%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SEU343+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 0.41s 0.57s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU343+1 : TPTP v9.0.0. Released v3.3.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.35 % Computer : n012.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 20 06:48:40 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.41/0.57 % SZS status Theorem
% 0.41/0.57 % SZS output start Proof
% 0.41/0.57 tff(set_intersection2_type, type, (
% 0.41/0.57 set_intersection2: ( $i * $i ) > $i)).
% 0.41/0.57 tff(tptp_fun_C_19_type, type, (
% 0.41/0.57 tptp_fun_C_19: $i)).
% 0.41/0.57 tff(tptp_fun_B_17_type, type, (
% 0.41/0.57 tptp_fun_B_17: $i)).
% 0.41/0.57 tff(meet_type, type, (
% 0.41/0.57 meet: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(boole_lattice_type, type, (
% 0.41/0.57 boole_lattice: $i > $i)).
% 0.41/0.57 tff(tptp_fun_A_18_type, type, (
% 0.41/0.57 tptp_fun_A_18: $i)).
% 0.41/0.57 tff(subset_intersection2_type, type, (
% 0.41/0.57 subset_intersection2: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(element_type, type, (
% 0.41/0.57 element: ( $i * $i ) > $o)).
% 0.41/0.57 tff(powerset_type, type, (
% 0.41/0.57 powerset: $i > $i)).
% 0.41/0.57 tff(the_carrier_type, type, (
% 0.41/0.57 the_carrier: $i > $i)).
% 0.41/0.57 tff(latt_str_of_type, type, (
% 0.41/0.57 latt_str_of: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(the_L_meet_type, type, (
% 0.41/0.57 the_L_meet: $i > $i)).
% 0.41/0.57 tff(the_L_join_type, type, (
% 0.41/0.57 the_L_join: $i > $i)).
% 0.41/0.57 tff(latt_str_type, type, (
% 0.41/0.57 latt_str: $i > $o)).
% 0.41/0.57 tff(strict_latt_str_type, type, (
% 0.41/0.57 strict_latt_str: $i > $o)).
% 0.41/0.57 tff(apply_binary_type, type, (
% 0.41/0.57 apply_binary: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(subset_union2_type, type, (
% 0.41/0.57 subset_union2: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(tptp_fun_D_1_type, type, (
% 0.41/0.57 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.41/0.57 tff(tptp_fun_C_0_type, type, (
% 0.41/0.57 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.41/0.57 tff(set_union2_type, type, (
% 0.41/0.57 set_union2: ( $i * $i ) > $i)).
% 0.41/0.57 tff(join_type, type, (
% 0.41/0.57 join: ( $i * $i * $i ) > $i)).
% 0.41/0.57 tff(apply_binary_as_element_type, type, (
% 0.41/0.57 apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.41/0.57 tff(relation_of2_type, type, (
% 0.41/0.57 relation_of2: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(cartesian_product2_type, type, (
% 0.41/0.57 cartesian_product2: ( $i * $i ) > $i)).
% 0.41/0.57 tff(relation_of2_as_subset_type, type, (
% 0.41/0.57 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(quasi_total_type, type, (
% 0.41/0.57 quasi_total: ( $i * $i * $i ) > $o)).
% 0.41/0.57 tff(function_type, type, (
% 0.41/0.57 function: $i > $o)).
% 0.41/0.57 tff(meet_semilatt_str_type, type, (
% 0.41/0.57 meet_semilatt_str: $i > $o)).
% 0.41/0.57 tff(join_semilatt_str_type, type, (
% 0.41/0.57 join_semilatt_str: $i > $o)).
% 0.41/0.57 tff(empty_type, type, (
% 0.41/0.57 empty: $i > $o)).
% 0.41/0.57 tff(empty_carrier_type, type, (
% 0.41/0.57 empty_carrier: $i > $o)).
% 0.41/0.57 tff(1,plain,
% 0.41/0.57 (^[A: $i] : refl((~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(2,plain,
% 0.41/0.57 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[1])).
% 0.41/0.57 tff(3,plain,
% 0.41/0.57 (^[A: $i] : rewrite((strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(4,plain,
% 0.41/0.57 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[3])).
% 0.41/0.57 tff(5,plain,
% 0.41/0.57 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A))) <=> ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(6,axiom,(![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lattice3')).
% 0.41/0.57 tff(7,plain,
% 0.41/0.57 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.41/0.57 tff(8,plain,(
% 0.41/0.57 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.41/0.57 inference(skolemize,[status(sab)],[7])).
% 0.41/0.57 tff(9,plain,
% 0.41/0.57 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.41/0.57 tff(10,plain,
% 0.41/0.57 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.41/0.57 tff(11,plain,
% 0.41/0.57 ((~![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))) | (~((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(12,plain,
% 0.41/0.57 (~((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18))))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.41/0.57 tff(13,plain,
% 0.41/0.57 (((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))) | latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(14,plain,
% 0.41/0.57 (latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.41/0.57 tff(15,plain,
% 0.41/0.57 (((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))) | strict_latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(tautology,[status(thm)],[])).
% 0.41/0.57 tff(16,plain,
% 0.41/0.57 (strict_latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.41/0.57 tff(17,plain,
% 0.41/0.57 (^[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))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(18,plain,
% 0.41/0.57 (![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)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[17])).
% 0.41/0.57 tff(19,plain,
% 0.41/0.57 (![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)))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(20,plain,
% 0.41/0.57 (^[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)))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(21,plain,
% 0.41/0.57 (![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)))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[20])).
% 0.41/0.57 tff(22,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/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 0.41/0.57 tff(23,plain,
% 0.41/0.57 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.41/0.57 tff(24,plain,
% 0.41/0.57 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.41/0.57 tff(25,plain,(
% 0.41/0.57 ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.41/0.57 inference(skolemize,[status(sab)],[24])).
% 0.41/0.57 tff(26,plain,
% 0.41/0.57 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.41/0.57 tff(27,plain,
% 0.41/0.57 (((~![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!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) | (~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18))))) <=> ((~![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!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) | (~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18))))),
% 0.41/0.57 inference(rewrite,[status(thm)],[])).
% 0.41/0.57 tff(28,plain,
% 0.41/0.57 ((~![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!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) | (~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18))))),
% 0.41/0.57 inference(quant_inst,[status(thm)],[])).
% 0.41/0.57 tff(29,plain,
% 0.41/0.57 ((~![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!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) | (~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.41/0.57 tff(30,plain,
% 0.41/0.57 ((boole_lattice(A!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) | (~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.41/0.57 tff(31,plain,
% 0.41/0.57 (boole_lattice(A!18) = latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))),
% 0.41/0.57 inference(unit_resolution,[status(thm)],[30, 16, 14])).
% 0.41/0.57 tff(32,plain,
% 0.41/0.57 (latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)),
% 0.41/0.57 inference(symmetry,[status(thm)],[31])).
% 0.41/0.57 tff(33,plain,
% 0.41/0.57 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = the_carrier(boole_lattice(A!18))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[32])).
% 0.41/0.57 tff(34,plain,
% 0.41/0.57 (strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) <=> strict_latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[32])).
% 0.41/0.57 tff(35,plain,
% 0.41/0.57 (strict_latt_str(boole_lattice(A!18)) <=> strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.41/0.57 inference(symmetry,[status(thm)],[34])).
% 0.41/0.57 tff(36,plain,
% 0.41/0.57 (strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[16, 35])).
% 0.41/0.57 tff(37,plain,
% 0.41/0.57 (latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) <=> latt_str(boole_lattice(A!18))),
% 0.41/0.57 inference(monotonicity,[status(thm)],[32])).
% 0.41/0.57 tff(38,plain,
% 0.41/0.57 (latt_str(boole_lattice(A!18)) <=> latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.41/0.57 inference(symmetry,[status(thm)],[37])).
% 0.41/0.57 tff(39,plain,
% 0.41/0.57 (latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.41/0.57 inference(modus_ponens,[status(thm)],[14, 38])).
% 0.41/0.57 tff(40,plain,
% 0.41/0.57 (^[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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))) <=> (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))))) <=> ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(41,plain,
% 0.41/0.57 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[40])).
% 0.41/0.57 tff(42,plain,
% 0.41/0.57 (^[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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(43,plain,
% 0.41/0.57 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[42])).
% 0.41/0.57 tff(44,plain,
% 0.41/0.57 (^[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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))))))),
% 0.41/0.57 inference(bind,[status(th)],[])).
% 0.41/0.57 tff(45,plain,
% 0.41/0.57 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.57 inference(quant_intro,[status(thm)],[44])).
% 0.41/0.57 tff(46,plain,
% 0.41/0.57 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.57 inference(transitivity,[status(thm)],[45, 43])).
% 0.41/0.57 tff(47,plain,
% 0.41/0.57 (^[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_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))) <=> (~((~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))), ((element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))) <=> (element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))), rewrite((element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))) <=> (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))), ((element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))) <=> (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))), (((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))), rewrite(((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))), (((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (element(tptp_fun_C_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))) <=> ((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(48,plain,
% 0.41/0.58 (![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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[47])).
% 0.41/0.58 tff(49,plain,
% 0.41/0.58 (^[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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(50,plain,
% 0.41/0.58 (![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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[49])).
% 0.41/0.58 tff(51,plain,
% 0.41/0.58 (![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))))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(52,plain,
% 0.41/0.58 (^[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))))))))))),
% 0.41/0.58 inference(bind,[status(th)],[])).
% 0.41/0.58 tff(53,plain,
% 0.41/0.58 (![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))))))))),
% 0.41/0.58 inference(quant_intro,[status(thm)],[52])).
% 0.41/0.58 tff(54,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/sandbox/benchmark/theBenchmark.p','d1_lattice3')).
% 0.41/0.58 tff(55,plain,
% 0.41/0.58 (![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))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.41/0.58 tff(56,plain,
% 0.41/0.58 (![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))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.41/0.58 tff(57,plain,(
% 0.41/0.58 ![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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))),
% 0.41/0.58 inference(skolemize,[status(sab)],[56])).
% 0.41/0.58 tff(58,plain,
% 0.41/0.58 (![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_0(B, A), powerset(A)) & (~((~element(tptp_fun_D_1(B, A), powerset(A))) | ((apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))) & (apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A))))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.41/0.58 tff(59,plain,
% 0.41/0.58 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.41/0.58 tff(60,plain,
% 0.41/0.58 (![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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))))))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.41/0.58 tff(61,plain,
% 0.41/0.58 (![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))),
% 0.41/0.58 inference(modus_ponens,[status(thm)],[60, 41])).
% 0.41/0.58 tff(62,plain,
% 0.41/0.58 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))) <=> ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(63,plain,
% 0.41/0.58 (((~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))))) <=> ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))),
% 0.41/0.58 inference(rewrite,[status(thm)],[])).
% 0.41/0.58 tff(64,plain,
% 0.41/0.58 ((~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))) <=> (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))),
% 0.41/0.59 inference(rewrite,[status(thm)],[])).
% 0.41/0.59 tff(65,plain,
% 0.41/0.59 (((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))) <=> ((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[64])).
% 0.41/0.59 tff(66,plain,
% 0.41/0.59 ((~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))) <=> (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))),
% 0.41/0.59 inference(monotonicity,[status(thm)],[65])).
% 0.41/0.59 tff(67,plain,
% 0.41/0.59 (((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))) <=> ((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[66])).
% 0.43/0.59 tff(68,plain,
% 0.43/0.59 ((~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))) <=> (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[67])).
% 0.43/0.59 tff(69,plain,
% 0.43/0.59 ((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) <=> (~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18))))))))))),
% 0.43/0.59 inference(rewrite,[status(thm)],[])).
% 0.43/0.59 tff(70,plain,
% 0.43/0.59 (((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))) <=> ((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[69, 68])).
% 0.43/0.59 tff(71,plain,
% 0.43/0.59 ((~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) <=> (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[70])).
% 0.43/0.59 tff(72,plain,
% 0.43/0.59 (((~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))))) <=> ((~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))))),
% 0.43/0.59 inference(monotonicity,[status(thm)],[71])).
% 0.43/0.59 tff(73,plain,
% 0.43/0.59 (((~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))))) <=> ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[72, 63])).
% 0.43/0.60 tff(74,plain,
% 0.43/0.60 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, 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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))))),
% 0.43/0.60 inference(monotonicity,[status(thm)],[73])).
% 0.43/0.60 tff(75,plain,
% 0.43/0.60 (((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, 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_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))),
% 0.43/0.60 inference(transitivity,[status(thm)],[74, 62])).
% 0.43/0.60 tff(76,plain,
% 0.43/0.60 ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))))),
% 0.43/0.60 inference(quant_inst,[status(thm)],[])).
% 0.43/0.60 tff(77,plain,
% 0.43/0.60 ((~![A: $i, B: $i] : ((~strict_latt_str(B)) | (~latt_str(B)) | (~((~((B = boole_lattice(A)) | (~(the_carrier(B) = powerset(A))) | (~((~element(tptp_fun_C_0(B, A), powerset(A))) | (~element(tptp_fun_D_1(B, A), powerset(A))) | (~((~(apply_binary(the_L_join(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_union2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)))) | (~(apply_binary(the_L_meet(B), tptp_fun_C_0(B, A), tptp_fun_D_1(B, A)) = subset_intersection2(A, tptp_fun_C_0(B, A), tptp_fun_D_1(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)))))))))))))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.43/0.61 tff(78,plain,
% 0.43/0.61 ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))) | (~strict_latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[77, 61])).
% 0.43/0.61 tff(79,plain,
% 0.43/0.61 (~((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[78, 39, 36])).
% 0.43/0.61 tff(80,plain,
% 0.43/0.61 (((~((latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18)) | (~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~((~element(tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~element(tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_union2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)) = subset_intersection2(A!18, tptp_fun_C_0(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18), tptp_fun_D_1(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))), A!18)))))))))) | (~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))))) | ((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(81,plain,
% 0.43/0.61 ((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.43/0.61 tff(82,plain,
% 0.43/0.61 ((~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))) | (~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(83,plain,
% 0.43/0.61 ((~((~(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))) = boole_lattice(A!18))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))))) | (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[82, 32])).
% 0.43/0.61 tff(84,plain,
% 0.43/0.61 (~((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[83, 81])).
% 0.43/0.61 tff(85,plain,
% 0.43/0.61 (((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))) | (the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(86,plain,
% 0.43/0.61 (the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.43/0.61 tff(87,plain,
% 0.43/0.61 (powerset(A!18) = the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.43/0.61 inference(symmetry,[status(thm)],[86])).
% 0.43/0.61 tff(88,plain,
% 0.43/0.61 (powerset(A!18) = the_carrier(boole_lattice(A!18))),
% 0.43/0.61 inference(transitivity,[status(thm)],[87, 33])).
% 0.43/0.61 tff(89,plain,
% 0.43/0.61 (element(C!19, powerset(A!18)) <=> element(C!19, the_carrier(boole_lattice(A!18)))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[88])).
% 0.43/0.61 tff(90,plain,
% 0.43/0.61 (element(C!19, the_carrier(boole_lattice(A!18))) <=> element(C!19, powerset(A!18))),
% 0.43/0.61 inference(symmetry,[status(thm)],[89])).
% 0.43/0.61 tff(91,plain,
% 0.43/0.61 ((~![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))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(92,plain,
% 0.43/0.61 ((~![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))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(93,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/sandbox/benchmark/theBenchmark.p','t1_lattice3')).
% 0.43/0.61 tff(94,plain,
% 0.43/0.61 (~![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)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[93, 92])).
% 0.43/0.61 tff(95,plain,
% 0.43/0.61 (~![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)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[94, 91])).
% 0.43/0.61 tff(96,plain,
% 0.43/0.61 (~![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)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.43/0.61 tff(97,plain,
% 0.43/0.61 (~![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)))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[96, 91])).
% 0.43/0.61 tff(98,plain,
% 0.43/0.61 (~((~element(C!19, the_carrier(boole_lattice(A!18)))) | ((join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)) & (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19))))),
% 0.43/0.61 inference(and_elim,[status(thm)],[97])).
% 0.43/0.61 tff(99,plain,
% 0.43/0.61 (element(C!19, the_carrier(boole_lattice(A!18)))),
% 0.43/0.61 inference(or_elim,[status(thm)],[98])).
% 0.43/0.61 tff(100,plain,
% 0.43/0.61 (element(C!19, powerset(A!18))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[99, 90])).
% 0.43/0.61 tff(101,plain,
% 0.43/0.61 (element(B!17, powerset(A!18)) <=> element(B!17, the_carrier(boole_lattice(A!18)))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[88])).
% 0.43/0.61 tff(102,plain,
% 0.43/0.61 (element(B!17, the_carrier(boole_lattice(A!18))) <=> element(B!17, powerset(A!18))),
% 0.43/0.61 inference(symmetry,[status(thm)],[101])).
% 0.43/0.61 tff(103,plain,
% 0.43/0.61 (element(B!17, the_carrier(boole_lattice(A!18)))),
% 0.43/0.61 inference(and_elim,[status(thm)],[97])).
% 0.43/0.61 tff(104,plain,
% 0.43/0.61 (element(B!17, powerset(A!18))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.43/0.61 tff(105,plain,
% 0.43/0.61 (^[A: $i, B: $i, C: $i] : refl(((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(106,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[105])).
% 0.43/0.61 tff(107,plain,
% 0.43/0.61 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(C, powerset(A))) | (~element(B, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))))), rewrite((~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(108,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[107])).
% 0.43/0.61 tff(109,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(110,plain,
% 0.43/0.61 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C))))),
% 0.43/0.61 inference(bind,[status(th)],[])).
% 0.43/0.61 tff(111,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.43/0.61 inference(quant_intro,[status(thm)],[110])).
% 0.43/0.61 tff(112,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_intersection2(A, B, C) = set_intersection2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k5_subset_1')).
% 0.43/0.61 tff(113,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.43/0.61 tff(114,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[113, 109])).
% 0.43/0.61 tff(115,plain,(
% 0.43/0.61 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.43/0.61 inference(skolemize,[status(sab)],[114])).
% 0.43/0.61 tff(116,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[115, 108])).
% 0.43/0.61 tff(117,plain,
% 0.43/0.61 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[116, 106])).
% 0.43/0.61 tff(118,plain,
% 0.43/0.61 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(119,plain,
% 0.43/0.61 (((subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18)))) <=> ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(120,plain,
% 0.43/0.61 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19))))),
% 0.43/0.61 inference(monotonicity,[status(thm)],[119])).
% 0.43/0.61 tff(121,plain,
% 0.43/0.61 (((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)))),
% 0.43/0.61 inference(transitivity,[status(thm)],[120, 118])).
% 0.43/0.61 tff(122,plain,
% 0.43/0.61 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(123,plain,
% 0.43/0.61 ((~![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19))),
% 0.43/0.61 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.43/0.61 tff(124,plain,
% 0.43/0.61 (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[123, 117, 104, 100])).
% 0.43/0.61 tff(125,plain,
% 0.43/0.61 (((~(the_carrier(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = powerset(A!18))) | (~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D))))))))) | ![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))),
% 0.43/0.61 inference(tautology,[status(thm)],[])).
% 0.43/0.61 tff(126,plain,
% 0.43/0.61 (![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))),
% 0.43/0.61 inference(unit_resolution,[status(thm)],[125, 84])).
% 0.43/0.61 tff(127,plain,
% 0.43/0.61 (((~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))) | ((~element(B!17, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D)))))))) <=> ((~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))) | (~element(B!17, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D)))))))),
% 0.43/0.61 inference(rewrite,[status(thm)],[])).
% 0.43/0.61 tff(128,plain,
% 0.43/0.61 ((~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))) | ((~element(B!17, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D)))))))),
% 0.43/0.61 inference(quant_inst,[status(thm)],[])).
% 0.43/0.61 tff(129,plain,
% 0.43/0.61 ((~![C: $i] : ((~element(C, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_union2(A!18, C, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), C, D) = subset_intersection2(A!18, C, D)))))))) | (~element(B!17, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[128, 127])).
% 0.43/0.62 tff(130,plain,
% 0.43/0.62 ((~element(B!17, powerset(A!18))) | ![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[129, 126])).
% 0.43/0.62 tff(131,plain,
% 0.43/0.62 (![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[130, 104])).
% 0.43/0.62 tff(132,plain,
% 0.43/0.62 (((~![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))) | ((~element(C!19, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19))))))) <=> ((~![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))) | (~element(C!19, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(133,plain,
% 0.43/0.62 ((~![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))) | ((~element(C!19, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19))))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(134,plain,
% 0.43/0.62 ((~![D: $i] : ((~element(D, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_union2(A!18, B!17, D))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, D) = subset_intersection2(A!18, B!17, D))))))) | (~element(C!19, powerset(A!18))) | (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19)))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.43/0.62 tff(135,plain,
% 0.43/0.62 (~((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[134, 100, 131])).
% 0.43/0.62 tff(136,plain,
% 0.43/0.62 (((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19)))) | (apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(137,plain,
% 0.43/0.62 (apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19)),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[136, 135])).
% 0.43/0.62 tff(138,plain,
% 0.43/0.62 (the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = the_L_meet(boole_lattice(A!18))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[32])).
% 0.43/0.62 tff(139,plain,
% 0.43/0.62 (the_L_meet(boole_lattice(A!18)) = the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.43/0.62 inference(symmetry,[status(thm)],[138])).
% 0.43/0.62 tff(140,plain,
% 0.43/0.62 (apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19)),
% 0.43/0.62 inference(monotonicity,[status(thm)],[139])).
% 0.43/0.62 tff(141,plain,
% 0.43/0.62 (^[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)))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(142,plain,
% 0.43/0.62 (![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))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[141])).
% 0.43/0.62 tff(143,plain,
% 0.43/0.62 (![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))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(144,axiom,(![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.43/0.62 tff(145,plain,
% 0.43/0.62 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.43/0.62 tff(146,plain,(
% 0.43/0.62 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.43/0.62 inference(skolemize,[status(sab)],[145])).
% 0.43/0.62 tff(147,plain,
% 0.43/0.62 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.43/0.62 tff(148,plain,
% 0.43/0.62 ((~![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!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(149,plain,
% 0.43/0.62 (relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.43/0.62 tff(150,plain,
% 0.43/0.62 (meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) <=> meet_semilatt_str(boole_lattice(A!18))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[32])).
% 0.43/0.62 tff(151,plain,
% 0.43/0.62 (^[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))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(152,plain,
% 0.43/0.62 (![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)))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[151])).
% 0.43/0.62 tff(153,plain,
% 0.43/0.62 (^[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))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(154,plain,
% 0.43/0.62 (![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)))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[153])).
% 0.43/0.62 tff(155,plain,
% 0.43/0.62 (![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)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(156,plain,
% 0.43/0.62 (^[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))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(157,plain,
% 0.43/0.62 (![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)))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[156])).
% 0.43/0.62 tff(158,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.43/0.62 tff(159,plain,
% 0.43/0.62 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.43/0.62 tff(160,plain,
% 0.43/0.62 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.43/0.62 tff(161,plain,(
% 0.43/0.62 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.43/0.62 inference(skolemize,[status(sab)],[160])).
% 0.43/0.62 tff(162,plain,
% 0.43/0.62 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.43/0.62 tff(163,plain,
% 0.43/0.62 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.43/0.62 tff(164,plain,
% 0.43/0.62 (((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))))) <=> ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(165,plain,
% 0.43/0.62 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(166,plain,
% 0.43/0.62 ((~![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))) | (~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.43/0.62 tff(167,plain,
% 0.43/0.62 ((~latt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[166, 163])).
% 0.43/0.62 tff(168,plain,
% 0.43/0.62 (~((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[167, 39])).
% 0.43/0.62 tff(169,plain,
% 0.43/0.62 (((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))) | meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(170,plain,
% 0.43/0.62 (meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[169, 168])).
% 0.43/0.62 tff(171,plain,
% 0.43/0.62 (meet_semilatt_str(boole_lattice(A!18))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[170, 150])).
% 0.43/0.62 tff(172,plain,
% 0.43/0.62 (^[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)))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(173,plain,
% 0.43/0.62 (![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))))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[172])).
% 0.43/0.62 tff(174,plain,
% 0.43/0.62 (^[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)))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(175,plain,
% 0.43/0.62 (![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))))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[174])).
% 0.43/0.62 tff(176,plain,
% 0.43/0.62 (![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))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(177,plain,
% 0.43/0.62 (^[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))))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(178,plain,
% 0.43/0.62 (![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))))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[177])).
% 0.43/0.62 tff(179,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/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.43/0.62 tff(180,plain,
% 0.43/0.62 (![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))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.43/0.62 tff(181,plain,
% 0.43/0.62 (![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))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.43/0.62 tff(182,plain,(
% 0.43/0.62 ![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))))),
% 0.43/0.62 inference(skolemize,[status(sab)],[181])).
% 0.43/0.62 tff(183,plain,
% 0.43/0.62 (![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))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.43/0.62 tff(184,plain,
% 0.43/0.62 (![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))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[183, 173])).
% 0.43/0.62 tff(185,plain,
% 0.43/0.62 (((~![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(boole_lattice(A!18))) | (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))) <=> ((~![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(boole_lattice(A!18))) | (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(186,plain,
% 0.43/0.62 ((~![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(boole_lattice(A!18))) | (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(187,plain,
% 0.43/0.62 ((~![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(boole_lattice(A!18))) | (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.43/0.62 tff(188,plain,
% 0.43/0.62 ((~meet_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[187, 184])).
% 0.43/0.62 tff(189,plain,
% 0.43/0.62 (~((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[188, 171])).
% 0.43/0.62 tff(190,plain,
% 0.43/0.62 (((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(191,plain,
% 0.43/0.62 (relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.43/0.62 tff(192,plain,
% 0.43/0.62 ((~(relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(193,plain,
% 0.43/0.62 ((~(relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[192, 191])).
% 0.43/0.62 tff(194,plain,
% 0.43/0.62 (relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[193, 149])).
% 0.43/0.62 tff(195,plain,
% 0.43/0.62 (((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(196,plain,
% 0.43/0.62 (quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[195, 189])).
% 0.43/0.62 tff(197,plain,
% 0.43/0.62 (((~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | function(the_L_meet(boole_lattice(A!18)))),
% 0.43/0.62 inference(tautology,[status(thm)],[])).
% 0.43/0.62 tff(198,plain,
% 0.43/0.62 (function(the_L_meet(boole_lattice(A!18)))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[197, 189])).
% 0.43/0.62 tff(199,plain,
% 0.43/0.62 (empty(powerset(A!18)) <=> empty(the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[88])).
% 0.43/0.62 tff(200,plain,
% 0.43/0.62 ((~empty(powerset(A!18))) <=> (~empty(the_carrier(boole_lattice(A!18))))),
% 0.43/0.62 inference(monotonicity,[status(thm)],[199])).
% 0.43/0.62 tff(201,plain,
% 0.43/0.62 (^[A: $i] : refl((~empty(powerset(A))) <=> (~empty(powerset(A))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(202,plain,
% 0.43/0.62 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[201])).
% 0.43/0.62 tff(203,plain,
% 0.43/0.62 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.43/0.62 inference(rewrite,[status(thm)],[])).
% 0.43/0.62 tff(204,axiom,(![A: $i] : (~empty(powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_subset_1')).
% 0.43/0.62 tff(205,plain,
% 0.43/0.62 (![A: $i] : (~empty(powerset(A)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[204, 203])).
% 0.43/0.62 tff(206,plain,(
% 0.43/0.62 ![A: $i] : (~empty(powerset(A)))),
% 0.43/0.62 inference(skolemize,[status(sab)],[205])).
% 0.43/0.62 tff(207,plain,
% 0.43/0.62 (![A: $i] : (~empty(powerset(A)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[206, 202])).
% 0.43/0.62 tff(208,plain,
% 0.43/0.62 ((~![A: $i] : (~empty(powerset(A)))) | (~empty(powerset(A!18)))),
% 0.43/0.62 inference(quant_inst,[status(thm)],[])).
% 0.43/0.62 tff(209,plain,
% 0.43/0.62 (~empty(powerset(A!18))),
% 0.43/0.62 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.43/0.62 tff(210,plain,
% 0.43/0.62 (~empty(the_carrier(boole_lattice(A!18)))),
% 0.43/0.62 inference(modus_ponens,[status(thm)],[209, 200])).
% 0.43/0.62 tff(211,plain,
% 0.43/0.62 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B))))),
% 0.43/0.62 inference(bind,[status(th)],[])).
% 0.43/0.62 tff(212,plain,
% 0.43/0.62 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 0.43/0.62 inference(quant_intro,[status(thm)],[211])).
% 0.43/0.62 tff(213,plain,
% 0.43/0.62 (^[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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ((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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))))), 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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(214,plain,
% 0.43/0.63 (![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[213])).
% 0.43/0.63 tff(215,plain,
% 0.43/0.63 (![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(216,plain,
% 0.43/0.63 (^[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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> (((~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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))))), 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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ((~((~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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))), (((((((((~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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ((~((~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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(217,plain,
% 0.43/0.63 (![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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F))) <=> ![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[216])).
% 0.43/0.63 tff(218,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)) => (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_binop_1')).
% 0.43/0.63 tff(219,plain,
% 0.43/0.63 (![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[218, 217])).
% 0.43/0.63 tff(220,plain,
% 0.43/0.63 (![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[219, 215])).
% 0.43/0.63 tff(221,plain,(
% 0.43/0.63 ![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))) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)))),
% 0.43/0.63 inference(skolemize,[status(sab)],[220])).
% 0.43/0.63 tff(222,plain,
% 0.43/0.63 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[221, 214])).
% 0.43/0.63 tff(223,plain,
% 0.43/0.63 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~function(D)) | (~quasi_total(D, cartesian_product2(A, B), C)) | (~relation_of2(D, cartesian_product2(A, B), C)) | (~element(E, A)) | (~element(F, B)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[222, 212])).
% 0.43/0.63 tff(224,plain,
% 0.43/0.63 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(225,plain,
% 0.43/0.63 ((empty(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18))))) <=> ((~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(226,plain,
% 0.43/0.63 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19))))),
% 0.43/0.63 inference(monotonicity,[status(thm)],[225])).
% 0.43/0.63 tff(227,plain,
% 0.43/0.63 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)))),
% 0.43/0.63 inference(transitivity,[status(thm)],[226, 224])).
% 0.43/0.63 tff(228,plain,
% 0.43/0.63 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))),
% 0.43/0.63 inference(quant_inst,[status(thm)],[])).
% 0.43/0.63 tff(229,plain,
% 0.43/0.63 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_meet(boole_lattice(A!18)))) | (~quasi_total(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_meet(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[228, 227])).
% 0.43/0.63 tff(230,plain,
% 0.43/0.63 (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_meet(boole_lattice(A!18)), B!17, C!19)),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[229, 223, 103, 99, 210, 198, 196, 194])).
% 0.43/0.63 tff(231,plain,
% 0.43/0.63 (^[A: $i] : refl((~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(232,plain,
% 0.43/0.63 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[231])).
% 0.43/0.63 tff(233,plain,
% 0.43/0.63 (^[A: $i] : rewrite(((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A))))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(234,plain,
% 0.43/0.63 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> ![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[233])).
% 0.43/0.63 tff(235,plain,
% 0.43/0.63 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A))) <=> ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 0.43/0.63 inference(rewrite,[status(thm)],[])).
% 0.43/0.63 tff(236,axiom,(![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_lattice3')).
% 0.43/0.63 tff(237,plain,
% 0.43/0.63 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.43/0.63 tff(238,plain,(
% 0.43/0.63 ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 0.43/0.63 inference(skolemize,[status(sab)],[237])).
% 0.43/0.63 tff(239,plain,
% 0.43/0.63 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[238, 234])).
% 0.43/0.63 tff(240,plain,
% 0.43/0.63 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.43/0.63 inference(modus_ponens,[status(thm)],[239, 232])).
% 0.43/0.63 tff(241,plain,
% 0.43/0.63 ((~![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))) | (~(empty_carrier(boole_lattice(A!18)) | (~strict_latt_str(boole_lattice(A!18)))))),
% 0.43/0.63 inference(quant_inst,[status(thm)],[])).
% 0.43/0.63 tff(242,plain,
% 0.43/0.63 (~(empty_carrier(boole_lattice(A!18)) | (~strict_latt_str(boole_lattice(A!18))))),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[241, 240])).
% 0.43/0.63 tff(243,plain,
% 0.43/0.63 ((empty_carrier(boole_lattice(A!18)) | (~strict_latt_str(boole_lattice(A!18)))) | (~empty_carrier(boole_lattice(A!18)))),
% 0.43/0.63 inference(tautology,[status(thm)],[])).
% 0.43/0.63 tff(244,plain,
% 0.43/0.63 (~empty_carrier(boole_lattice(A!18))),
% 0.43/0.63 inference(unit_resolution,[status(thm)],[243, 242])).
% 0.43/0.63 tff(245,plain,
% 0.43/0.63 (^[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))))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(246,plain,
% 0.43/0.63 (![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)))))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[245])).
% 0.43/0.63 tff(247,plain,
% 0.43/0.63 (^[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))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(248,plain,
% 0.43/0.63 (![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)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[247])).
% 0.43/0.63 tff(249,plain,
% 0.43/0.63 (^[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))))),
% 0.43/0.63 inference(bind,[status(th)],[])).
% 0.43/0.63 tff(250,plain,
% 0.43/0.63 (![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)))),
% 0.43/0.63 inference(quant_intro,[status(thm)],[249])).
% 0.43/0.63 tff(251,plain,
% 0.43/0.63 (![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)))),
% 0.43/0.63 inference(transitivity,[status(thm)],[250, 248])).
% 0.47/0.63 tff(252,plain,
% 0.47/0.63 (^[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)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(253,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[252])).
% 0.47/0.63 tff(254,plain,
% 0.47/0.63 (![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)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(255,plain,
% 0.47/0.63 (^[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)))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(256,plain,
% 0.47/0.63 (![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)))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[255])).
% 0.47/0.63 tff(257,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/sandbox/benchmark/theBenchmark.p','d2_lattices')).
% 0.47/0.63 tff(258,plain,
% 0.47/0.63 (![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)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.47/0.63 tff(259,plain,
% 0.47/0.63 (![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)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[258, 254])).
% 0.47/0.63 tff(260,plain,(
% 0.47/0.63 ![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)))))),
% 0.47/0.63 inference(skolemize,[status(sab)],[259])).
% 0.47/0.63 tff(261,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[260, 253])).
% 0.47/0.63 tff(262,plain,
% 0.47/0.63 (![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)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[261, 251])).
% 0.47/0.63 tff(263,plain,
% 0.47/0.63 (![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)))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[262, 246])).
% 0.47/0.63 tff(264,plain,
% 0.47/0.63 (((~![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!18)) | (~meet_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), 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!18)) | (~meet_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C)))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(265,plain,
% 0.47/0.63 ((~![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!18)) | (~meet_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C)))))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(266,plain,
% 0.47/0.64 ((~![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!18)) | (~meet_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.47/0.64 tff(267,plain,
% 0.47/0.64 (empty_carrier(boole_lattice(A!18)) | (~meet_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[266, 263])).
% 0.47/0.64 tff(268,plain,
% 0.47/0.64 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[267, 171, 244])).
% 0.47/0.64 tff(269,plain,
% 0.47/0.64 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))) | ((~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(270,plain,
% 0.47/0.64 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))) | ((~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(271,plain,
% 0.47/0.64 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B, C))))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.47/0.64 tff(272,plain,
% 0.47/0.64 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[271, 103, 268])).
% 0.47/0.64 tff(273,plain,
% 0.47/0.64 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))) | ((~element(C!19, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19)))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(274,plain,
% 0.47/0.64 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))) | ((~element(C!19, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(275,plain,
% 0.47/0.64 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | (meet(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.47/0.64 tff(276,plain,
% 0.47/0.64 (meet(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)), B!17, C!19)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[275, 99, 272])).
% 0.47/0.64 tff(277,plain,
% 0.47/0.64 (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)),
% 0.47/0.64 inference(transitivity,[status(thm)],[276, 230, 140, 137, 124])).
% 0.47/0.64 tff(278,plain,
% 0.47/0.64 (^[A: $i, B: $i, C: $i] : refl(((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(279,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A)))) <=> ![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[278])).
% 0.47/0.64 tff(280,plain,
% 0.47/0.64 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((element(B, powerset(A)) & element(C, powerset(A))) <=> (~((~element(C, powerset(A))) | (~element(B, powerset(A)))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> (~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))))), rewrite((~(~((~element(C, powerset(A))) | (~element(B, powerset(A)))))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A))))), ((~(element(B, powerset(A)) & element(C, powerset(A)))) <=> ((~element(C, powerset(A))) | (~element(B, powerset(A)))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))) <=> (((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))))), rewrite((((~element(C, powerset(A))) | (~element(B, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))) <=> ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))), (((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))) <=> ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(281,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[280])).
% 0.47/0.64 tff(282,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(283,plain,
% 0.47/0.64 (^[A: $i, B: $i, C: $i] : rewrite(((element(B, powerset(A)) & element(C, powerset(A))) => (subset_union2(A, B, C) = set_union2(B, C))) <=> ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(284,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_union2(A, B, C) = set_union2(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[283])).
% 0.47/0.64 tff(285,axiom,(![A: $i, B: $i, C: $i] : ((element(B, powerset(A)) & element(C, powerset(A))) => (subset_union2(A, B, C) = set_union2(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_subset_1')).
% 0.47/0.64 tff(286,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.47/0.64 tff(287,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[286, 282])).
% 0.47/0.64 tff(288,plain,(
% 0.47/0.64 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[287])).
% 0.47/0.64 tff(289,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[288, 281])).
% 0.47/0.64 tff(290,plain,
% 0.47/0.64 (![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[289, 279])).
% 0.47/0.64 tff(291,plain,
% 0.47/0.64 (((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(292,plain,
% 0.47/0.64 (((subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18)))) <=> ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(293,plain,
% 0.47/0.64 (((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[292])).
% 0.47/0.64 tff(294,plain,
% 0.47/0.64 (((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))) <=> ((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[293, 291])).
% 0.47/0.64 tff(295,plain,
% 0.47/0.64 ((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | ((subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)) | (~element(C!19, powerset(A!18))) | (~element(B!17, powerset(A!18))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(296,plain,
% 0.47/0.64 ((~![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))) | (~element(B!17, powerset(A!18))) | (~element(C!19, powerset(A!18))) | (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.47/0.64 tff(297,plain,
% 0.47/0.64 (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[296, 290, 104, 100])).
% 0.47/0.64 tff(298,plain,
% 0.47/0.64 (((~(apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))) | (~(apply_binary(the_L_meet(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_intersection2(A!18, B!17, C!19)))) | (apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(299,plain,
% 0.47/0.64 (apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19) = subset_union2(A!18, B!17, C!19)),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[298, 135])).
% 0.47/0.64 tff(300,plain,
% 0.47/0.64 (the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) = the_L_join(boole_lattice(A!18))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[32])).
% 0.47/0.64 tff(301,plain,
% 0.47/0.64 (the_L_join(boole_lattice(A!18)) = the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.48/0.64 inference(symmetry,[status(thm)],[300])).
% 0.48/0.64 tff(302,plain,
% 0.48/0.64 (apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))), B!17, C!19)),
% 0.48/0.64 inference(monotonicity,[status(thm)],[301])).
% 0.48/0.64 tff(303,plain,
% 0.48/0.64 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(304,plain,
% 0.48/0.64 (relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[303, 147])).
% 0.48/0.64 tff(305,plain,
% 0.48/0.64 (join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))) <=> join_semilatt_str(boole_lattice(A!18))),
% 0.48/0.64 inference(monotonicity,[status(thm)],[32])).
% 0.48/0.64 tff(306,plain,
% 0.48/0.64 (((~meet_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))) | (~join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18)))))) | join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(307,plain,
% 0.48/0.64 (join_semilatt_str(latt_str_of(the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), the_L_meet(boole_lattice(A!18))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[306, 168])).
% 0.48/0.64 tff(308,plain,
% 0.48/0.64 (join_semilatt_str(boole_lattice(A!18))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[307, 305])).
% 0.48/0.64 tff(309,plain,
% 0.48/0.64 (^[A: $i] : refl(((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))) <=> ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(310,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))) <=> ![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[309])).
% 0.48/0.64 tff(311,plain,
% 0.48/0.64 (^[A: $i] : rewrite(((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(312,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[311])).
% 0.48/0.64 tff(313,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(314,plain,
% 0.48/0.64 (^[A: $i] : trans(monotonicity(rewrite(((function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) <=> (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))), ((join_semilatt_str(A) => ((function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> (join_semilatt_str(A) => (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))))), rewrite((join_semilatt_str(A) => (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), ((join_semilatt_str(A) => ((function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 0.48/0.64 inference(bind,[status(th)],[])).
% 0.48/0.64 tff(315,plain,
% 0.48/0.64 (![A: $i] : (join_semilatt_str(A) => ((function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)))) <=> ![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 0.48/0.64 inference(quant_intro,[status(thm)],[314])).
% 0.48/0.64 tff(316,axiom,(![A: $i] : (join_semilatt_str(A) => ((function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.48/0.64 tff(317,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[316, 315])).
% 0.48/0.64 tff(318,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[317, 313])).
% 0.48/0.64 tff(319,plain,(
% 0.48/0.64 ![A: $i] : ((~join_semilatt_str(A)) | (function(the_L_join(A)) & quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A)) & relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))),
% 0.48/0.64 inference(skolemize,[status(sab)],[318])).
% 0.48/0.64 tff(320,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[319, 312])).
% 0.48/0.64 tff(321,plain,
% 0.48/0.64 (![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[320, 310])).
% 0.48/0.64 tff(322,plain,
% 0.48/0.64 (((~![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | ((~join_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))) <=> ((~![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | (~join_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))),
% 0.48/0.64 inference(rewrite,[status(thm)],[])).
% 0.48/0.64 tff(323,plain,
% 0.48/0.64 ((~![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | ((~join_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))))),
% 0.48/0.64 inference(quant_inst,[status(thm)],[])).
% 0.48/0.64 tff(324,plain,
% 0.48/0.64 ((~![A: $i] : ((~join_semilatt_str(A)) | (~((~function(the_L_join(A))) | (~quasi_total(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))) | (~relation_of2_as_subset(the_L_join(A), cartesian_product2(the_carrier(A), the_carrier(A)), the_carrier(A))))))) | (~join_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))))),
% 0.48/0.64 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.48/0.64 tff(325,plain,
% 0.48/0.64 ((~join_semilatt_str(boole_lattice(A!18))) | (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[324, 321])).
% 0.48/0.64 tff(326,plain,
% 0.48/0.64 (~((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[325, 308])).
% 0.48/0.64 tff(327,plain,
% 0.48/0.64 (((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(328,plain,
% 0.48/0.64 (relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.64 inference(unit_resolution,[status(thm)],[327, 326])).
% 0.48/0.64 tff(329,plain,
% 0.48/0.64 ((~(relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.64 inference(tautology,[status(thm)],[])).
% 0.48/0.64 tff(330,plain,
% 0.48/0.64 ((~(relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))) <=> relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[329, 328])).
% 0.48/0.65 tff(331,plain,
% 0.48/0.65 (relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[330, 304])).
% 0.48/0.65 tff(332,plain,
% 0.48/0.65 (((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(333,plain,
% 0.48/0.65 (quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[332, 326])).
% 0.48/0.65 tff(334,plain,
% 0.48/0.65 (((~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2_as_subset(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18))))) | function(the_L_join(boole_lattice(A!18)))),
% 0.48/0.65 inference(tautology,[status(thm)],[])).
% 0.48/0.65 tff(335,plain,
% 0.48/0.65 (function(the_L_join(boole_lattice(A!18)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[334, 326])).
% 0.48/0.65 tff(336,plain,
% 0.48/0.65 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(337,plain,
% 0.48/0.65 ((empty(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18))))) <=> ((~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(338,plain,
% 0.48/0.65 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19))))),
% 0.48/0.65 inference(monotonicity,[status(thm)],[337])).
% 0.48/0.65 tff(339,plain,
% 0.48/0.65 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[338, 336])).
% 0.48/0.65 tff(340,plain,
% 0.48/0.65 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(the_carrier(boole_lattice(A!18))) | empty(the_carrier(boole_lattice(A!18))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(341,plain,
% 0.48/0.65 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (empty(B) | empty(A) | (apply_binary_as_element(A, B, C, D, E, F) = apply_binary(D, E, F)) | (~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(B!17, the_carrier(boole_lattice(A!18)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | empty(the_carrier(boole_lattice(A!18))) | (~function(the_L_join(boole_lattice(A!18)))) | (~quasi_total(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (~relation_of2(the_L_join(boole_lattice(A!18)), cartesian_product2(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18))), the_carrier(boole_lattice(A!18)))) | (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.48/0.65 tff(342,plain,
% 0.48/0.65 (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[341, 223, 103, 99, 210, 335, 333, 331])).
% 0.48/0.65 tff(343,plain,
% 0.48/0.65 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(344,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[343])).
% 0.48/0.65 tff(345,plain,
% 0.48/0.65 (^[A: $i] : refl((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(346,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[345])).
% 0.48/0.65 tff(347,plain,
% 0.48/0.65 (^[A: $i] : rewrite((empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(348,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[347])).
% 0.48/0.65 tff(349,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(transitivity,[status(thm)],[348, 346])).
% 0.48/0.65 tff(350,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~empty_carrier(A)) & join_semilatt_str(A)) <=> (~(empty_carrier(A) | (~join_semilatt_str(A))))), ((~((~empty_carrier(A)) & join_semilatt_str(A))) <=> (~(~(empty_carrier(A) | (~join_semilatt_str(A))))))), rewrite((~(~(empty_carrier(A) | (~join_semilatt_str(A))))) <=> (empty_carrier(A) | (~join_semilatt_str(A)))), ((~((~empty_carrier(A)) & join_semilatt_str(A))) <=> (empty_carrier(A) | (~join_semilatt_str(A))))), (((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ((empty_carrier(A) | (~join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))))), rewrite(((empty_carrier(A) | (~join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))), (((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(351,plain,
% 0.48/0.65 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[350])).
% 0.48/0.65 tff(352,plain,
% 0.48/0.65 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(353,plain,
% 0.48/0.65 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))) <=> ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))), (![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))) <=> ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) <=> (element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))), rewrite((element(B, the_carrier(A)) => ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))), ((element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) <=> ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))))), (![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) <=> ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))), ((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))))), rewrite((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))), ((((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))))),
% 0.48/0.65 inference(bind,[status(th)],[])).
% 0.48/0.65 tff(354,plain,
% 0.48/0.65 (![A: $i] : (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C))))) <=> ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(quant_intro,[status(thm)],[353])).
% 0.48/0.65 tff(355,axiom,(![A: $i] : (((~empty_carrier(A)) & join_semilatt_str(A)) => ![B: $i] : (element(B, the_carrier(A)) => ![C: $i] : (element(C, the_carrier(A)) => (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_lattices')).
% 0.48/0.65 tff(356,plain,
% 0.48/0.65 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[355, 354])).
% 0.48/0.65 tff(357,plain,
% 0.48/0.65 (![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[356, 352])).
% 0.48/0.65 tff(358,plain,(
% 0.48/0.65 ![A: $i] : ((~((~empty_carrier(A)) & join_semilatt_str(A))) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(skolemize,[status(sab)],[357])).
% 0.48/0.65 tff(359,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[358, 351])).
% 0.48/0.65 tff(360,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))) | (~join_semilatt_str(A)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[359, 349])).
% 0.48/0.65 tff(361,plain,
% 0.48/0.65 (![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[360, 344])).
% 0.48/0.65 tff(362,plain,
% 0.48/0.65 (((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))) | (empty_carrier(boole_lattice(A!18)) | (~join_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C)))))) <=> ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))) | empty_carrier(boole_lattice(A!18)) | (~join_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C)))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(363,plain,
% 0.48/0.65 ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))) | (empty_carrier(boole_lattice(A!18)) | (~join_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C)))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(364,plain,
% 0.48/0.65 ((~![A: $i] : (empty_carrier(A) | (~join_semilatt_str(A)) | ![B: $i] : ((~element(B, the_carrier(A))) | ![C: $i] : ((~element(C, the_carrier(A))) | (join(A, B, C) = apply_binary_as_element(the_carrier(A), the_carrier(A), the_carrier(A), the_L_join(A), B, C)))))) | empty_carrier(boole_lattice(A!18)) | (~join_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.48/0.65 tff(365,plain,
% 0.48/0.65 (empty_carrier(boole_lattice(A!18)) | (~join_semilatt_str(boole_lattice(A!18))) | ![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[364, 361])).
% 0.48/0.65 tff(366,plain,
% 0.48/0.65 (![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[365, 308, 244])).
% 0.48/0.65 tff(367,plain,
% 0.48/0.65 (((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))) | ((~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C))))) <=> ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C))))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(368,plain,
% 0.48/0.65 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))) | ((~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C))))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(369,plain,
% 0.48/0.65 ((~![B: $i] : ((~element(B, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B, C))))) | (~element(B!17, the_carrier(boole_lattice(A!18)))) | ![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))),
% 0.48/0.65 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.48/0.65 tff(370,plain,
% 0.48/0.65 (![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))),
% 0.48/0.65 inference(unit_resolution,[status(thm)],[369, 103, 366])).
% 0.48/0.65 tff(371,plain,
% 0.48/0.65 (((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))) | ((~element(C!19, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19)))) <=> ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19)))),
% 0.48/0.65 inference(rewrite,[status(thm)],[])).
% 0.48/0.65 tff(372,plain,
% 0.48/0.65 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))) | ((~element(C!19, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19)))),
% 0.48/0.65 inference(quant_inst,[status(thm)],[])).
% 0.48/0.65 tff(373,plain,
% 0.48/0.65 ((~![C: $i] : ((~element(C, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C)))) | (~element(C!19, the_carrier(boole_lattice(A!18)))) | (join(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.48/0.66 tff(374,plain,
% 0.48/0.66 (join(boole_lattice(A!18), B!17, C!19) = apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19)),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[373, 99, 370])).
% 0.48/0.66 tff(375,plain,
% 0.48/0.66 (join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)),
% 0.48/0.66 inference(transitivity,[status(thm)],[374, 342, 302, 299, 297])).
% 0.48/0.66 tff(376,plain,
% 0.48/0.66 ((~(~((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))))) <=> ((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(377,plain,
% 0.48/0.66 (((join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)) & (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19))) <=> (~((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))))),
% 0.48/0.66 inference(rewrite,[status(thm)],[])).
% 0.48/0.66 tff(378,plain,
% 0.48/0.66 ((~((join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)) & (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))) <=> (~(~((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19))))))),
% 0.48/0.66 inference(monotonicity,[status(thm)],[377])).
% 0.48/0.66 tff(379,plain,
% 0.48/0.66 ((~((join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)) & (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))) <=> ((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19))))),
% 0.48/0.66 inference(transitivity,[status(thm)],[378, 376])).
% 0.48/0.66 tff(380,plain,
% 0.48/0.66 (~((join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)) & (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))),
% 0.48/0.66 inference(or_elim,[status(thm)],[98])).
% 0.48/0.66 tff(381,plain,
% 0.48/0.66 ((~(join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19))) | (~(meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)))),
% 0.48/0.66 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.48/0.66 tff(382,plain,
% 0.48/0.66 ($false),
% 0.48/0.66 inference(unit_resolution,[status(thm)],[381, 375, 277])).
% 0.48/0.66 % SZS output end Proof
% 0.48/0.66 % E exiting
%------------------------------------------------------------------------------