TSTP Solution File: SEU343+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 20 07:29:01 EDT 2022
% Result : Theorem 0.48s 0.55s
% Output : Proof 0.57s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU343+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Sep 3 12:18:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.48/0.55 % SZS status Theorem
% 0.48/0.55 % SZS output start Proof
% 0.48/0.55 tff(set_intersection2_type, type, (
% 0.48/0.55 set_intersection2: ( $i * $i ) > $i)).
% 0.48/0.55 tff(tptp_fun_C_19_type, type, (
% 0.48/0.55 tptp_fun_C_19: $i)).
% 0.48/0.55 tff(tptp_fun_B_17_type, type, (
% 0.48/0.55 tptp_fun_B_17: $i)).
% 0.48/0.55 tff(meet_type, type, (
% 0.48/0.55 meet: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(boole_lattice_type, type, (
% 0.48/0.55 boole_lattice: $i > $i)).
% 0.48/0.55 tff(tptp_fun_A_18_type, type, (
% 0.48/0.55 tptp_fun_A_18: $i)).
% 0.48/0.55 tff(subset_intersection2_type, type, (
% 0.48/0.55 subset_intersection2: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(element_type, type, (
% 0.48/0.55 element: ( $i * $i ) > $o)).
% 0.48/0.55 tff(powerset_type, type, (
% 0.48/0.55 powerset: $i > $i)).
% 0.48/0.55 tff(the_carrier_type, type, (
% 0.48/0.55 the_carrier: $i > $i)).
% 0.48/0.55 tff(latt_str_of_type, type, (
% 0.48/0.55 latt_str_of: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(the_L_meet_type, type, (
% 0.48/0.55 the_L_meet: $i > $i)).
% 0.48/0.55 tff(the_L_join_type, type, (
% 0.48/0.55 the_L_join: $i > $i)).
% 0.48/0.55 tff(latt_str_type, type, (
% 0.48/0.55 latt_str: $i > $o)).
% 0.48/0.55 tff(strict_latt_str_type, type, (
% 0.48/0.55 strict_latt_str: $i > $o)).
% 0.48/0.55 tff(apply_binary_type, type, (
% 0.48/0.55 apply_binary: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(subset_union2_type, type, (
% 0.48/0.55 subset_union2: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(tptp_fun_D_1_type, type, (
% 0.48/0.55 tptp_fun_D_1: ( $i * $i ) > $i)).
% 0.48/0.55 tff(tptp_fun_C_0_type, type, (
% 0.48/0.55 tptp_fun_C_0: ( $i * $i ) > $i)).
% 0.48/0.55 tff(set_union2_type, type, (
% 0.48/0.55 set_union2: ( $i * $i ) > $i)).
% 0.48/0.55 tff(join_type, type, (
% 0.48/0.55 join: ( $i * $i * $i ) > $i)).
% 0.48/0.55 tff(apply_binary_as_element_type, type, (
% 0.48/0.55 apply_binary_as_element: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.48/0.55 tff(relation_of2_type, type, (
% 0.48/0.55 relation_of2: ( $i * $i * $i ) > $o)).
% 0.48/0.55 tff(cartesian_product2_type, type, (
% 0.48/0.55 cartesian_product2: ( $i * $i ) > $i)).
% 0.48/0.55 tff(relation_of2_as_subset_type, type, (
% 0.48/0.55 relation_of2_as_subset: ( $i * $i * $i ) > $o)).
% 0.48/0.55 tff(quasi_total_type, type, (
% 0.48/0.55 quasi_total: ( $i * $i * $i ) > $o)).
% 0.48/0.55 tff(function_type, type, (
% 0.48/0.55 function: $i > $o)).
% 0.48/0.55 tff(meet_semilatt_str_type, type, (
% 0.48/0.55 meet_semilatt_str: $i > $o)).
% 0.48/0.55 tff(join_semilatt_str_type, type, (
% 0.48/0.55 join_semilatt_str: $i > $o)).
% 0.48/0.55 tff(empty_type, type, (
% 0.48/0.55 empty: $i > $o)).
% 0.48/0.55 tff(empty_carrier_type, type, (
% 0.48/0.55 empty_carrier: $i > $o)).
% 0.48/0.55 tff(1,plain,
% 0.48/0.55 (^[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))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(2,plain,
% 0.48/0.55 (![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)))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[1])).
% 0.48/0.55 tff(3,plain,
% 0.48/0.55 (^[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))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(4,plain,
% 0.48/0.55 (![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)))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[3])).
% 0.48/0.55 tff(5,plain,
% 0.48/0.55 (![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)))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 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')).
% 0.48/0.55 tff(7,plain,
% 0.48/0.55 (![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.48/0.55 tff(8,plain,(
% 0.48/0.55 ![A: $i] : (strict_latt_str(boole_lattice(A)) & latt_str(boole_lattice(A)))),
% 0.48/0.55 inference(skolemize,[status(sab)],[7])).
% 0.48/0.55 tff(9,plain,
% 0.48/0.55 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[8, 4])).
% 0.48/0.55 tff(10,plain,
% 0.48/0.55 (![A: $i] : (~((~strict_latt_str(boole_lattice(A))) | (~latt_str(boole_lattice(A)))))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.48/0.55 tff(11,plain,
% 0.48/0.55 ((~![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)))))),
% 0.48/0.55 inference(quant_inst,[status(thm)],[])).
% 0.48/0.55 tff(12,plain,
% 0.48/0.55 (~((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18))))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.48/0.55 tff(13,plain,
% 0.48/0.55 (((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))) | latt_str(boole_lattice(A!18))),
% 0.48/0.55 inference(tautology,[status(thm)],[])).
% 0.48/0.55 tff(14,plain,
% 0.48/0.55 (latt_str(boole_lattice(A!18))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[13, 12])).
% 0.48/0.55 tff(15,plain,
% 0.48/0.55 (((~strict_latt_str(boole_lattice(A!18))) | (~latt_str(boole_lattice(A!18)))) | strict_latt_str(boole_lattice(A!18))),
% 0.48/0.55 inference(tautology,[status(thm)],[])).
% 0.48/0.55 tff(16,plain,
% 0.48/0.55 (strict_latt_str(boole_lattice(A!18))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[15, 12])).
% 0.48/0.55 tff(17,plain,
% 0.48/0.55 (^[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))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(18,plain,
% 0.48/0.55 (![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)))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[17])).
% 0.48/0.55 tff(19,plain,
% 0.48/0.55 (![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)))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(20,plain,
% 0.48/0.55 (^[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)))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(21,plain,
% 0.48/0.55 (![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)))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[20])).
% 0.48/0.55 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')).
% 0.48/0.55 tff(23,plain,
% 0.48/0.55 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.48/0.55 tff(24,plain,
% 0.48/0.55 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[23, 19])).
% 0.48/0.55 tff(25,plain,(
% 0.48/0.55 ![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.48/0.55 inference(skolemize,[status(sab)],[24])).
% 0.48/0.55 tff(26,plain,
% 0.48/0.55 (![A: $i] : ((A = latt_str_of(the_carrier(A), the_L_join(A), the_L_meet(A))) | (~strict_latt_str(A)) | (~latt_str(A)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[25, 18])).
% 0.48/0.55 tff(27,plain,
% 0.48/0.55 (((~![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))))),
% 0.48/0.55 inference(rewrite,[status(thm)],[])).
% 0.48/0.55 tff(28,plain,
% 0.48/0.55 ((~![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))))),
% 0.48/0.55 inference(quant_inst,[status(thm)],[])).
% 0.48/0.55 tff(29,plain,
% 0.48/0.55 ((~![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)))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.48/0.55 tff(30,plain,
% 0.48/0.55 ((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)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[29, 26])).
% 0.48/0.55 tff(31,plain,
% 0.48/0.55 (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)))),
% 0.48/0.55 inference(unit_resolution,[status(thm)],[30, 16, 14])).
% 0.48/0.55 tff(32,plain,
% 0.48/0.55 (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)),
% 0.48/0.55 inference(symmetry,[status(thm)],[31])).
% 0.48/0.55 tff(33,plain,
% 0.48/0.55 (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))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[32])).
% 0.48/0.55 tff(34,plain,
% 0.48/0.55 (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))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[32])).
% 0.48/0.55 tff(35,plain,
% 0.48/0.55 (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))))),
% 0.48/0.55 inference(symmetry,[status(thm)],[34])).
% 0.48/0.55 tff(36,plain,
% 0.48/0.55 (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))))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[14, 35])).
% 0.48/0.55 tff(37,plain,
% 0.48/0.55 (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))),
% 0.48/0.55 inference(monotonicity,[status(thm)],[32])).
% 0.48/0.55 tff(38,plain,
% 0.48/0.55 (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))))),
% 0.48/0.55 inference(symmetry,[status(thm)],[37])).
% 0.48/0.55 tff(39,plain,
% 0.48/0.55 (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))))),
% 0.48/0.55 inference(modus_ponens,[status(thm)],[16, 38])).
% 0.48/0.55 tff(40,plain,
% 0.48/0.55 (^[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)))))))))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(41,plain,
% 0.48/0.55 (![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)))))))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[40])).
% 0.48/0.55 tff(42,plain,
% 0.48/0.55 (^[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))))))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(43,plain,
% 0.48/0.55 (![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)))))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[42])).
% 0.48/0.55 tff(44,plain,
% 0.48/0.55 (^[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))))))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(45,plain,
% 0.48/0.55 (![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)))))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[44])).
% 0.48/0.55 tff(46,plain,
% 0.48/0.55 (![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)))))))))))))),
% 0.48/0.55 inference(transitivity,[status(thm)],[45, 43])).
% 0.48/0.55 tff(47,plain,
% 0.48/0.55 (^[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)))))))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(48,plain,
% 0.48/0.55 (![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)))))))))))))),
% 0.48/0.55 inference(quant_intro,[status(thm)],[47])).
% 0.48/0.55 tff(49,plain,
% 0.48/0.55 (^[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)))))))))))),
% 0.48/0.55 inference(bind,[status(th)],[])).
% 0.48/0.55 tff(50,plain,
% 0.48/0.55 (![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))))))))))),
% 0.50/0.55 inference(quant_intro,[status(thm)],[49])).
% 0.50/0.55 tff(51,plain,
% 0.50/0.55 (![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))))))))),
% 0.50/0.55 inference(rewrite,[status(thm)],[])).
% 0.50/0.55 tff(52,plain,
% 0.50/0.55 (^[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))))))))))),
% 0.50/0.55 inference(bind,[status(th)],[])).
% 0.50/0.55 tff(53,plain,
% 0.50/0.55 (![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))))))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[52])).
% 0.50/0.56 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')).
% 0.50/0.56 tff(55,plain,
% 0.50/0.56 (![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))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.50/0.56 tff(56,plain,
% 0.50/0.56 (![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))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.50/0.56 tff(57,plain,(
% 0.50/0.56 ![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)))))))))))),
% 0.50/0.56 inference(skolemize,[status(sab)],[56])).
% 0.50/0.56 tff(58,plain,
% 0.50/0.56 (![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))))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.50/0.56 tff(59,plain,
% 0.50/0.56 (![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)))))))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[58, 48])).
% 0.50/0.56 tff(60,plain,
% 0.50/0.56 (![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)))))))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[59, 46])).
% 0.50/0.56 tff(61,plain,
% 0.50/0.56 (![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)))))))))))))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[60, 41])).
% 0.50/0.56 tff(62,plain,
% 0.50/0.56 (((~![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))))) | (~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_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))))) | (~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_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)))))))))))))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(63,plain,
% 0.50/0.56 (((~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))))) | (~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_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)))))))))))))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(64,plain,
% 0.50/0.56 ((~![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))))))))),
% 0.50/0.56 inference(rewrite,[status(thm)],[])).
% 0.50/0.56 tff(65,plain,
% 0.50/0.56 (((~(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)))))))))),
% 0.50/0.56 inference(monotonicity,[status(thm)],[64])).
% 0.50/0.56 tff(66,plain,
% 0.50/0.56 ((~((~(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))))))))))),
% 0.50/0.56 inference(monotonicity,[status(thm)],[65])).
% 0.50/0.56 tff(67,plain,
% 0.50/0.56 (((~(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)))))))))))),
% 0.50/0.56 inference(monotonicity,[status(thm)],[66])).
% 0.50/0.56 tff(68,plain,
% 0.50/0.56 ((~((~(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))))))))))))),
% 0.50/0.56 inference(monotonicity,[status(thm)],[67])).
% 0.50/0.56 tff(69,plain,
% 0.50/0.56 ((~((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))))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(70,plain,
% 0.50/0.57 (((~((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)) | (~(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)))))))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[69, 68])).
% 0.50/0.57 tff(71,plain,
% 0.50/0.57 ((~((~((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)) | (~(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))))))))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[70])).
% 0.50/0.57 tff(72,plain,
% 0.50/0.57 (((~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))))) | (~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)))))))))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[71])).
% 0.50/0.57 tff(73,plain,
% 0.50/0.57 (((~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))))) | (~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))))) | (~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_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)))))))))))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[72, 63])).
% 0.50/0.58 tff(74,plain,
% 0.50/0.58 (((~![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)))))))))))))))) | ((~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))))) | (~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_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))))))))))))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[73])).
% 0.50/0.58 tff(75,plain,
% 0.50/0.58 (((~![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)))))))))))))))) | ((~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))))) | (~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_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)))))))))))))))),
% 0.50/0.58 inference(transitivity,[status(thm)],[74, 62])).
% 0.50/0.58 tff(76,plain,
% 0.50/0.58 ((~![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)))))))))))))))) | ((~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)))))))))))))))),
% 0.50/0.58 inference(quant_inst,[status(thm)],[])).
% 0.50/0.58 tff(77,plain,
% 0.50/0.58 ((~![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))))) | (~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_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))))))))))))))),
% 0.50/0.58 inference(modus_ponens,[status(thm)],[76, 75])).
% 0.50/0.58 tff(78,plain,
% 0.50/0.58 ((~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(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))))))))))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[77, 61])).
% 0.50/0.58 tff(79,plain,
% 0.50/0.58 (~((~((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)))))))))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[78, 39, 36])).
% 0.50/0.59 tff(80,plain,
% 0.50/0.59 (((~((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))) | (~![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)))))))))))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(81,plain,
% 0.50/0.59 ((~(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))))))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.50/0.59 tff(82,plain,
% 0.50/0.59 ((~((~(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))))))))))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(83,plain,
% 0.50/0.59 ((~((~(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)))))))))))) | (~((~(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))))))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[82, 32])).
% 0.50/0.59 tff(84,plain,
% 0.50/0.59 (~((~(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)))))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[83, 81])).
% 0.50/0.59 tff(85,plain,
% 0.50/0.59 (((~(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))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(86,plain,
% 0.50/0.59 (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)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[85, 84])).
% 0.50/0.59 tff(87,plain,
% 0.50/0.59 (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))))),
% 0.50/0.59 inference(symmetry,[status(thm)],[86])).
% 0.50/0.59 tff(88,plain,
% 0.50/0.59 (powerset(A!18) = the_carrier(boole_lattice(A!18))),
% 0.50/0.59 inference(transitivity,[status(thm)],[87, 33])).
% 0.50/0.59 tff(89,plain,
% 0.50/0.59 (element(C!19, powerset(A!18)) <=> element(C!19, the_carrier(boole_lattice(A!18)))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[88])).
% 0.50/0.59 tff(90,plain,
% 0.50/0.59 (element(C!19, the_carrier(boole_lattice(A!18))) <=> element(C!19, powerset(A!18))),
% 0.50/0.59 inference(symmetry,[status(thm)],[89])).
% 0.50/0.59 tff(91,plain,
% 0.50/0.59 (((~(~element(B!17, the_carrier(boole_lattice(A!18))))) & (~((~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)))))) <=> (element(B!17, the_carrier(boole_lattice(A!18))) & (~((~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))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(92,plain,
% 0.50/0.59 ((~![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))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(93,plain,
% 0.50/0.59 ((~![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))))))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(94,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')).
% 0.50/0.59 tff(95,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.50/0.59 tff(96,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[95, 92])).
% 0.50/0.59 tff(97,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.50/0.59 tff(98,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[97, 92])).
% 0.50/0.59 tff(99,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[98, 92])).
% 0.50/0.59 tff(100,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.50/0.59 tff(101,plain,
% 0.50/0.59 (~![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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[100, 92])).
% 0.50/0.59 tff(102,plain,
% 0.50/0.59 (element(B!17, the_carrier(boole_lattice(A!18))) & (~((~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)))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[101, 91])).
% 0.50/0.59 tff(103,plain,
% 0.50/0.59 (~((~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))))),
% 0.50/0.59 inference(and_elim,[status(thm)],[102])).
% 0.50/0.59 tff(104,plain,
% 0.50/0.59 (element(C!19, the_carrier(boole_lattice(A!18)))),
% 0.50/0.59 inference(or_elim,[status(thm)],[103])).
% 0.50/0.59 tff(105,plain,
% 0.50/0.59 (element(C!19, powerset(A!18))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[104, 90])).
% 0.50/0.59 tff(106,plain,
% 0.50/0.59 (element(B!17, powerset(A!18)) <=> element(B!17, the_carrier(boole_lattice(A!18)))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[88])).
% 0.50/0.59 tff(107,plain,
% 0.50/0.59 (element(B!17, the_carrier(boole_lattice(A!18))) <=> element(B!17, powerset(A!18))),
% 0.50/0.59 inference(symmetry,[status(thm)],[106])).
% 0.50/0.59 tff(108,plain,
% 0.50/0.59 (element(B!17, the_carrier(boole_lattice(A!18)))),
% 0.50/0.59 inference(and_elim,[status(thm)],[102])).
% 0.50/0.59 tff(109,plain,
% 0.50/0.59 (element(B!17, powerset(A!18))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.50/0.59 tff(110,plain,
% 0.50/0.59 (^[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)))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(111,plain,
% 0.50/0.59 (![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))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[110])).
% 0.50/0.59 tff(112,plain,
% 0.50/0.59 (^[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))))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(113,plain,
% 0.50/0.59 (![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))))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[112])).
% 0.50/0.59 tff(114,plain,
% 0.50/0.59 (![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)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(115,plain,
% 0.50/0.59 (^[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))))),
% 0.50/0.59 inference(bind,[status(th)],[])).
% 0.50/0.59 tff(116,plain,
% 0.50/0.59 (![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)))),
% 0.50/0.59 inference(quant_intro,[status(thm)],[115])).
% 0.50/0.59 tff(117,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')).
% 0.50/0.59 tff(118,plain,
% 0.50/0.59 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.50/0.59 tff(119,plain,
% 0.50/0.59 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[118, 114])).
% 0.50/0.59 tff(120,plain,(
% 0.50/0.59 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_intersection2(A, B, C) = set_intersection2(B, C)))),
% 0.50/0.59 inference(skolemize,[status(sab)],[119])).
% 0.50/0.59 tff(121,plain,
% 0.50/0.59 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[120, 113])).
% 0.50/0.59 tff(122,plain,
% 0.50/0.59 (![A: $i, B: $i, C: $i] : ((subset_intersection2(A, B, C) = set_intersection2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[121, 111])).
% 0.50/0.59 tff(123,plain,
% 0.50/0.59 (((~![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)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(124,plain,
% 0.50/0.59 (((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)))),
% 0.50/0.59 inference(rewrite,[status(thm)],[])).
% 0.50/0.59 tff(125,plain,
% 0.50/0.59 (((~![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))))),
% 0.50/0.59 inference(monotonicity,[status(thm)],[124])).
% 0.50/0.59 tff(126,plain,
% 0.50/0.59 (((~![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)))),
% 0.50/0.59 inference(transitivity,[status(thm)],[125, 123])).
% 0.50/0.59 tff(127,plain,
% 0.50/0.59 ((~![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))))),
% 0.50/0.59 inference(quant_inst,[status(thm)],[])).
% 0.50/0.59 tff(128,plain,
% 0.50/0.59 ((~![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))),
% 0.50/0.59 inference(modus_ponens,[status(thm)],[127, 126])).
% 0.50/0.59 tff(129,plain,
% 0.50/0.59 (subset_intersection2(A!18, B!17, C!19) = set_intersection2(B!17, C!19)),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[128, 122, 109, 105])).
% 0.50/0.59 tff(130,plain,
% 0.50/0.59 (((~(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))))))))) | ![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)))))))),
% 0.50/0.59 inference(tautology,[status(thm)],[])).
% 0.50/0.59 tff(131,plain,
% 0.50/0.59 (![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)))))))),
% 0.50/0.59 inference(unit_resolution,[status(thm)],[130, 84])).
% 0.50/0.59 tff(132,plain,
% 0.50/0.59 (((~![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)))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(133,plain,
% 0.50/0.60 ((~![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)))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(134,plain,
% 0.50/0.60 ((~![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))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.50/0.60 tff(135,plain,
% 0.50/0.60 ((~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))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.50/0.60 tff(136,plain,
% 0.50/0.60 (![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))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[135, 109])).
% 0.50/0.60 tff(137,plain,
% 0.50/0.60 (((~![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))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(138,plain,
% 0.50/0.60 ((~![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))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(139,plain,
% 0.50/0.60 ((~![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)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.50/0.60 tff(140,plain,
% 0.50/0.60 (~((~(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))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[139, 136, 105])).
% 0.50/0.60 tff(141,plain,
% 0.50/0.60 (((~(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))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(142,plain,
% 0.50/0.60 (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)),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[141, 140])).
% 0.50/0.60 tff(143,plain,
% 0.50/0.60 (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))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[32])).
% 0.50/0.60 tff(144,plain,
% 0.50/0.60 (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))))),
% 0.50/0.60 inference(symmetry,[status(thm)],[143])).
% 0.50/0.60 tff(145,plain,
% 0.50/0.60 (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)),
% 0.50/0.60 inference(monotonicity,[status(thm)],[144])).
% 0.50/0.60 tff(146,plain,
% 0.50/0.60 (^[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)))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(147,plain,
% 0.50/0.60 (![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))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[146])).
% 0.50/0.60 tff(148,plain,
% 0.50/0.60 (![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))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(149,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')).
% 0.50/0.60 tff(150,plain,
% 0.50/0.60 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.50/0.60 tff(151,plain,(
% 0.50/0.60 ![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.50/0.60 inference(skolemize,[status(sab)],[150])).
% 0.50/0.60 tff(152,plain,
% 0.50/0.60 (![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[151, 147])).
% 0.50/0.60 tff(153,plain,
% 0.50/0.60 ((~![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))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(154,plain,
% 0.50/0.60 (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)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[153, 152])).
% 0.50/0.60 tff(155,plain,
% 0.50/0.60 (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))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[32])).
% 0.50/0.60 tff(156,plain,
% 0.50/0.60 (^[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))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(157,plain,
% 0.50/0.60 (![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)))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[156])).
% 0.50/0.60 tff(158,plain,
% 0.50/0.60 (^[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))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(159,plain,
% 0.50/0.60 (![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)))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[158])).
% 0.50/0.60 tff(160,plain,
% 0.50/0.60 (![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)))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(161,plain,
% 0.50/0.60 (^[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))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(162,plain,
% 0.50/0.60 (![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)))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[161])).
% 0.50/0.60 tff(163,axiom,(![A: $i] : (latt_str(A) => (meet_semilatt_str(A) & join_semilatt_str(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.50/0.60 tff(164,plain,
% 0.50/0.60 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[163, 162])).
% 0.50/0.60 tff(165,plain,
% 0.50/0.60 (![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[164, 160])).
% 0.50/0.60 tff(166,plain,(
% 0.50/0.60 ![A: $i] : ((~latt_str(A)) | (meet_semilatt_str(A) & join_semilatt_str(A)))),
% 0.50/0.60 inference(skolemize,[status(sab)],[165])).
% 0.50/0.60 tff(167,plain,
% 0.50/0.60 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[166, 159])).
% 0.50/0.60 tff(168,plain,
% 0.50/0.60 (![A: $i] : ((~latt_str(A)) | (~((~meet_semilatt_str(A)) | (~join_semilatt_str(A)))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[167, 157])).
% 0.50/0.60 tff(169,plain,
% 0.50/0.60 (((~![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))))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(170,plain,
% 0.50/0.60 ((~![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))))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(171,plain,
% 0.50/0.60 ((~![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)))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[170, 169])).
% 0.50/0.60 tff(172,plain,
% 0.50/0.60 ((~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)))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[171, 168])).
% 0.50/0.60 tff(173,plain,
% 0.50/0.60 (~((~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))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[172, 36])).
% 0.50/0.60 tff(174,plain,
% 0.50/0.60 (((~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))))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(175,plain,
% 0.50/0.60 (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))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[174, 173])).
% 0.50/0.60 tff(176,plain,
% 0.50/0.60 (meet_semilatt_str(boole_lattice(A!18))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[175, 155])).
% 0.50/0.60 tff(177,plain,
% 0.50/0.60 (^[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)))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(178,plain,
% 0.50/0.60 (![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))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[177])).
% 0.50/0.60 tff(179,plain,
% 0.50/0.60 (^[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)))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(180,plain,
% 0.50/0.60 (![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))))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[179])).
% 0.50/0.60 tff(181,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(182,plain,
% 0.50/0.60 (^[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))))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(183,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[182])).
% 0.50/0.60 tff(184,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')).
% 0.50/0.60 tff(185,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.50/0.60 tff(186,plain,
% 0.50/0.60 (![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))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.50/0.60 tff(187,plain,(
% 0.50/0.60 ![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))))),
% 0.50/0.60 inference(skolemize,[status(sab)],[186])).
% 0.50/0.60 tff(188,plain,
% 0.50/0.60 (![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))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.50/0.60 tff(189,plain,
% 0.50/0.60 (![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))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.50/0.60 tff(190,plain,
% 0.50/0.60 (((~![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)))))))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(191,plain,
% 0.50/0.60 ((~![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)))))))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(192,plain,
% 0.50/0.60 ((~![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))))))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.50/0.60 tff(193,plain,
% 0.50/0.60 ((~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))))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.50/0.60 tff(194,plain,
% 0.50/0.60 (~((~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)))))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[193, 176])).
% 0.50/0.60 tff(195,plain,
% 0.50/0.60 (((~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)))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(196,plain,
% 0.50/0.60 (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)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[195, 194])).
% 0.50/0.60 tff(197,plain,
% 0.50/0.60 ((~(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)))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(198,plain,
% 0.50/0.60 ((~(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)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.50/0.60 tff(199,plain,
% 0.50/0.60 (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)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[198, 154])).
% 0.50/0.60 tff(200,plain,
% 0.50/0.60 (((~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)))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(201,plain,
% 0.50/0.60 (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)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[200, 194])).
% 0.50/0.60 tff(202,plain,
% 0.50/0.60 (((~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)))),
% 0.50/0.60 inference(tautology,[status(thm)],[])).
% 0.50/0.60 tff(203,plain,
% 0.50/0.60 (function(the_L_meet(boole_lattice(A!18)))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[202, 194])).
% 0.50/0.60 tff(204,plain,
% 0.50/0.60 (empty(powerset(A!18)) <=> empty(the_carrier(boole_lattice(A!18)))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[88])).
% 0.50/0.60 tff(205,plain,
% 0.50/0.60 ((~empty(powerset(A!18))) <=> (~empty(the_carrier(boole_lattice(A!18))))),
% 0.50/0.60 inference(monotonicity,[status(thm)],[204])).
% 0.50/0.60 tff(206,plain,
% 0.50/0.60 (^[A: $i] : refl((~empty(powerset(A))) <=> (~empty(powerset(A))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(207,plain,
% 0.50/0.60 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.50/0.60 inference(quant_intro,[status(thm)],[206])).
% 0.50/0.60 tff(208,plain,
% 0.50/0.60 (![A: $i] : (~empty(powerset(A))) <=> ![A: $i] : (~empty(powerset(A)))),
% 0.50/0.60 inference(rewrite,[status(thm)],[])).
% 0.50/0.60 tff(209,axiom,(![A: $i] : (~empty(powerset(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_subset_1')).
% 0.50/0.60 tff(210,plain,
% 0.50/0.60 (![A: $i] : (~empty(powerset(A)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[209, 208])).
% 0.50/0.60 tff(211,plain,(
% 0.50/0.60 ![A: $i] : (~empty(powerset(A)))),
% 0.50/0.60 inference(skolemize,[status(sab)],[210])).
% 0.50/0.60 tff(212,plain,
% 0.50/0.60 (![A: $i] : (~empty(powerset(A)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.50/0.60 tff(213,plain,
% 0.50/0.60 ((~![A: $i] : (~empty(powerset(A)))) | (~empty(powerset(A!18)))),
% 0.50/0.60 inference(quant_inst,[status(thm)],[])).
% 0.50/0.60 tff(214,plain,
% 0.50/0.60 (~empty(powerset(A!18))),
% 0.50/0.60 inference(unit_resolution,[status(thm)],[213, 212])).
% 0.50/0.60 tff(215,plain,
% 0.50/0.60 (~empty(the_carrier(boole_lattice(A!18)))),
% 0.50/0.60 inference(modus_ponens,[status(thm)],[214, 205])).
% 0.50/0.60 tff(216,plain,
% 0.50/0.60 (^[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))))),
% 0.50/0.60 inference(bind,[status(th)],[])).
% 0.50/0.60 tff(217,plain,
% 0.50/0.60 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[216])).
% 0.50/0.61 tff(218,plain,
% 0.50/0.61 (^[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)))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(219,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[218])).
% 0.50/0.61 tff(220,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(221,plain,
% 0.50/0.61 (^[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)))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(222,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[221])).
% 0.50/0.61 tff(223,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')).
% 0.50/0.61 tff(224,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.50/0.61 tff(225,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.50/0.61 tff(226,plain,(
% 0.50/0.61 ![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)))),
% 0.50/0.61 inference(skolemize,[status(sab)],[225])).
% 0.50/0.61 tff(227,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.50/0.61 tff(228,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[227, 217])).
% 0.50/0.61 tff(229,plain,
% 0.50/0.61 (((~![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)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(230,plain,
% 0.50/0.61 ((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)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(231,plain,
% 0.50/0.61 (((~![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))))),
% 0.50/0.61 inference(monotonicity,[status(thm)],[230])).
% 0.50/0.61 tff(232,plain,
% 0.50/0.61 (((~![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)))),
% 0.50/0.61 inference(transitivity,[status(thm)],[231, 229])).
% 0.50/0.61 tff(233,plain,
% 0.50/0.61 ((~![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)))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(234,plain,
% 0.50/0.61 ((~![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))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.50/0.61 tff(235,plain,
% 0.50/0.61 (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)),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[234, 228, 108, 104, 215, 203, 201, 199])).
% 0.50/0.61 tff(236,plain,
% 0.50/0.61 (^[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))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(237,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[236])).
% 0.50/0.61 tff(238,plain,
% 0.50/0.61 (^[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))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(239,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[238])).
% 0.50/0.61 tff(240,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(241,axiom,(![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_lattice3')).
% 0.50/0.61 tff(242,plain,
% 0.50/0.61 (![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.50/0.61 tff(243,plain,(
% 0.50/0.61 ![A: $i] : ((~empty_carrier(boole_lattice(A))) & strict_latt_str(boole_lattice(A)))),
% 0.50/0.61 inference(skolemize,[status(sab)],[242])).
% 0.50/0.61 tff(244,plain,
% 0.50/0.61 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[243, 239])).
% 0.50/0.61 tff(245,plain,
% 0.50/0.61 (![A: $i] : (~(empty_carrier(boole_lattice(A)) | (~strict_latt_str(boole_lattice(A)))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.50/0.61 tff(246,plain,
% 0.50/0.61 ((~![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)))))),
% 0.50/0.61 inference(quant_inst,[status(thm)],[])).
% 0.50/0.61 tff(247,plain,
% 0.50/0.61 (~(empty_carrier(boole_lattice(A!18)) | (~strict_latt_str(boole_lattice(A!18))))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[246, 245])).
% 0.50/0.61 tff(248,plain,
% 0.50/0.61 ((empty_carrier(boole_lattice(A!18)) | (~strict_latt_str(boole_lattice(A!18)))) | (~empty_carrier(boole_lattice(A!18)))),
% 0.50/0.61 inference(tautology,[status(thm)],[])).
% 0.50/0.61 tff(249,plain,
% 0.50/0.61 (~empty_carrier(boole_lattice(A!18))),
% 0.50/0.61 inference(unit_resolution,[status(thm)],[248, 247])).
% 0.50/0.61 tff(250,plain,
% 0.50/0.61 (^[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))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(251,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[250])).
% 0.50/0.61 tff(252,plain,
% 0.50/0.61 (^[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))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(253,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[252])).
% 0.50/0.61 tff(254,plain,
% 0.50/0.61 (^[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))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(255,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[254])).
% 0.50/0.61 tff(256,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(transitivity,[status(thm)],[255, 253])).
% 0.50/0.61 tff(257,plain,
% 0.50/0.61 (^[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)))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(258,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[257])).
% 0.50/0.61 tff(259,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(rewrite,[status(thm)],[])).
% 0.50/0.61 tff(260,plain,
% 0.50/0.61 (^[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)))))))),
% 0.50/0.61 inference(bind,[status(th)],[])).
% 0.50/0.61 tff(261,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(quant_intro,[status(thm)],[260])).
% 0.50/0.61 tff(262,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')).
% 0.50/0.61 tff(263,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.50/0.61 tff(264,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.50/0.61 tff(265,plain,(
% 0.50/0.61 ![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)))))),
% 0.50/0.61 inference(skolemize,[status(sab)],[264])).
% 0.50/0.61 tff(266,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.50/0.61 tff(267,plain,
% 0.50/0.61 (![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)))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[266, 256])).
% 0.50/0.61 tff(268,plain,
% 0.50/0.61 (![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)))))),
% 0.50/0.61 inference(modus_ponens,[status(thm)],[267, 251])).
% 0.50/0.61 tff(269,plain,
% 0.50/0.61 (((~![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)))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(270,plain,
% 0.50/0.62 ((~![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)))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(271,plain,
% 0.50/0.62 ((~![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))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.50/0.62 tff(272,plain,
% 0.50/0.62 (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))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[271, 268])).
% 0.50/0.62 tff(273,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[272, 176, 249])).
% 0.50/0.62 tff(274,plain,
% 0.50/0.62 (((~![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))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(275,plain,
% 0.50/0.62 ((~![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))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(276,plain,
% 0.50/0.62 ((~![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)))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.50/0.62 tff(277,plain,
% 0.50/0.62 (![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)))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[276, 108, 273])).
% 0.50/0.62 tff(278,plain,
% 0.50/0.62 (((~![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)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(279,plain,
% 0.50/0.62 ((~![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)))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(280,plain,
% 0.50/0.62 ((~![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))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.50/0.62 tff(281,plain,
% 0.50/0.62 (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)),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[280, 104, 277])).
% 0.50/0.62 tff(282,plain,
% 0.50/0.62 (meet(boole_lattice(A!18), B!17, C!19) = set_intersection2(B!17, C!19)),
% 0.50/0.62 inference(transitivity,[status(thm)],[281, 235, 145, 142, 129])).
% 0.50/0.62 tff(283,plain,
% 0.50/0.62 (^[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)))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(284,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[283])).
% 0.50/0.62 tff(285,plain,
% 0.50/0.62 (^[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))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(286,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[285])).
% 0.50/0.62 tff(287,plain,
% 0.50/0.62 (![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)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(288,plain,
% 0.50/0.62 (^[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))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(289,plain,
% 0.50/0.62 (![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)))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[288])).
% 0.50/0.62 tff(290,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')).
% 0.50/0.62 tff(291,plain,
% 0.50/0.62 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.50/0.62 tff(292,plain,
% 0.50/0.62 (![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[291, 287])).
% 0.50/0.62 tff(293,plain,(
% 0.50/0.62 ![A: $i, B: $i, C: $i] : ((~(element(B, powerset(A)) & element(C, powerset(A)))) | (subset_union2(A, B, C) = set_union2(B, C)))),
% 0.50/0.62 inference(skolemize,[status(sab)],[292])).
% 0.50/0.62 tff(294,plain,
% 0.50/0.62 (![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[293, 286])).
% 0.50/0.62 tff(295,plain,
% 0.50/0.62 (![A: $i, B: $i, C: $i] : ((subset_union2(A, B, C) = set_union2(B, C)) | (~element(C, powerset(A))) | (~element(B, powerset(A))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[294, 284])).
% 0.50/0.62 tff(296,plain,
% 0.50/0.62 (((~![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)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(297,plain,
% 0.50/0.62 (((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)))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(298,plain,
% 0.50/0.62 (((~![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))))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[297])).
% 0.50/0.62 tff(299,plain,
% 0.50/0.62 (((~![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)))),
% 0.50/0.62 inference(transitivity,[status(thm)],[298, 296])).
% 0.50/0.62 tff(300,plain,
% 0.50/0.62 ((~![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))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(301,plain,
% 0.50/0.62 ((~![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))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.50/0.62 tff(302,plain,
% 0.50/0.62 (subset_union2(A!18, B!17, C!19) = set_union2(B!17, C!19)),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[301, 295, 109, 105])).
% 0.50/0.62 tff(303,plain,
% 0.50/0.62 (((~(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_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))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(304,plain,
% 0.50/0.62 (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)),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[303, 140])).
% 0.50/0.62 tff(305,plain,
% 0.50/0.62 (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))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[32])).
% 0.50/0.62 tff(306,plain,
% 0.50/0.62 (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))))),
% 0.50/0.62 inference(symmetry,[status(thm)],[305])).
% 0.50/0.62 tff(307,plain,
% 0.50/0.62 (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)),
% 0.50/0.62 inference(monotonicity,[status(thm)],[306])).
% 0.50/0.62 tff(308,plain,
% 0.50/0.62 ((~![A: $i, B: $i, C: $i] : (relation_of2_as_subset(C, A, B) <=> relation_of2(C, A, B))) | (relation_of2_as_subset(the_L_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))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(309,plain,
% 0.50/0.62 (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)))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[308, 152])).
% 0.50/0.62 tff(310,plain,
% 0.50/0.62 (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))),
% 0.50/0.62 inference(monotonicity,[status(thm)],[32])).
% 0.50/0.62 tff(311,plain,
% 0.50/0.62 (((~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)))))) | 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))))),
% 0.50/0.62 inference(tautology,[status(thm)],[])).
% 0.50/0.62 tff(312,plain,
% 0.50/0.62 (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))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[311, 173])).
% 0.50/0.62 tff(313,plain,
% 0.50/0.62 (join_semilatt_str(boole_lattice(A!18))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[312, 310])).
% 0.50/0.62 tff(314,plain,
% 0.50/0.62 (^[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)))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(315,plain,
% 0.50/0.62 (![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))))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[314])).
% 0.50/0.62 tff(316,plain,
% 0.50/0.62 (^[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)))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(317,plain,
% 0.50/0.62 (![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))))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[316])).
% 0.50/0.62 tff(318,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(319,plain,
% 0.50/0.62 (^[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))))))),
% 0.50/0.62 inference(bind,[status(th)],[])).
% 0.50/0.62 tff(320,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(quant_intro,[status(thm)],[319])).
% 0.50/0.62 tff(321,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')).
% 0.50/0.62 tff(322,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.50/0.62 tff(323,plain,
% 0.50/0.62 (![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))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[322, 318])).
% 0.50/0.62 tff(324,plain,(
% 0.50/0.62 ![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))))),
% 0.50/0.62 inference(skolemize,[status(sab)],[323])).
% 0.50/0.62 tff(325,plain,
% 0.50/0.62 (![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))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[324, 317])).
% 0.50/0.62 tff(326,plain,
% 0.50/0.62 (![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))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[325, 315])).
% 0.50/0.62 tff(327,plain,
% 0.50/0.62 (((~![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)))))))),
% 0.50/0.62 inference(rewrite,[status(thm)],[])).
% 0.50/0.62 tff(328,plain,
% 0.50/0.62 ((~![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)))))))),
% 0.50/0.62 inference(quant_inst,[status(thm)],[])).
% 0.50/0.62 tff(329,plain,
% 0.50/0.62 ((~![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))))))),
% 0.50/0.62 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.50/0.62 tff(330,plain,
% 0.50/0.62 ((~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))))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[329, 326])).
% 0.50/0.62 tff(331,plain,
% 0.50/0.62 (~((~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)))))),
% 0.50/0.62 inference(unit_resolution,[status(thm)],[330, 313])).
% 0.50/0.63 tff(332,plain,
% 0.50/0.63 (((~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)))),
% 0.50/0.63 inference(tautology,[status(thm)],[])).
% 0.50/0.63 tff(333,plain,
% 0.50/0.63 (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)))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[332, 331])).
% 0.50/0.63 tff(334,plain,
% 0.50/0.63 ((~(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)))),
% 0.50/0.63 inference(tautology,[status(thm)],[])).
% 0.50/0.63 tff(335,plain,
% 0.50/0.63 ((~(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)))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[334, 333])).
% 0.50/0.63 tff(336,plain,
% 0.50/0.63 (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)))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[335, 309])).
% 0.50/0.63 tff(337,plain,
% 0.50/0.63 (((~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)))),
% 0.50/0.63 inference(tautology,[status(thm)],[])).
% 0.50/0.63 tff(338,plain,
% 0.50/0.63 (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)))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[337, 331])).
% 0.50/0.63 tff(339,plain,
% 0.50/0.63 (((~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)))),
% 0.50/0.63 inference(tautology,[status(thm)],[])).
% 0.50/0.63 tff(340,plain,
% 0.50/0.63 (function(the_L_join(boole_lattice(A!18)))),
% 0.50/0.63 inference(unit_resolution,[status(thm)],[339, 331])).
% 0.50/0.63 tff(341,plain,
% 0.50/0.63 (((~![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_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)))),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(342,plain,
% 0.50/0.63 ((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_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)))),
% 0.50/0.63 inference(rewrite,[status(thm)],[])).
% 0.50/0.63 tff(343,plain,
% 0.50/0.63 (((~![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_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))))),
% 0.50/0.63 inference(monotonicity,[status(thm)],[342])).
% 0.50/0.63 tff(344,plain,
% 0.50/0.63 (((~![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_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)))),
% 0.57/0.63 inference(transitivity,[status(thm)],[343, 341])).
% 0.57/0.63 tff(345,plain,
% 0.57/0.63 ((~![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_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)))))),
% 0.57/0.63 inference(quant_inst,[status(thm)],[])).
% 0.57/0.63 tff(346,plain,
% 0.57/0.63 ((~![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_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))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.57/0.63 tff(347,plain,
% 0.57/0.63 (apply_binary_as_element(the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_carrier(boole_lattice(A!18)), the_L_join(boole_lattice(A!18)), B!17, C!19) = apply_binary(the_L_join(boole_lattice(A!18)), B!17, C!19)),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[346, 228, 108, 104, 215, 340, 338, 336])).
% 0.57/0.63 tff(348,plain,
% 0.57/0.63 (^[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))))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(349,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[348])).
% 0.57/0.63 tff(350,plain,
% 0.57/0.63 (^[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))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(351,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[350])).
% 0.57/0.63 tff(352,plain,
% 0.57/0.63 (^[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))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(353,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[352])).
% 0.57/0.63 tff(354,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(transitivity,[status(thm)],[353, 351])).
% 0.57/0.63 tff(355,plain,
% 0.57/0.63 (^[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)))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(356,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[355])).
% 0.57/0.63 tff(357,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(358,plain,
% 0.57/0.63 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((element(C, the_carrier(A)) => (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)))))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(359,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[358])).
% 0.57/0.63 tff(360,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')).
% 0.57/0.63 tff(361,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.57/0.63 tff(362,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[361, 357])).
% 0.57/0.63 tff(363,plain,(
% 0.57/0.63 ![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)))))),
% 0.57/0.63 inference(skolemize,[status(sab)],[362])).
% 0.57/0.63 tff(364,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[363, 356])).
% 0.57/0.63 tff(365,plain,
% 0.57/0.63 (![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)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[364, 354])).
% 0.57/0.63 tff(366,plain,
% 0.57/0.63 (![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)))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[365, 349])).
% 0.57/0.63 tff(367,plain,
% 0.57/0.63 (((~![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)))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(368,plain,
% 0.57/0.63 ((~![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)))))),
% 0.57/0.63 inference(quant_inst,[status(thm)],[])).
% 0.57/0.63 tff(369,plain,
% 0.57/0.63 ((~![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))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[368, 367])).
% 0.57/0.63 tff(370,plain,
% 0.57/0.63 (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))))),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[369, 366])).
% 0.57/0.64 tff(371,plain,
% 0.57/0.64 (![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))))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[370, 313, 249])).
% 0.57/0.64 tff(372,plain,
% 0.57/0.64 (((~![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))))),
% 0.57/0.64 inference(rewrite,[status(thm)],[])).
% 0.57/0.64 tff(373,plain,
% 0.57/0.64 ((~![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))))),
% 0.57/0.64 inference(quant_inst,[status(thm)],[])).
% 0.57/0.64 tff(374,plain,
% 0.57/0.64 ((~![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)))),
% 0.57/0.64 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.57/0.64 tff(375,plain,
% 0.57/0.64 (![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)))),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[374, 108, 371])).
% 0.57/0.64 tff(376,plain,
% 0.57/0.64 (((~![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)))),
% 0.57/0.64 inference(rewrite,[status(thm)],[])).
% 0.57/0.64 tff(377,plain,
% 0.57/0.64 ((~![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)))),
% 0.57/0.64 inference(quant_inst,[status(thm)],[])).
% 0.57/0.64 tff(378,plain,
% 0.57/0.64 ((~![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))),
% 0.57/0.64 inference(modus_ponens,[status(thm)],[377, 376])).
% 0.57/0.64 tff(379,plain,
% 0.57/0.64 (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)),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[378, 104, 375])).
% 0.57/0.64 tff(380,plain,
% 0.57/0.64 (join(boole_lattice(A!18), B!17, C!19) = set_union2(B!17, C!19)),
% 0.57/0.64 inference(transitivity,[status(thm)],[379, 347, 307, 304, 302])).
% 0.57/0.64 tff(381,plain,
% 0.57/0.64 ((~(~((~(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))))),
% 0.57/0.64 inference(rewrite,[status(thm)],[])).
% 0.57/0.64 tff(382,plain,
% 0.57/0.64 (((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)))))),
% 0.57/0.64 inference(rewrite,[status(thm)],[])).
% 0.57/0.64 tff(383,plain,
% 0.57/0.64 ((~((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))))))),
% 0.57/0.64 inference(monotonicity,[status(thm)],[382])).
% 0.57/0.64 tff(384,plain,
% 0.57/0.64 ((~((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))))),
% 0.57/0.64 inference(transitivity,[status(thm)],[383, 381])).
% 0.57/0.64 tff(385,plain,
% 0.57/0.64 (~((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)))),
% 0.57/0.64 inference(or_elim,[status(thm)],[103])).
% 0.57/0.64 tff(386,plain,
% 0.57/0.64 ((~(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)))),
% 0.57/0.64 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.57/0.64 tff(387,plain,
% 0.57/0.64 ($false),
% 0.57/0.64 inference(unit_resolution,[status(thm)],[386, 380, 282])).
% 0.57/0.64 % SZS output end Proof
%------------------------------------------------------------------------------