,[status(thm)],[335, 326, 17, 313])).
% 10.77/10.98 tff(337,plain,
% 10.77/10.98 (~((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))))),
% 10.77/10.98 inference(unit_resolution,[status(thm)],[336, 120])).
% 10.77/10.98 tff(338,plain,
% 10.77/10.98 (((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))) | quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))),
% 10.77/10.98 inference(tautology,[status(thm)],[])).
% 10.77/10.98 tff(339,plain,
% 10.77/10.98 (quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))),
% 10.77/10.98 inference(unit_resolution,[status(thm)],[338, 337])).
% 10.77/10.98 tff(340,plain,
% 10.77/10.98 (quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[339, 311])).
% 10.77/10.98 tff(341,plain,
% 10.77/10.98 (cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) = cartesian_product2(powerset(A!20), powerset(A!20))),
% 10.77/10.98 inference(symmetry,[status(thm)],[309])).
% 10.77/10.98 tff(342,plain,
% 10.77/10.98 (relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)) <=> relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))),
% 10.77/10.98 inference(monotonicity,[status(thm)],[341])).
% 10.77/10.98 tff(343,plain,
% 10.77/10.98 (^[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)))),
% 10.77/10.98 inference(bind,[status(th)],[])).
% 10.77/10.98 tff(344,plain,
% 10.77/10.98 (![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))),
% 10.77/10.98 inference(quant_intro,[status(thm)],[343])).
% 10.77/10.98 tff(345,plain,
% 10.77/10.98 (![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))),
% 10.77/10.98 inference(rewrite,[status(thm)],[])).
% 10.77/10.98 tff(346,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')).
% 10.77/10.98 tff(347,plain,
% 10.77/10.98 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[346, 345])).
% 10.77/10.98 tff(348,plain,(
% 10.77/10.98 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 10.77/10.98 inference(skolemize,[status(sab)],[347])).
% 10.77/10.98 tff(349,plain,
% 10.77/10.98 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[348, 344])).
% 10.77/10.98 tff(350,plain,
% 10.77/10.98 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)) <=> relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)))),
% 10.77/10.98 inference(quant_inst,[status(thm)],[])).
% 10.77/10.98 tff(351,plain,
% 10.77/10.98 (relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)) <=> relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))),
% 10.77/10.98 inference(unit_resolution,[status(thm)],[350, 349])).
% 10.77/10.98 tff(352,plain,
% 10.77/10.98 (cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) = cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.77/10.98 inference(monotonicity,[status(thm)],[52, 52])).
% 10.77/10.98 tff(353,plain,
% 10.77/10.98 (cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))) = cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.98 inference(symmetry,[status(thm)],[352])).
% 10.77/10.98 tff(354,plain,
% 10.77/10.98 (the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) = the_L_meet(boole_lattice(A!20))),
% 10.77/10.98 inference(monotonicity,[status(thm)],[51])).
% 10.77/10.98 tff(355,plain,
% 10.77/10.98 (the_L_meet(boole_lattice(A!20)) = the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.98 inference(symmetry,[status(thm)],[354])).
% 10.77/10.98 tff(356,plain,
% 10.77/10.98 (relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)) <=> relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.77/10.98 inference(monotonicity,[status(thm)],[355, 353, 280])).
% 10.77/10.98 tff(357,plain,
% 10.77/10.98 (relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) <=> relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))),
% 10.77/10.98 inference(symmetry,[status(thm)],[356])).
% 10.77/10.98 tff(358,plain,
% 10.77/10.98 (meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))) <=> meet_semilatt_str(boole_lattice(A!20))),
% 10.77/10.98 inference(monotonicity,[status(thm)],[51])).
% 10.77/10.98 tff(359,plain,
% 10.77/10.98 (meet_semilatt_str(boole_lattice(A!20)) <=> meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.98 inference(symmetry,[status(thm)],[358])).
% 10.77/10.98 tff(360,plain,
% 10.77/10.98 (meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[120, 359])).
% 10.77/10.98 tff(361,plain,
% 10.77/10.98 (^[A: $i] : refl(((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))) <=> ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))))),
% 10.77/10.98 inference(bind,[status(th)],[])).
% 10.77/10.98 tff(362,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))) <=> ![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.98 inference(quant_intro,[status(thm)],[361])).
% 10.77/10.98 tff(363,plain,
% 10.77/10.98 (^[A: $i] : rewrite(((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))))),
% 10.77/10.98 inference(bind,[status(th)],[])).
% 10.77/10.98 tff(364,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.98 inference(quant_intro,[status(thm)],[363])).
% 10.77/10.98 tff(365,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.98 inference(rewrite,[status(thm)],[])).
% 10.77/10.98 tff(366,plain,
% 10.77/10.98 (^[A: $i] : trans(monotonicity(rewrite(((function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))), ((meet_semilatt_str(A) => ((function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> (meet_semilatt_str(A) => (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))), rewrite((meet_semilatt_str(A) => (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), ((meet_semilatt_str(A) => ((function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.98 inference(bind,[status(th)],[])).
% 10.77/10.98 tff(367,plain,
% 10.77/10.98 (![A: $i] : (meet_semilatt_str(A) => ((function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.98 inference(quant_intro,[status(thm)],[366])).
% 10.77/10.98 tff(368,axiom,(![A: $i] : (meet_semilatt_str(A) => ((function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 10.77/10.98 tff(369,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[368, 367])).
% 10.77/10.98 tff(370,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[369, 365])).
% 10.77/10.98 tff(371,plain,(
% 10.77/10.98 ![A: $i] : ((~meet_semilatt_str(A)) | (function(the_L_meet(A)) & quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 10.77/10.98 inference(skolemize,[status(sab)],[370])).
% 10.77/10.98 tff(372,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[371, 364])).
% 10.77/10.98 tff(373,plain,
% 10.77/10.98 (![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 10.77/10.98 inference(modus_ponens,[status(thm)],[372, 362])).
% 10.77/10.98 tff(374,plain,
% 10.77/10.98 (((~![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | ((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) | (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))))))) <=> ((~![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | (~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) | (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))))))),
% 10.77/10.98 inference(rewrite,[status(thm)],[])).
% 10.77/10.98 tff(375,plain,
% 10.77/10.98 ((~![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | ((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) | (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))))))),
% 10.77/10.98 inference(quant_inst,[status(thm)],[])).
% 10.77/10.98 tff(376,plain,
% 10.77/10.98 ((~![A: $i] : ((~meet_semilatt_str(A)) | (~((~function(the_L_meet(A))) | (~quasi_total(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_meet(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | (~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) | (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))))))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[375, 374])).
% 10.83/10.98 tff(377,plain,
% 10.83/10.98 ((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))) | (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))))))),
% 10.83/10.98 inference(unit_resolution,[status(thm)],[376, 373])).
% 10.83/10.98 tff(378,plain,
% 10.83/10.98 (~((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))))),
% 10.83/10.98 inference(unit_resolution,[status(thm)],[377, 360])).
% 10.83/10.98 tff(379,plain,
% 10.83/10.98 (((~function(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~quasi_total(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))) | (~relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))))) | relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.83/10.98 inference(tautology,[status(thm)],[])).
% 10.83/10.98 tff(380,plain,
% 10.83/10.98 (relation_of2_as_subset(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), cartesian_product2(the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.83/10.98 inference(unit_resolution,[status(thm)],[379, 378])).
% 10.83/10.98 tff(381,plain,
% 10.83/10.98 (relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[380, 357])).
% 10.83/10.98 tff(382,plain,
% 10.83/10.98 ((~(relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)) <=> relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))) | relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))),
% 10.83/10.98 inference(tautology,[status(thm)],[])).
% 10.83/10.98 tff(383,plain,
% 10.83/10.98 (relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), powerset(A!20))),
% 10.83/10.98 inference(unit_resolution,[status(thm)],[382, 381, 351])).
% 10.83/10.98 tff(384,plain,
% 10.83/10.98 (relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[383, 342])).
% 10.83/10.98 tff(385,plain,
% 10.83/10.98 (((~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~relation(the_L_meet(boole_lattice(A!20)))) | (~v1_partfun1(the_L_meet(boole_lattice(A!20)), cartesian_product2(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))), the_carrier(boole_lattice(A!20)))) | (~v2_binop_1(the_L_meet(boole_lattice(A!20)), the_carrier(boole_lattice(A!20))))) | function(the_L_meet(boole_lattice(A!20)))),
% 10.83/10.98 inference(tautology,[status(thm)],[])).
% 10.83/10.98 tff(386,plain,
% 10.83/10.98 (function(the_L_meet(boole_lattice(A!20)))),
% 10.83/10.98 inference(unit_resolution,[status(thm)],[385, 337])).
% 10.83/10.98 tff(387,plain,
% 10.83/10.98 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))) <=> (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))),
% 10.83/10.98 inference(bind,[status(th)],[])).
% 10.83/10.98 tff(388,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 10.83/10.98 inference(quant_intro,[status(thm)],[387])).
% 10.83/10.98 tff(389,plain,
% 10.83/10.98 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B)) <=> (~(empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))), ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) <=> (~(~(empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))))), rewrite((~(~(empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))) <=> (empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))), ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) <=> (empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))), (((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ((empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)))), rewrite(((empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))), (((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))))),
% 10.83/10.98 inference(bind,[status(th)],[])).
% 10.83/10.98 tff(390,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 10.83/10.98 inference(quant_intro,[status(thm)],[389])).
% 10.83/10.98 tff(391,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))),
% 10.83/10.98 inference(rewrite,[status(thm)],[])).
% 10.83/10.98 tff(392,plain,
% 10.83/10.98 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~empty(A)) & (~empty(B))) & function(D)) <=> ((~empty(A)) & (~empty(B)) & function(D))), (((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) <=> (((~empty(A)) & (~empty(B)) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)))), rewrite((((~empty(A)) & (~empty(B)) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C))), (((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C)))), ((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) <=> (((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)))), rewrite((((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C))), ((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C)))), (((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) <=> (((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)))), rewrite((((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A))), (((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A)))), ((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) <=> (((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A)) & element(F, B)))), rewrite((((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A)) & element(F, B)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))), ((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) <=> ((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B)))), (((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> (((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C)))), rewrite((((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))), (((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))))),
% 10.83/10.98 inference(bind,[status(th)],[])).
% 10.83/10.98 tff(393,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))),
% 10.83/10.98 inference(quant_intro,[status(thm)],[392])).
% 10.83/10.98 tff(394,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~empty(A)) & (~empty(B))) & function(D)) & quasi_total(D, cartesian_product2(A, B), C)) & relation_of2(D, cartesian_product2(A, B), C)) & element(E, A)) & element(F, B)) => element(apply_binary_as_element(A, B, C, D, E, F), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_binop_1')).
% 10.83/10.98 tff(395,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[394, 393])).
% 10.83/10.98 tff(396,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[395, 391])).
% 10.83/10.98 tff(397,plain,(
% 10.83/10.98 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~empty(A)) & (~empty(B)) & function(D) & quasi_total(D, cartesian_product2(A, B), C) & relation_of2(D, cartesian_product2(A, B), C) & element(E, A) & element(F, B))) | element(apply_binary_as_element(A, B, C, D, E, F), C))),
% 10.83/10.98 inference(skolemize,[status(sab)],[396])).
% 10.83/10.98 tff(398,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[397, 390])).
% 10.83/10.98 tff(399,plain,
% 10.83/10.98 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 10.83/10.98 inference(modus_ponens,[status(thm)],[398, 388])).
% 10.83/10.98 tff(400,plain,
% 10.83/10.98 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | ((~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)))),
% 10.83/10.98 inference(rewrite,[status(thm)],[])).
% 10.83/10.98 tff(401,plain,
% 10.83/10.98 ((element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)) | empty(powerset(A!20)) | empty(powerset(A!20)) | (~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20)))) <=> ((~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)))),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(402,plain,
% 10.83/10.99 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)) | empty(powerset(A!20)) | empty(powerset(A!20)) | (~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | ((~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20))))),
% 10.83/10.99 inference(monotonicity,[status(thm)],[401])).
% 10.83/10.99 tff(403,plain,
% 10.83/10.99 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)) | empty(powerset(A!20)) | empty(powerset(A!20)) | (~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)))),
% 10.83/10.99 inference(transitivity,[status(thm)],[402, 400])).
% 10.83/10.99 tff(404,plain,
% 10.83/10.99 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20)) | empty(powerset(A!20)) | empty(powerset(A!20)) | (~function(the_L_meet(boole_lattice(A!20)))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))))),
% 10.83/10.99 inference(quant_inst,[status(thm)],[])).
% 10.83/10.99 tff(405,plain,
% 10.83/10.99 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (element(apply_binary_as_element(A, B, C, D, E, F), C) | empty(B) | empty(A) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))) | (~function(the_L_meet(boole_lattice(A!20)))) | (~relation_of2(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | (~quasi_total(the_L_meet(boole_lattice(A!20)), cartesian_product2(powerset(A!20), powerset(A!20)), powerset(A!20))) | empty(powerset(A!20)) | (~element(A!12, powerset(A!20))) | (~element(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), powerset(A!20))) | element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20))),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[404, 403])).
% 10.83/10.99 tff(406,plain,
% 10.83/10.99 (element(apply_binary_as_element(powerset(A!20), powerset(A!20), powerset(A!20), the_L_meet(boole_lattice(A!20)), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), powerset(A!20))),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[405, 399, 386, 384, 340, 308, 299, 296])).
% 10.83/10.99 tff(407,plain,
% 10.83/10.99 (element(meet(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20))), A!12, tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20))), the_carrier(latt_str_of(the_carrier(boole_lattice(A!20)), the_L_join(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)))))),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[406, 293])).
% 10.83/10.99 tff(408,plain,
% 10.83/10.99 (element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[407, 278])).
% 10.83/10.99 tff(409,plain,
% 10.83/10.99 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))))))),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(410,plain,
% 10.83/10.99 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))))))),
% 10.83/10.99 inference(quant_inst,[status(thm)],[])).
% 10.83/10.99 tff(411,plain,
% 10.83/10.99 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)))))))),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[410, 409])).
% 10.83/10.99 tff(412,plain,
% 10.83/10.99 ((~element(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)))))))),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[411, 205])).
% 10.83/10.99 tff(413,plain,
% 10.83/10.99 (~((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))))),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[412, 408])).
% 10.83/10.99 tff(414,plain,
% 10.83/10.99 (empty(empty_set) <=> empty(empty_set)),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(415,axiom,(empty(empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_xboole_0')).
% 10.83/10.99 tff(416,plain,
% 10.83/10.99 (empty(empty_set)),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[415, 414])).
% 10.83/10.99 tff(417,plain,
% 10.83/10.99 (((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!12)) | (empty_set = A!12))) <=> ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!12)) | (empty_set = A!12))),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(418,plain,
% 10.83/10.99 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | ((~empty(empty_set)) | (~empty(A!12)) | (empty_set = A!12))),
% 10.83/10.99 inference(quant_inst,[status(thm)],[])).
% 10.83/10.99 tff(419,plain,
% 10.83/10.99 ((~![A: $i, B: $i] : ((~empty(A)) | (~empty(B)) | (A = B))) | (~empty(empty_set)) | (~empty(A!12)) | (empty_set = A!12)),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[418, 417])).
% 10.83/10.99 tff(420,plain,
% 10.83/10.99 (empty_set = A!12),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[419, 416, 84, 80])).
% 10.83/10.99 tff(421,plain,
% 10.83/10.99 (A!12 = empty_set),
% 10.83/10.99 inference(symmetry,[status(thm)],[420])).
% 10.83/10.99 tff(422,plain,
% 10.83/10.99 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), empty_set)),
% 10.83/10.99 inference(monotonicity,[status(thm)],[421])).
% 10.83/10.99 tff(423,plain,
% 10.83/10.99 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), empty_set) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)),
% 10.83/10.99 inference(symmetry,[status(thm)],[422])).
% 10.83/10.99 tff(424,plain,
% 10.83/10.99 (^[A: $i] : refl((set_intersection2(A, empty_set) = empty_set) <=> (set_intersection2(A, empty_set) = empty_set))),
% 10.83/10.99 inference(bind,[status(th)],[])).
% 10.83/10.99 tff(425,plain,
% 10.83/10.99 (![A: $i] : (set_intersection2(A, empty_set) = empty_set) <=> ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 10.83/10.99 inference(quant_intro,[status(thm)],[424])).
% 10.83/10.99 tff(426,plain,
% 10.83/10.99 (![A: $i] : (set_intersection2(A, empty_set) = empty_set) <=> ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(427,axiom,(![A: $i] : (set_intersection2(A, empty_set) = empty_set)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t2_boole')).
% 10.83/10.99 tff(428,plain,
% 10.83/10.99 (![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[427, 426])).
% 10.83/10.99 tff(429,plain,(
% 10.83/10.99 ![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 10.83/10.99 inference(skolemize,[status(sab)],[428])).
% 10.83/10.99 tff(430,plain,
% 10.83/10.99 (![A: $i] : (set_intersection2(A, empty_set) = empty_set)),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[429, 425])).
% 10.83/10.99 tff(431,plain,
% 10.83/10.99 ((~![A: $i] : (set_intersection2(A, empty_set) = empty_set)) | (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), empty_set) = empty_set)),
% 10.83/10.99 inference(quant_inst,[status(thm)],[])).
% 10.83/10.99 tff(432,plain,
% 10.83/10.99 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), empty_set) = empty_set),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[431, 430])).
% 10.83/10.99 tff(433,plain,
% 10.83/10.99 (empty_set = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), empty_set)),
% 10.83/10.99 inference(symmetry,[status(thm)],[432])).
% 10.83/10.99 tff(434,plain,
% 10.83/10.99 ((~![A: $i] : (set_intersection2(A, empty_set) = empty_set)) | (set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set) = empty_set)),
% 10.83/10.99 inference(quant_inst,[status(thm)],[])).
% 10.83/10.99 tff(435,plain,
% 10.83/10.99 (set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set) = empty_set),
% 10.83/10.99 inference(unit_resolution,[status(thm)],[434, 430])).
% 10.83/10.99 tff(436,plain,
% 10.83/10.99 (set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set)),
% 10.83/10.99 inference(monotonicity,[status(thm)],[421])).
% 10.83/10.99 tff(437,plain,
% 10.83/10.99 (element(A!12, the_carrier(boole_lattice(A!20))) <=> element(tptp_fun_B_13(A!20), powerset(A!20))),
% 10.83/10.99 inference(monotonicity,[status(thm)],[88, 245])).
% 10.83/10.99 tff(438,plain,
% 10.83/10.99 (element(tptp_fun_B_13(A!20), powerset(A!20)) <=> element(A!12, the_carrier(boole_lattice(A!20)))),
% 10.83/10.99 inference(symmetry,[status(thm)],[437])).
% 10.83/10.99 tff(439,plain,
% 10.83/10.99 (element(A!12, the_carrier(boole_lattice(A!20)))),
% 10.83/10.99 inference(modus_ponens,[status(thm)],[249, 438])).
% 10.83/10.99 tff(440,plain,
% 10.83/10.99 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12)))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12)))))))),
% 10.83/10.99 inference(rewrite,[status(thm)],[])).
% 10.83/10.99 tff(441,plain,
% 10.83/10.99 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | ((~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12)))))))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(442,plain,
% 10.83/11.00 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))) | (~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12))))))),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[441, 440])).
% 10.83/11.00 tff(443,plain,
% 10.83/11.00 (~((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12)))))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[442, 205, 439])).
% 10.83/11.00 tff(444,plain,
% 10.83/11.00 (((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = A!12)) | (~(meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = A!12))))) | element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.83/11.00 inference(tautology,[status(thm)],[])).
% 10.83/11.00 tff(445,plain,
% 10.83/11.00 (element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[444, 443])).
% 10.83/11.00 tff(446,plain,
% 10.83/11.00 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C)))))))),
% 10.83/11.00 inference(rewrite,[status(thm)],[])).
% 10.83/11.00 tff(447,plain,
% 10.83/11.00 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C)))))))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(448,plain,
% 10.83/11.00 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[447, 446])).
% 10.83/11.00 tff(449,plain,
% 10.83/11.00 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[448, 157, 445])).
% 10.83/11.00 tff(450,plain,
% 10.83/11.00 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))) | ((~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))) | (~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))))))),
% 10.83/11.00 inference(rewrite,[status(thm)],[])).
% 10.83/11.00 tff(451,plain,
% 10.83/11.00 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))) | ((~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))))))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(452,plain,
% 10.83/11.00 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), C) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), C))))))) | (~element(A!12, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)))))),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[451, 450])).
% 10.83/11.00 tff(453,plain,
% 10.83/11.00 (~((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[452, 439, 449])).
% 10.83/11.00 tff(454,plain,
% 10.83/11.00 (((~(join(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)))) | (meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))),
% 10.83/11.00 inference(tautology,[status(thm)],[])).
% 10.83/11.00 tff(455,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[454, 453])).
% 10.83/11.00 tff(456,plain,
% 10.83/11.00 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12) = A!12),
% 10.83/11.00 inference(transitivity,[status(thm)],[422, 432, 420])).
% 10.83/11.00 tff(457,plain,
% 10.83/11.00 (tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)) = tptp_fun_C_1(A!12, boole_lattice(A!20))),
% 10.83/11.00 inference(monotonicity,[status(thm)],[456])).
% 10.83/11.00 tff(458,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = meet(boole_lattice(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(monotonicity,[status(thm)],[457, 456])).
% 10.83/11.00 tff(459,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(transitivity,[status(thm)],[458, 455, 436, 435, 433, 423])).
% 10.83/11.00 tff(460,plain,
% 10.83/11.00 ((~![A: $i, B: $i] : (set_intersection2(A, B) = set_intersection2(B, A))) | (set_intersection2(A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(461,plain,
% 10.83/11.00 (set_intersection2(A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[460, 272])).
% 10.83/11.00 tff(462,plain,
% 10.83/11.00 (set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(A!12, tptp_fun_C_1(A!12, boole_lattice(A!20)))),
% 10.83/11.00 inference(monotonicity,[status(thm)],[263])).
% 10.83/11.00 tff(463,plain,
% 10.83/11.00 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | ((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | (~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))))))),
% 10.83/11.00 inference(rewrite,[status(thm)],[])).
% 10.83/11.00 tff(464,plain,
% 10.83/11.00 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | ((~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))))))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(465,plain,
% 10.83/11.00 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_union2(tptp_fun_B_13(A!20), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), C) = set_intersection2(tptp_fun_B_13(A!20), C))))))) | (~element(tptp_fun_C_1(A!12, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)))))))),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[464, 463])).
% 10.83/11.00 tff(466,plain,
% 10.83/11.00 (~((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[465, 255, 445])).
% 10.83/11.00 tff(467,plain,
% 10.83/11.00 (((~(join(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_union2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))) | (~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)))))) | (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))))),
% 10.83/11.00 inference(tautology,[status(thm)],[])).
% 10.83/11.00 tff(468,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20))) = set_intersection2(tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[467, 466])).
% 10.83/11.00 tff(469,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20))) = meet(boole_lattice(A!20), tptp_fun_B_13(A!20), tptp_fun_C_1(A!12, boole_lattice(A!20)))),
% 10.83/11.00 inference(monotonicity,[status(thm)],[88])).
% 10.83/11.00 tff(470,plain,
% 10.83/11.00 (^[A: $i] : refl((set_union2(A, empty_set) = A) <=> (set_union2(A, empty_set) = A))),
% 10.83/11.00 inference(bind,[status(th)],[])).
% 10.83/11.00 tff(471,plain,
% 10.83/11.00 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 10.83/11.00 inference(quant_intro,[status(thm)],[470])).
% 10.83/11.00 tff(472,plain,
% 10.83/11.00 (![A: $i] : (set_union2(A, empty_set) = A) <=> ![A: $i] : (set_union2(A, empty_set) = A)),
% 10.83/11.00 inference(rewrite,[status(thm)],[])).
% 10.83/11.00 tff(473,axiom,(![A: $i] : (set_union2(A, empty_set) = A)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_boole')).
% 10.83/11.00 tff(474,plain,
% 10.83/11.00 (![A: $i] : (set_union2(A, empty_set) = A)),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[473, 472])).
% 10.83/11.00 tff(475,plain,(
% 10.83/11.00 ![A: $i] : (set_union2(A, empty_set) = A)),
% 10.83/11.00 inference(skolemize,[status(sab)],[474])).
% 10.83/11.00 tff(476,plain,
% 10.83/11.00 (![A: $i] : (set_union2(A, empty_set) = A)),
% 10.83/11.00 inference(modus_ponens,[status(thm)],[475, 471])).
% 10.83/11.00 tff(477,plain,
% 10.83/11.00 ((~![A: $i] : (set_union2(A, empty_set) = A)) | (set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set) = tptp_fun_C_1(A!12, boole_lattice(A!20)))),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(478,plain,
% 10.83/11.00 (set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set) = tptp_fun_C_1(A!12, boole_lattice(A!20))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[477, 476])).
% 10.83/11.00 tff(479,plain,
% 10.83/11.00 (set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(monotonicity,[status(thm)],[420])).
% 10.83/11.00 tff(480,plain,
% 10.83/11.00 (set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set)),
% 10.83/11.00 inference(symmetry,[status(thm)],[479])).
% 10.83/11.00 tff(481,plain,
% 10.83/11.00 (set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12) = tptp_fun_C_1(A!12, boole_lattice(A!20))),
% 10.83/11.00 inference(transitivity,[status(thm)],[480, 478])).
% 10.83/11.00 tff(482,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), tptp_fun_B_13(A!20), set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)) = meet(boole_lattice(A!20), A!12, tptp_fun_C_1(A!12, boole_lattice(A!20)))),
% 10.83/11.00 inference(monotonicity,[status(thm)],[263, 481])).
% 10.83/11.00 tff(483,plain,
% 10.83/11.00 (tptp_fun_C_1(A!12, boole_lattice(A!20)) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), empty_set)),
% 10.83/11.00 inference(symmetry,[status(thm)],[478])).
% 10.83/11.00 tff(484,plain,
% 10.83/11.00 (tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)) = set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(transitivity,[status(thm)],[457, 483, 479])).
% 10.83/11.00 tff(485,plain,
% 10.83/11.00 (set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12) = tptp_fun_B_13(A!20)),
% 10.83/11.00 inference(transitivity,[status(thm)],[422, 432, 420, 88])).
% 10.83/11.00 tff(486,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = meet(boole_lattice(A!20), tptp_fun_B_13(A!20), set_union2(tptp_fun_C_1(A!12, boole_lattice(A!20)), A!12))),
% 10.83/11.00 inference(monotonicity,[status(thm)],[485, 484])).
% 10.83/11.00 tff(487,plain,
% 10.83/11.00 (meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)),
% 10.83/11.00 inference(transitivity,[status(thm)],[486, 482, 469, 468, 462, 461, 436, 435, 433, 423])).
% 10.83/11.00 tff(488,plain,
% 10.83/11.00 ((~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)))),
% 10.83/11.00 inference(tautology,[status(thm)],[])).
% 10.83/11.00 tff(489,plain,
% 10.83/11.00 (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[488, 487, 459])).
% 10.83/11.00 tff(490,plain,
% 10.83/11.00 (((~element(tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)))))) | ((~(meet(boole_lattice(A!20), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20)), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12)) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))) | (~(meet(boole_lattice(A!20), set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), tptp_fun_C_1(set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12), boole_lattice(A!20))) = set_intersection2(tptp_fun_C_1(apply_binary_as_element(the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)), the_L_meet(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))), boole_lattice(A!20)), A!12))))),
% 10.83/11.00 inference(tautology,[status(thm)],[])).
% 10.83/11.00 tff(491,plain,
% 10.83/11.00 ($false),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[490, 489, 413])).
% 10.83/11.00 tff(492,plain,(~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))), inference(lemma,lemma(discharge,[]))).
% 10.83/11.00 tff(493,plain,
% 10.83/11.00 ((~![A: $i] : (set_intersection2(A, empty_set) = empty_set)) | (set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), empty_set) = empty_set)),
% 10.83/11.00 inference(quant_inst,[status(thm)],[])).
% 10.83/11.00 tff(494,plain,
% 10.83/11.00 (set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), empty_set) = empty_set),
% 10.83/11.00 inference(unit_resolution,[status(thm)],[493, 430])).
% 10.83/11.00 tff(495,plain,
% 10.83/11.00 (tptp_fun_B_13(A!20) = empty_set),
% 10.83/11.00 inference(transitivity,[status(thm)],[263, 421])).
% 10.83/11.00 tff(496,plain,
% 10.83/11.00 (set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), empty_set)),
% 10.83/11.00 inference(monotonicity,[status(thm)],[495])).
% 10.83/11.00 tff(497,plain,
% 10.83/11.00 (^[A: $i] : refl((empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))),
% 10.83/11.00 inference(bind,[status(th)],[])).
% 10.83/11.00 tff(498,plain,
% 10.83/11.00 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.00 inference(quant_intro,[status(thm)],[497])).
% 10.83/11.00 tff(499,plain,
% 10.83/11.00 (^[A: $i] : rewrite((empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))),
% 10.83/11.00 inference(bind,[status(th)],[])).
% 10.83/11.00 tff(500,plain,
% 10.83/11.00 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.00 inference(quant_intro,[status(thm)],[499])).
% 10.83/11.00 tff(501,plain,
% 10.83/11.00 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.00 inference(transitivity,[status(thm)],[500, 498])).
% 10.83/11.00 tff(502,plain,
% 10.83/11.00 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_semilatt_str(A)) <=> (~(empty_carrier(A) | (~meet_semilatt_str(A))))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~meet_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~meet_semilatt_str(A))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_semilatt_str(A))))), trans(monotonicity(rewrite(((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) <=> ((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))), rewrite((lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))) <=> (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))), ((((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))) <=> (((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))), rewrite((((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))) <=> (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))), ((((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))) <=> (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> ((empty_carrier(A) | (~meet_semilatt_str(A))) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))), rewrite(((empty_carrier(A) | (~meet_semilatt_str(A))) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))))),
% 10.83/11.01 inference(bind,[status(th)],[])).
% 10.83/11.01 tff(503,plain,
% 10.83/11.01 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> ![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.01 inference(quant_intro,[status(thm)],[502])).
% 10.83/11.01 tff(504,plain,
% 10.83/11.01 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.01 inference(rewrite,[status(thm)],[])).
% 10.83/11.01 tff(505,plain,
% 10.83/11.01 (^[A: $i] : trans(monotonicity(rewrite((lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))) <=> (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> (((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))))), rewrite((((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))))),
% 10.83/11.01 inference(bind,[status(th)],[])).
% 10.83/11.01 tff(506,plain,
% 10.83/11.01 (![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.01 inference(quant_intro,[status(thm)],[505])).
% 10.83/11.01 tff(507,axiom,(![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d13_lattices')).
% 10.83/11.01 tff(508,plain,
% 10.83/11.01 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[507, 506])).
% 10.83/11.01 tff(509,plain,
% 10.83/11.01 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (lower_bounded_semilattstr(A) <=> ?[B: $i] : (element(B, the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[508, 504])).
% 10.83/11.01 tff(510,plain,(
% 10.83/11.01 ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (((~lower_bounded_semilattstr(A)) | (element(tptp_fun_B_0(A), the_carrier(A)) & ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A)) & (meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A)))))) & (lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))))),
% 10.83/11.01 inference(skolemize,[status(sab)],[509])).
% 10.83/11.01 tff(511,plain,
% 10.83/11.01 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[510, 503])).
% 10.83/11.01 tff(512,plain,
% 10.83/11.01 (![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[511, 501])).
% 10.83/11.01 tff(513,plain,
% 10.83/11.01 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.01 inference(rewrite,[status(thm)],[])).
% 10.83/11.01 tff(514,plain,
% 10.83/11.01 ((empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)))))))))))) <=> (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.01 inference(rewrite,[status(thm)],[])).
% 10.83/11.01 tff(515,plain,
% 10.83/11.01 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))))),
% 10.83/11.01 inference(monotonicity,[status(thm)],[514])).
% 10.83/11.01 tff(516,plain,
% 10.83/11.01 (((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.01 inference(transitivity,[status(thm)],[515, 513])).
% 10.83/11.01 tff(517,plain,
% 10.83/11.01 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))),
% 10.83/11.01 inference(quant_inst,[status(thm)],[])).
% 10.83/11.01 tff(518,plain,
% 10.83/11.01 ((~![A: $i] : (empty_carrier(A) | (~meet_semilatt_str(A)) | (~((~((~lower_bounded_semilattstr(A)) | (~((~element(tptp_fun_B_0(A), the_carrier(A))) | (~![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, tptp_fun_B_0(A), C) = tptp_fun_B_0(A))) | (~(meet(A, C, tptp_fun_B_0(A)) = tptp_fun_B_0(A))))))))))) | (~(lower_bounded_semilattstr(A) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[517, 516])).
% 10.83/11.01 tff(519,plain,
% 10.83/11.01 ((~meet_semilatt_str(boole_lattice(A!20))) | (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[518, 512, 17])).
% 10.83/11.01 tff(520,plain,
% 10.83/11.01 (~((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[519, 120])).
% 10.83/11.01 tff(521,plain,
% 10.83/11.01 (((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))) | ((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(522,plain,
% 10.83/11.01 ((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[521, 520])).
% 10.83/11.01 tff(523,plain,
% 10.83/11.01 (((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))) | (lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(524,plain,
% 10.83/11.01 (lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[523, 520])).
% 10.83/11.01 tff(525,plain,
% 10.83/11.01 ((~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))) | lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(526,plain,
% 10.83/11.01 ((~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))) | lower_bounded_semilattstr(boole_lattice(A!20))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[525, 492])).
% 10.83/11.01 tff(527,plain,
% 10.83/11.01 (lower_bounded_semilattstr(boole_lattice(A!20))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[526, 524])).
% 10.83/11.01 tff(528,plain,
% 10.83/11.01 ((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))))))))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(529,plain,
% 10.83/11.01 (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[528, 527, 522])).
% 10.83/11.01 tff(530,plain,
% 10.83/11.01 (((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))))))) | element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(531,plain,
% 10.83/11.01 (element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[530, 529])).
% 10.83/11.01 tff(532,plain,
% 10.83/11.01 (((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C)))))))) <=> ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C)))))))),
% 10.83/11.01 inference(rewrite,[status(thm)],[])).
% 10.83/11.01 tff(533,plain,
% 10.83/11.01 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | ((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C)))))))),
% 10.83/11.01 inference(quant_inst,[status(thm)],[])).
% 10.83/11.01 tff(534,plain,
% 10.83/11.01 ((~![A: $i, B: $i] : ((~element(B, the_carrier(boole_lattice(A)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A)))) | (~((~(join(boole_lattice(A), B, C) = set_union2(B, C))) | (~(meet(boole_lattice(A), B, C) = set_intersection2(B, C)))))))) | (~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[533, 532])).
% 10.83/11.01 tff(535,plain,
% 10.83/11.01 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[534, 157, 531])).
% 10.83/11.01 tff(536,plain,
% 10.83/11.01 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))))))),
% 10.83/11.01 inference(rewrite,[status(thm)],[])).
% 10.83/11.01 tff(537,plain,
% 10.83/11.01 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))))))),
% 10.83/11.01 inference(quant_inst,[status(thm)],[])).
% 10.83/11.01 tff(538,plain,
% 10.83/11.01 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), C))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), C))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20))))))),
% 10.83/11.01 inference(modus_ponens,[status(thm)],[537, 536])).
% 10.83/11.01 tff(539,plain,
% 10.83/11.01 ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[538, 535])).
% 10.83/11.01 tff(540,plain,
% 10.83/11.01 (~((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[539, 250])).
% 10.83/11.01 tff(541,plain,
% 10.83/11.01 (((~(join(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_union2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))) | (~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20))))) | (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(542,plain,
% 10.83/11.01 (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = set_intersection2(tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[541, 540])).
% 10.83/11.01 tff(543,plain,
% 10.83/11.01 (((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))))))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))),
% 10.83/11.01 inference(tautology,[status(thm)],[])).
% 10.83/11.01 tff(544,plain,
% 10.83/11.01 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))),
% 10.83/11.01 inference(unit_resolution,[status(thm)],[543, 529])).
% 10.83/11.01 tff(545,plain,
% 10.83/11.01 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(546,plain,
% 10.83/11.02 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))),
% 10.83/11.02 inference(quant_inst,[status(thm)],[])).
% 10.83/11.02 tff(547,plain,
% 10.83/11.02 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[546, 545])).
% 10.83/11.02 tff(548,plain,
% 10.83/11.02 (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))),
% 10.83/11.02 inference(unit_resolution,[status(thm)],[547, 141, 544])).
% 10.83/11.02 tff(549,plain,
% 10.83/11.02 (((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))))) | (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))),
% 10.83/11.02 inference(tautology,[status(thm)],[])).
% 10.83/11.02 tff(550,plain,
% 10.83/11.02 (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20))),
% 10.83/11.02 inference(unit_resolution,[status(thm)],[549, 548])).
% 10.83/11.02 tff(551,plain,
% 10.83/11.02 (^[A: $i] : refl((empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))),
% 10.83/11.02 inference(bind,[status(th)],[])).
% 10.83/11.02 tff(552,plain,
% 10.83/11.02 (![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(quant_intro,[status(thm)],[551])).
% 10.83/11.02 tff(553,plain,
% 10.83/11.02 (^[A: $i] : rewrite((empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))),
% 10.83/11.02 inference(bind,[status(th)],[])).
% 10.83/11.02 tff(554,plain,
% 10.83/11.02 (![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(quant_intro,[status(thm)],[553])).
% 10.83/11.02 tff(555,plain,
% 10.83/11.02 (![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> ![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(transitivity,[status(thm)],[554, 552])).
% 10.83/11.02 tff(556,plain,
% 10.83/11.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & meet_semilatt_str(A)) <=> (~(empty_carrier(A) | (~meet_semilatt_str(A))))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~meet_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~meet_semilatt_str(A))))) <=> (empty_carrier(A) | (~meet_semilatt_str(A)))), ((~((~empty_carrier(A)) & meet_semilatt_str(A))) <=> (empty_carrier(A) | (~meet_semilatt_str(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))) <=> ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))), (![B: $i] : ((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> ((empty_carrier(A) | (~meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))))), rewrite(((empty_carrier(A) | (~meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B)))))))))))) <=> (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))), (((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))))),
% 10.83/11.02 inference(bind,[status(th)],[])).
% 10.83/11.02 tff(557,plain,
% 10.83/11.02 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B)))))))) <=> ![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(quant_intro,[status(thm)],[556])).
% 10.83/11.02 tff(558,plain,
% 10.83/11.02 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(559,plain,
% 10.83/11.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite(((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) <=> ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))), ((element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))) <=> (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), rewrite((element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))) <=> ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))), ((element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))) <=> ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))))), (![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), ((lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> (lower_bounded_semilattstr(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))))), rewrite((lower_bounded_semilattstr(A) => ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ((~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), ((lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))) <=> ((~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))) <=> (((~empty_carrier(A)) & meet_semilatt_str(A)) => ((~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))))), rewrite((((~empty_carrier(A)) & meet_semilatt_str(A)) => ((~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))), ((((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))) <=> ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))))),
% 10.83/11.02 inference(bind,[status(th)],[])).
% 10.83/11.02 tff(560,plain,
% 10.83/11.02 (![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.02 inference(quant_intro,[status(thm)],[559])).
% 10.83/11.02 tff(561,axiom,(![A: $i] : (((~empty_carrier(A)) & meet_semilatt_str(A)) => (lower_bounded_semilattstr(A) => ![B: $i] : (element(B, the_carrier(A)) => ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : (element(C, the_carrier(A)) => ((meet(A, B, C) = B) & (meet(A, C, B) = B)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_lattices')).
% 10.83/11.02 tff(562,plain,
% 10.83/11.02 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[561, 560])).
% 10.83/11.02 tff(563,plain,
% 10.83/11.02 (![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ((B = bottom_of_semilattstr(A)) <=> ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[562, 558])).
% 10.83/11.02 tff(564,plain,(
% 10.83/11.02 ![A: $i] : ((~((~empty_carrier(A)) & meet_semilatt_str(A))) | (~lower_bounded_semilattstr(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | ((meet(A, B, C) = B) & (meet(A, C, B) = B)))) & ((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | ((meet(A, B, tptp_fun_C_1(B, A)) = B) & (meet(A, tptp_fun_C_1(B, A), B) = B))))))))),
% 10.83/11.02 inference(skolemize,[status(sab)],[563])).
% 10.83/11.02 tff(565,plain,
% 10.83/11.02 (![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[564, 557])).
% 10.83/11.02 tff(566,plain,
% 10.83/11.02 (![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[565, 555])).
% 10.83/11.02 tff(567,plain,
% 10.83/11.02 (((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(568,plain,
% 10.83/11.02 ((empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)))))))))))) <=> (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(569,plain,
% 10.83/11.02 (((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))))),
% 10.83/11.02 inference(monotonicity,[status(thm)],[568])).
% 10.83/11.02 tff(570,plain,
% 10.83/11.02 (((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))) <=> ((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))))))),
% 10.83/11.02 inference(transitivity,[status(thm)],[569, 567])).
% 10.83/11.02 tff(571,plain,
% 10.83/11.02 ((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)) | (~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B))))))))))))),
% 10.83/11.02 inference(quant_inst,[status(thm)],[])).
% 10.83/11.02 tff(572,plain,
% 10.83/11.02 ((~![A: $i] : (empty_carrier(A) | (~lower_bounded_semilattstr(A)) | (~meet_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | (~((~((~(B = bottom_of_semilattstr(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (~((~(meet(A, C, B) = B)) | (~(meet(A, B, C) = B))))))) | (~((B = bottom_of_semilattstr(A)) | (~((~element(tptp_fun_C_1(B, A), the_carrier(A))) | (~((~(meet(A, B, tptp_fun_C_1(B, A)) = B)) | (~(meet(A, tptp_fun_C_1(B, A), B) = B))))))))))))) | empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[571, 570])).
% 10.83/11.02 tff(573,plain,
% 10.83/11.02 (empty_carrier(boole_lattice(A!20)) | (~lower_bounded_semilattstr(boole_lattice(A!20))) | (~meet_semilatt_str(boole_lattice(A!20))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))),
% 10.83/11.02 inference(unit_resolution,[status(thm)],[572, 566])).
% 10.83/11.02 tff(574,plain,
% 10.83/11.02 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))),
% 10.83/11.02 inference(unit_resolution,[status(thm)],[573, 527, 17, 120])).
% 10.83/11.02 tff(575,plain,
% 10.83/11.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(576,plain,
% 10.83/11.02 (((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~((~(bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))) | (~((bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))))))))))))) <=> ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.83/11.02 inference(rewrite,[status(thm)],[])).
% 10.83/11.02 tff(577,plain,
% 10.83/11.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~((~(bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))) | (~((bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))))),
% 10.83/11.02 inference(monotonicity,[status(thm)],[576])).
% 10.83/11.02 tff(578,plain,
% 10.83/11.02 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~((~(bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))) | (~((bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))))))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))),
% 10.83/11.02 inference(transitivity,[status(thm)],[577, 575])).
% 10.83/11.02 tff(579,plain,
% 10.83/11.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | ((~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~((~(bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20))))))))) | (~((bottom_of_semilattstr(boole_lattice(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_C_1(bottom_of_semilattstr(boole_lattice(A!20)), boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))))))))),
% 10.83/11.02 inference(quant_inst,[status(thm)],[])).
% 10.83/11.02 tff(580,plain,
% 10.83/11.02 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~((~(B = bottom_of_semilattstr(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, B) = B)) | (~(meet(boole_lattice(A!20), B, C) = B))))))) | (~((B = bottom_of_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))))) | (~element(bottom_of_semilattstr(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.02 inference(modus_ponens,[status(thm)],[579, 578])).
% 10.83/11.02 tff(581,plain,
% 10.83/11.02 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.02 inference(unit_resolution,[status(thm)],[580, 574, 141])).
% 10.83/11.02 tff(582,plain,
% 10.83/11.02 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | ((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | (~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.03 inference(rewrite,[status(thm)],[])).
% 10.83/11.03 tff(583,plain,
% 10.83/11.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | ((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.03 inference(quant_inst,[status(thm)],[])).
% 10.83/11.03 tff(584,plain,
% 10.83/11.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | (~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))))))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[583, 582])).
% 10.83/11.03 tff(585,plain,
% 10.83/11.03 (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[584, 531, 581])).
% 10.83/11.03 tff(586,plain,
% 10.83/11.03 (((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_0(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))))) | (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.83/11.03 inference(tautology,[status(thm)],[])).
% 10.83/11.03 tff(587,plain,
% 10.83/11.03 (meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[586, 585])).
% 10.83/11.03 tff(588,plain,
% 10.83/11.03 (bottom_of_semilattstr(boole_lattice(A!20)) = meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.83/11.03 inference(symmetry,[status(thm)],[587])).
% 10.83/11.03 tff(589,plain,
% 10.83/11.03 (bottom_of_semilattstr(boole_lattice(A!20)) = tptp_fun_B_0(boole_lattice(A!20))),
% 10.83/11.03 inference(transitivity,[status(thm)],[588, 550])).
% 10.83/11.03 tff(590,plain,
% 10.83/11.03 (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), tptp_fun_B_13(A!20))),
% 10.83/11.03 inference(monotonicity,[status(thm)],[589])).
% 10.83/11.03 tff(591,plain,
% 10.83/11.03 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))))))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.03 inference(rewrite,[status(thm)],[])).
% 10.83/11.03 tff(592,plain,
% 10.83/11.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))))))),
% 10.83/11.03 inference(quant_inst,[status(thm)],[])).
% 10.83/11.03 tff(593,plain,
% 10.83/11.03 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), C, bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), C) = bottom_of_semilattstr(boole_lattice(A!20)))))))) | (~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))))))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[592, 591])).
% 10.83/11.03 tff(594,plain,
% 10.83/11.03 ((~element(tptp_fun_B_13(A!20), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))))))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[593, 581])).
% 10.83/11.03 tff(595,plain,
% 10.83/11.03 (~((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[594, 250])).
% 10.83/11.03 tff(596,plain,
% 10.83/11.03 (((~(meet(boole_lattice(A!20), tptp_fun_B_13(A!20), bottom_of_semilattstr(boole_lattice(A!20))) = bottom_of_semilattstr(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))))) | (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20)))),
% 10.83/11.03 inference(tautology,[status(thm)],[])).
% 10.83/11.03 tff(597,plain,
% 10.83/11.03 (meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20)) = bottom_of_semilattstr(boole_lattice(A!20))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[596, 595])).
% 10.83/11.03 tff(598,plain,
% 10.83/11.03 (bottom_of_semilattstr(boole_lattice(A!20)) = meet(boole_lattice(A!20), bottom_of_semilattstr(boole_lattice(A!20)), tptp_fun_B_13(A!20))),
% 10.83/11.03 inference(symmetry,[status(thm)],[597])).
% 10.83/11.03 tff(599,plain,
% 10.83/11.03 (bottom_of_semilattstr(boole_lattice(A!20)) = empty_set),
% 10.83/11.03 inference(transitivity,[status(thm)],[598, 590, 542, 496, 494])).
% 10.83/11.03 tff(600,assumption,(~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set)), introduced(assumption)).
% 10.83/11.03 tff(601,plain,
% 10.83/11.03 ($false),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[600, 599])).
% 10.83/11.03 tff(602,plain,(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set), inference(lemma,lemma(discharge,[]))).
% 10.83/11.03 tff(603,plain,
% 10.83/11.03 ((~(~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))))) <=> ((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set)))),
% 10.83/11.03 inference(rewrite,[status(thm)],[])).
% 10.83/11.03 tff(604,plain,
% 10.83/11.03 ((lower_bounded_semilattstr(boole_lattice(A!20)) & (bottom_of_semilattstr(boole_lattice(A!20)) = empty_set)) <=> (~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))))),
% 10.83/11.03 inference(rewrite,[status(thm)],[])).
% 10.83/11.03 tff(605,plain,
% 10.83/11.03 ((~(lower_bounded_semilattstr(boole_lattice(A!20)) & (bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))) <=> (~(~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set)))))),
% 10.83/11.03 inference(monotonicity,[status(thm)],[604])).
% 10.83/11.03 tff(606,plain,
% 10.83/11.03 ((~(lower_bounded_semilattstr(boole_lattice(A!20)) & (bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))) <=> ((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set)))),
% 10.83/11.03 inference(transitivity,[status(thm)],[605, 603])).
% 10.83/11.03 tff(607,plain,
% 10.83/11.03 ((~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))) <=> (~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set)))),
% 10.83/11.03 inference(rewrite,[status(thm)],[])).
% 10.83/11.03 tff(608,axiom,(~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_lattice3')).
% 10.83/11.03 tff(609,plain,
% 10.83/11.03 (~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[608, 607])).
% 10.83/11.03 tff(610,plain,
% 10.83/11.03 (~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[609, 607])).
% 10.83/11.03 tff(611,plain,
% 10.83/11.03 (~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[610, 607])).
% 10.83/11.03 tff(612,plain,
% 10.83/11.03 (~![A: $i] : (lower_bounded_semilattstr(boole_lattice(A)) & (bottom_of_semilattstr(boole_lattice(A)) = empty_set))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[611, 607])).
% 10.83/11.03 tff(613,plain,(
% 10.83/11.03 ~(lower_bounded_semilattstr(boole_lattice(A!20)) & (bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))),
% 10.83/11.03 inference(skolemize,[status(sab)],[612])).
% 10.83/11.03 tff(614,plain,
% 10.83/11.03 ((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~(bottom_of_semilattstr(boole_lattice(A!20)) = empty_set))),
% 10.83/11.03 inference(modus_ponens,[status(thm)],[613, 606])).
% 10.83/11.03 tff(615,plain,
% 10.83/11.03 (~lower_bounded_semilattstr(boole_lattice(A!20))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[614, 602])).
% 10.83/11.03 tff(616,plain,
% 10.83/11.03 (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B))))))))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[525, 615, 492])).
% 10.83/11.03 tff(617,plain,
% 10.83/11.03 ((~((~lower_bounded_semilattstr(boole_lattice(A!20))) | (~((~element(tptp_fun_B_0(boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_B_0(boole_lattice(A!20)), C) = tptp_fun_B_0(boole_lattice(A!20)))) | (~(meet(boole_lattice(A!20), C, tptp_fun_B_0(boole_lattice(A!20))) = tptp_fun_B_0(boole_lattice(A!20)))))))))))) | (~(lower_bounded_semilattstr(boole_lattice(A!20)) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!20)))) | (~((~element(tptp_fun_C_1(B, boole_lattice(A!20)), the_carrier(boole_lattice(A!20)))) | (~((~(meet(boole_lattice(A!20), tptp_fun_C_1(B, boole_lattice(A!20)), B) = B)) | (~(meet(boole_lattice(A!20), B, tptp_fun_C_1(B, boole_lattice(A!20))) = B)))))))))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[523, 616])).
% 10.83/11.03 tff(618,plain,
% 10.83/11.03 (empty_carrier(boole_lattice(A!20)) | (~meet_semilatt_str(boole_lattice(A!20)))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[518, 512, 617])).
% 10.83/11.03 tff(619,plain,
% 10.83/11.03 (~meet_semilatt_str(boole_lattice(A!20))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[618, 17])).
% 10.83/11.03 tff(620,plain,
% 10.83/11.03 ((~meet_semilatt_str(boole_lattice(A!20))) | (~join_semilatt_str(boole_lattice(A!20)))),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[119, 619])).
% 10.83/11.03 tff(621,plain,
% 10.83/11.03 ($false),
% 10.83/11.03 inference(unit_resolution,[status(thm)],[117, 114, 31, 620])).
% 10.83/11.03 % SZS output end Proof
% 10.94/11.08 % E exiting
%------------------------------------------------------------------------------