TSTP Solution File: LAT330+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT330+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:33:09 EDT 2022
% Result : Theorem 20.79s 13.61s
% Output : Proof 21.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT330+1 : TPTP v8.1.0. Released v3.4.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n020.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 : Thu Sep 1 14:46:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 20.79/13.61 % SZS status Theorem
% 20.79/13.61 % SZS output start Proof
% 20.79/13.61 tff(tptp_fun_D_2_type, type, (
% 20.79/13.61 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 20.79/13.61 tff(u1_struct_0_type, type, (
% 20.79/13.61 u1_struct_0: $i > $i)).
% 20.79/13.61 tff(tptp_fun_A_0_type, type, (
% 20.79/13.61 tptp_fun_A_0: $i)).
% 20.79/13.61 tff(k22_filter_2_type, type, (
% 20.79/13.61 k22_filter_2: ( $i * $i * $i ) > $i)).
% 20.79/13.61 tff(tptp_fun_B_1_type, type, (
% 20.79/13.61 tptp_fun_B_1: $i)).
% 20.79/13.61 tff(k5_lattices_type, type, (
% 20.79/13.61 k5_lattices: $i > $i)).
% 20.79/13.61 tff(a_2_0_filter_2_type, type, (
% 20.79/13.61 a_2_0_filter_2: ( $i * $i ) > $i)).
% 20.79/13.61 tff(r3_lattices_type, type, (
% 20.79/13.61 r3_lattices: ( $i * $i * $i ) > $o)).
% 20.79/13.61 tff(m1_subset_1_type, type, (
% 20.79/13.61 m1_subset_1: ( $i * $i ) > $o)).
% 20.79/13.61 tff(r2_hidden_type, type, (
% 20.79/13.61 r2_hidden: ( $i * $i ) > $o)).
% 20.79/13.61 tff(tptp_fun_D_10_type, type, (
% 20.79/13.61 tptp_fun_D_10: ( $i * $i * $i ) > $i)).
% 20.79/13.61 tff(r1_filter_2_type, type, (
% 20.79/13.61 r1_filter_2: ( $i * $i * $i ) > $o)).
% 20.79/13.61 tff(k1_zfmisc_1_type, type, (
% 20.79/13.61 k1_zfmisc_1: $i > $i)).
% 20.79/13.61 tff(v1_xboole_0_type, type, (
% 20.79/13.61 v1_xboole_0: $i > $o)).
% 20.79/13.61 tff(l1_struct_0_type, type, (
% 20.79/13.61 l1_struct_0: $i > $o)).
% 20.79/13.61 tff(l2_lattices_type, type, (
% 20.79/13.61 l2_lattices: $i > $o)).
% 20.79/13.61 tff(l1_lattices_type, type, (
% 20.79/13.61 l1_lattices: $i > $o)).
% 20.79/13.61 tff(l3_lattices_type, type, (
% 20.79/13.61 l3_lattices: $i > $o)).
% 20.79/13.61 tff(k18_filter_2_type, type, (
% 20.79/13.61 k18_filter_2: ( $i * $i ) > $i)).
% 20.79/13.61 tff(v13_lattices_type, type, (
% 20.79/13.61 v13_lattices: $i > $o)).
% 20.79/13.61 tff(v10_lattices_type, type, (
% 20.79/13.61 v10_lattices: $i > $o)).
% 20.79/13.61 tff(v3_struct_0_type, type, (
% 20.79/13.61 v3_struct_0: $i > $o)).
% 20.79/13.61 tff(m2_lattice4_type, type, (
% 20.79/13.61 m2_lattice4: ( $i * $i ) > $o)).
% 20.79/13.61 tff(m2_filter_2_type, type, (
% 20.79/13.61 m2_filter_2: ( $i * $i ) > $o)).
% 20.79/13.61 tff(1,assumption,((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))), introduced(assumption)).
% 20.79/13.61 tff(2,plain,
% 20.79/13.61 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(3,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[2])).
% 20.79/13.61 tff(4,plain,
% 20.79/13.61 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(5,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[4])).
% 20.79/13.61 tff(6,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(7,plain,
% 20.79/13.61 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(8,plain,
% 20.79/13.61 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[7])).
% 20.79/13.61 tff(9,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 20.79/13.61 tff(10,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[9, 8])).
% 20.79/13.61 tff(11,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[10, 6])).
% 20.79/13.61 tff(12,plain,(
% 20.79/13.61 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 20.79/13.61 inference(skolemize,[status(sab)],[11])).
% 20.79/13.61 tff(13,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[12, 5])).
% 20.79/13.61 tff(14,plain,
% 20.79/13.61 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[13, 3])).
% 20.79/13.61 tff(15,plain,
% 20.79/13.61 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(16,plain,
% 20.79/13.61 ((~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(17,plain,
% 20.79/13.61 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(18,plain,
% 20.79/13.61 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 20.79/13.61 inference(monotonicity,[status(thm)],[17, 16])).
% 20.79/13.61 tff(19,plain,
% 20.79/13.61 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & (~(r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~v13_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 20.79/13.61 inference(transitivity,[status(thm)],[18, 15])).
% 20.79/13.61 tff(20,plain,
% 20.79/13.61 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(21,plain,
% 20.79/13.61 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v13_lattices(A) => r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(22,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v13_lattices(A) => r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t67_filter_2')).
% 20.79/13.61 tff(23,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[22, 21])).
% 20.79/13.61 tff(24,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[23, 20])).
% 20.79/13.61 tff(25,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[24, 20])).
% 20.79/13.61 tff(26,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[25, 20])).
% 20.79/13.61 tff(27,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[26, 20])).
% 20.79/13.61 tff(28,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[27, 20])).
% 20.79/13.61 tff(29,plain,
% 20.79/13.61 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k18_filter_2(A, B), k22_filter_2(A, k5_lattices(A), B)) | (~v13_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[28, 20])).
% 20.79/13.61 tff(30,plain,
% 20.79/13.61 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[29, 19])).
% 20.79/13.61 tff(31,plain,
% 20.79/13.61 (l3_lattices(A!0)),
% 20.79/13.61 inference(and_elim,[status(thm)],[30])).
% 20.79/13.61 tff(32,plain,
% 20.79/13.61 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(33,plain,
% 20.79/13.61 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 20.79/13.61 inference(quant_inst,[status(thm)],[])).
% 20.79/13.61 tff(34,plain,
% 20.79/13.61 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[33, 32])).
% 20.79/13.61 tff(35,plain,
% 20.79/13.61 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 20.79/13.61 inference(unit_resolution,[status(thm)],[34, 31, 14])).
% 20.79/13.61 tff(36,plain,
% 20.79/13.61 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 20.79/13.61 inference(tautology,[status(thm)],[])).
% 20.79/13.61 tff(37,plain,
% 20.79/13.61 (l2_lattices(A!0)),
% 20.79/13.61 inference(unit_resolution,[status(thm)],[36, 35])).
% 20.79/13.61 tff(38,plain,
% 20.79/13.61 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(39,plain,
% 20.79/13.61 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[38])).
% 20.79/13.61 tff(40,plain,
% 20.79/13.61 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(41,plain,
% 20.79/13.61 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(42,plain,
% 20.79/13.61 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[41])).
% 20.79/13.61 tff(43,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 20.79/13.61 tff(44,plain,
% 20.79/13.61 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[43, 42])).
% 20.79/13.61 tff(45,plain,
% 20.79/13.61 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[44, 40])).
% 20.79/13.61 tff(46,plain,(
% 20.79/13.61 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(skolemize,[status(sab)],[45])).
% 20.79/13.61 tff(47,plain,
% 20.79/13.61 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[46, 39])).
% 20.79/13.61 tff(48,plain,
% 20.79/13.61 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(49,plain,
% 20.79/13.61 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 20.79/13.61 inference(quant_inst,[status(thm)],[])).
% 20.79/13.61 tff(50,plain,
% 20.79/13.61 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[49, 48])).
% 20.79/13.61 tff(51,plain,
% 20.79/13.61 (l1_struct_0(A!0)),
% 20.79/13.61 inference(unit_resolution,[status(thm)],[50, 47, 37])).
% 20.79/13.61 tff(52,plain,
% 20.79/13.61 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(53,plain,
% 20.79/13.61 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[52])).
% 20.79/13.61 tff(54,plain,
% 20.79/13.61 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(55,plain,
% 20.79/13.61 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[54])).
% 20.79/13.61 tff(56,plain,
% 20.79/13.61 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(57,plain,
% 20.79/13.61 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(58,plain,
% 20.79/13.61 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 20.79/13.61 inference(quant_intro,[status(thm)],[57])).
% 20.79/13.61 tff(59,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 20.79/13.61 tff(60,plain,
% 20.79/13.61 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[59, 58])).
% 20.79/13.61 tff(61,plain,
% 20.79/13.61 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[60, 56])).
% 20.79/13.61 tff(62,plain,(
% 20.79/13.61 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 20.79/13.61 inference(skolemize,[status(sab)],[61])).
% 20.79/13.61 tff(63,plain,
% 20.79/13.61 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[62, 55])).
% 20.79/13.61 tff(64,plain,
% 20.79/13.61 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[63, 53])).
% 20.79/13.61 tff(65,plain,
% 20.79/13.61 (~v3_struct_0(A!0)),
% 20.79/13.61 inference(and_elim,[status(thm)],[30])).
% 20.79/13.61 tff(66,plain,
% 20.79/13.61 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(67,plain,
% 20.79/13.61 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 20.79/13.61 inference(rewrite,[status(thm)],[])).
% 20.79/13.61 tff(68,plain,
% 20.79/13.61 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 20.79/13.61 inference(monotonicity,[status(thm)],[67])).
% 20.79/13.61 tff(69,plain,
% 20.79/13.61 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 20.79/13.61 inference(transitivity,[status(thm)],[68, 66])).
% 20.79/13.61 tff(70,plain,
% 20.79/13.61 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 20.79/13.61 inference(quant_inst,[status(thm)],[])).
% 20.79/13.61 tff(71,plain,
% 20.79/13.61 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 20.79/13.61 inference(modus_ponens,[status(thm)],[70, 69])).
% 20.79/13.61 tff(72,plain,
% 20.79/13.61 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 20.79/13.61 inference(unit_resolution,[status(thm)],[71, 65, 64])).
% 20.79/13.61 tff(73,plain,
% 20.79/13.61 (~v1_xboole_0(u1_struct_0(A!0))),
% 20.79/13.61 inference(unit_resolution,[status(thm)],[72, 51])).
% 20.79/13.61 tff(74,plain,
% 20.79/13.61 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 20.79/13.61 inference(bind,[status(th)],[])).
% 20.79/13.61 tff(75,plain,
% 20.79/13.61 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[74])).
% 20.79/13.62 tff(76,plain,
% 20.79/13.62 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(77,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[76])).
% 20.79/13.62 tff(78,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(transitivity,[status(thm)],[77, 75])).
% 20.79/13.62 tff(79,plain,
% 20.79/13.62 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(80,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[79])).
% 20.79/13.62 tff(81,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 20.79/13.62 inference(rewrite,[status(thm)],[])).
% 20.79/13.62 tff(82,plain,
% 20.79/13.62 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))) <=> (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(83,plain,
% 20.79/13.62 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[82])).
% 20.79/13.62 tff(84,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_filter_2')).
% 20.79/13.62 tff(85,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[84, 83])).
% 20.79/13.62 tff(86,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[85, 81])).
% 20.79/13.62 tff(87,plain,(
% 20.79/13.62 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))),
% 20.79/13.62 inference(skolemize,[status(sab)],[86])).
% 20.79/13.62 tff(88,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[87, 80])).
% 20.79/13.62 tff(89,plain,
% 20.79/13.62 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[88, 78])).
% 20.79/13.62 tff(90,plain,
% 20.79/13.62 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 20.79/13.62 inference(rewrite,[status(thm)],[])).
% 20.79/13.62 tff(91,plain,
% 20.79/13.62 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 20.79/13.62 inference(quant_inst,[status(thm)],[])).
% 20.79/13.62 tff(92,plain,
% 20.79/13.62 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[91, 90])).
% 20.79/13.62 tff(93,plain,
% 20.79/13.62 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 20.79/13.62 inference(unit_resolution,[status(thm)],[92, 89, 73])).
% 20.79/13.62 tff(94,plain,
% 20.79/13.62 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 20.79/13.62 inference(tautology,[status(thm)],[])).
% 20.79/13.62 tff(95,plain,
% 20.79/13.62 (l1_lattices(A!0)),
% 20.79/13.62 inference(unit_resolution,[status(thm)],[94, 35])).
% 20.79/13.62 tff(96,plain,
% 20.79/13.62 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(97,plain,
% 20.79/13.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[96])).
% 20.79/13.62 tff(98,plain,
% 20.79/13.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(99,plain,
% 20.79/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[98])).
% 20.79/13.62 tff(100,plain,
% 20.79/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 20.79/13.62 inference(rewrite,[status(thm)],[])).
% 20.79/13.62 tff(101,plain,
% 20.79/13.62 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(102,plain,
% 20.79/13.62 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[101])).
% 20.79/13.62 tff(103,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattices')).
% 20.79/13.62 tff(104,plain,
% 20.79/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[103, 102])).
% 20.79/13.62 tff(105,plain,
% 20.79/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[104, 100])).
% 20.79/13.62 tff(106,plain,(
% 20.79/13.62 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 20.79/13.62 inference(skolemize,[status(sab)],[105])).
% 20.79/13.62 tff(107,plain,
% 20.79/13.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[106, 99])).
% 20.79/13.62 tff(108,plain,
% 20.79/13.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[107, 97])).
% 20.79/13.62 tff(109,plain,
% 20.79/13.62 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 20.79/13.62 inference(rewrite,[status(thm)],[])).
% 20.79/13.62 tff(110,plain,
% 20.79/13.62 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 20.79/13.62 inference(quant_inst,[status(thm)],[])).
% 20.79/13.62 tff(111,plain,
% 20.79/13.62 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[110, 109])).
% 20.79/13.62 tff(112,plain,
% 20.79/13.62 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))),
% 20.79/13.62 inference(unit_resolution,[status(thm)],[111, 65, 108])).
% 20.79/13.62 tff(113,plain,
% 20.79/13.62 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 20.79/13.62 inference(unit_resolution,[status(thm)],[112, 95])).
% 20.79/13.62 tff(114,plain,
% 20.79/13.62 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(115,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[114])).
% 20.79/13.62 tff(116,plain,
% 20.79/13.62 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite(((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)) <=> (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(117,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[116])).
% 20.79/13.62 tff(118,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 20.79/13.62 inference(rewrite,[status(thm)],[])).
% 20.79/13.62 tff(119,plain,
% 20.79/13.62 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 20.79/13.62 inference(bind,[status(th)],[])).
% 20.79/13.62 tff(120,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 20.79/13.62 inference(quant_intro,[status(thm)],[119])).
% 20.79/13.62 tff(121,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k22_filter_2')).
% 20.79/13.62 tff(122,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[121, 120])).
% 20.79/13.62 tff(123,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[122, 118])).
% 20.79/13.62 tff(124,plain,(
% 20.79/13.62 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 20.79/13.62 inference(skolemize,[status(sab)],[123])).
% 20.79/13.62 tff(125,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[124, 117])).
% 20.79/13.62 tff(126,plain,
% 20.79/13.62 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 20.79/13.62 inference(modus_ponens,[status(thm)],[125, 115])).
% 20.79/13.62 tff(127,plain,
% 20.79/13.62 (~((~v13_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 20.79/13.62 inference(and_elim,[status(thm)],[30])).
% 20.79/13.62 tff(128,plain,
% 20.79/13.62 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 20.79/13.62 inference(or_elim,[status(thm)],[127])).
% 20.79/13.62 tff(129,plain,
% 20.79/13.62 (v10_lattices(A!0)),
% 20.79/13.62 inference(and_elim,[status(thm)],[30])).
% 20.79/13.62 tff(130,plain,
% 20.79/13.62 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 20.94/13.62 inference(rewrite,[status(thm)],[])).
% 20.94/13.62 tff(131,plain,
% 20.94/13.62 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 20.94/13.62 inference(rewrite,[status(thm)],[])).
% 20.94/13.62 tff(132,plain,
% 20.94/13.62 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))))),
% 20.94/13.62 inference(monotonicity,[status(thm)],[131])).
% 20.94/13.62 tff(133,plain,
% 20.94/13.62 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 20.94/13.62 inference(transitivity,[status(thm)],[132, 130])).
% 20.94/13.62 tff(134,plain,
% 20.94/13.62 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))))),
% 20.94/13.62 inference(quant_inst,[status(thm)],[])).
% 20.94/13.62 tff(135,plain,
% 20.94/13.62 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))),
% 20.94/13.62 inference(modus_ponens,[status(thm)],[134, 133])).
% 20.94/13.62 tff(136,plain,
% 20.94/13.62 ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))))),
% 20.94/13.62 inference(unit_resolution,[status(thm)],[135, 65, 129, 31, 128, 126])).
% 20.94/13.62 tff(137,plain,
% 20.94/13.62 (~(v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)))),
% 20.94/13.62 inference(unit_resolution,[status(thm)],[136, 113])).
% 20.94/13.62 tff(138,plain,
% 20.94/13.62 ((v1_xboole_0(k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0))) | m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)),
% 20.94/13.62 inference(tautology,[status(thm)],[])).
% 20.94/13.62 tff(139,plain,
% 20.94/13.62 (m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)),
% 20.94/13.62 inference(unit_resolution,[status(thm)],[138, 137])).
% 20.94/13.62 tff(140,plain,
% 20.94/13.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 20.94/13.62 inference(bind,[status(th)],[])).
% 20.94/13.62 tff(141,plain,
% 20.94/13.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.62 inference(quant_intro,[status(thm)],[140])).
% 20.94/13.62 tff(142,plain,
% 20.94/13.62 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 20.94/13.62 inference(bind,[status(th)],[])).
% 20.94/13.62 tff(143,plain,
% 20.94/13.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.62 inference(quant_intro,[status(thm)],[142])).
% 20.94/13.62 tff(144,plain,
% 20.94/13.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 20.94/13.62 inference(bind,[status(th)],[])).
% 20.94/13.62 tff(145,plain,
% 20.94/13.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.62 inference(quant_intro,[status(thm)],[144])).
% 20.94/13.62 tff(146,plain,
% 20.94/13.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.62 inference(transitivity,[status(thm)],[145, 143])).
% 20.94/13.62 tff(147,plain,
% 20.94/13.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 20.94/13.62 inference(bind,[status(th)],[])).
% 20.94/13.62 tff(148,plain,
% 20.94/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.62 inference(quant_intro,[status(thm)],[147])).
% 20.94/13.62 tff(149,plain,
% 20.94/13.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.62 inference(rewrite,[status(thm)],[])).
% 20.94/13.62 tff(150,plain,
% 20.94/13.62 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 20.94/13.62 inference(bind,[status(th)],[])).
% 20.94/13.62 tff(151,plain,
% 20.94/13.62 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[150])).
% 20.94/13.63 tff(152,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 20.94/13.63 tff(153,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[152, 151])).
% 20.94/13.63 tff(154,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[153, 149])).
% 20.94/13.63 tff(155,plain,(
% 20.94/13.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.63 inference(skolemize,[status(sab)],[154])).
% 20.94/13.63 tff(156,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[155, 148])).
% 20.94/13.63 tff(157,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[156, 146])).
% 20.94/13.63 tff(158,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[157, 141])).
% 20.94/13.63 tff(159,plain,
% 20.94/13.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(160,plain,
% 20.94/13.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(161,plain,
% 20.94/13.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[160, 159])).
% 20.94/13.63 tff(162,plain,
% 20.94/13.63 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[161, 65, 129, 31, 158])).
% 20.94/13.63 tff(163,plain,
% 20.94/13.63 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(164,plain,
% 20.94/13.63 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(165,plain,
% 20.94/13.63 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, k5_lattices(A!0), B!1), A!0)) | m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[164, 163])).
% 20.94/13.63 tff(166,plain,
% 20.94/13.63 (m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[165, 162, 139])).
% 20.94/13.63 tff(167,plain,
% 20.94/13.63 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C))))))))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(168,plain,
% 20.94/13.63 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C))))))))))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(169,plain,
% 20.94/13.63 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[168, 167])).
% 20.94/13.63 tff(170,plain,
% 20.94/13.63 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[169, 166, 93])).
% 20.94/13.63 tff(171,plain,
% 20.94/13.63 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(172,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[171])).
% 20.94/13.63 tff(173,plain,
% 20.94/13.63 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(174,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[173])).
% 20.94/13.63 tff(175,plain,
% 20.94/13.63 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(176,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[175])).
% 20.94/13.63 tff(177,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(transitivity,[status(thm)],[176, 174])).
% 20.94/13.63 tff(178,plain,
% 20.94/13.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(179,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[178])).
% 20.94/13.63 tff(180,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(181,plain,
% 20.94/13.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(182,plain,
% 20.94/13.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[181])).
% 20.94/13.63 tff(183,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_filter_2')).
% 20.94/13.63 tff(184,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[183, 182])).
% 20.94/13.63 tff(185,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[184, 180])).
% 20.94/13.63 tff(186,plain,(
% 20.94/13.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(skolemize,[status(sab)],[185])).
% 20.94/13.63 tff(187,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[186, 179])).
% 20.94/13.63 tff(188,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[187, 177])).
% 20.94/13.63 tff(189,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[188, 172])).
% 20.94/13.63 tff(190,plain,
% 20.94/13.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(191,plain,
% 20.94/13.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(192,plain,
% 20.94/13.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[191, 190])).
% 20.94/13.63 tff(193,plain,
% 20.94/13.63 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[192, 65, 129, 31, 189])).
% 20.94/13.63 tff(194,plain,
% 20.94/13.63 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(195,plain,
% 20.94/13.63 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(196,plain,
% 20.94/13.63 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[195, 194])).
% 20.94/13.63 tff(197,plain,
% 20.94/13.63 (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[196, 128, 193])).
% 20.94/13.63 tff(198,plain,
% 20.94/13.63 (a_2_0_filter_2(A!0, B!1) = k18_filter_2(A!0, B!1)),
% 20.94/13.63 inference(symmetry,[status(thm)],[197])).
% 20.94/13.63 tff(199,plain,
% 20.94/13.63 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0) <=> m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 20.94/13.63 inference(monotonicity,[status(thm)],[198])).
% 20.94/13.63 tff(200,plain,
% 20.94/13.63 (m2_lattice4(k18_filter_2(A!0, B!1), A!0) <=> m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 20.94/13.63 inference(symmetry,[status(thm)],[199])).
% 20.94/13.63 tff(201,plain,
% 20.94/13.63 (^[A: $i, B: $i] : refl((m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(202,plain,
% 20.94/13.63 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[201])).
% 20.94/13.63 tff(203,plain,
% 20.94/13.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(204,plain,
% 20.94/13.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[203])).
% 20.94/13.63 tff(205,plain,
% 20.94/13.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(206,plain,
% 20.94/13.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(207,plain,
% 20.94/13.63 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[206])).
% 20.94/13.63 tff(208,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k18_filter_2')).
% 20.94/13.63 tff(209,plain,
% 20.94/13.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[208, 207])).
% 20.94/13.63 tff(210,plain,
% 20.94/13.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[209, 205])).
% 20.94/13.63 tff(211,plain,(
% 20.94/13.63 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 20.94/13.63 inference(skolemize,[status(sab)],[210])).
% 20.94/13.63 tff(212,plain,
% 20.94/13.63 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[211, 204])).
% 20.94/13.63 tff(213,plain,
% 20.94/13.63 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[212, 202])).
% 20.94/13.63 tff(214,plain,
% 20.94/13.63 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(215,plain,
% 20.94/13.63 ((m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(216,plain,
% 20.94/13.63 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)))),
% 20.94/13.63 inference(monotonicity,[status(thm)],[215])).
% 20.94/13.63 tff(217,plain,
% 20.94/13.63 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 20.94/13.63 inference(transitivity,[status(thm)],[216, 214])).
% 20.94/13.63 tff(218,plain,
% 20.94/13.63 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 20.94/13.63 inference(quant_inst,[status(thm)],[])).
% 20.94/13.63 tff(219,plain,
% 20.94/13.63 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[218, 217])).
% 20.94/13.63 tff(220,plain,
% 20.94/13.63 (m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 20.94/13.63 inference(unit_resolution,[status(thm)],[219, 65, 129, 31, 128, 213])).
% 20.94/13.63 tff(221,plain,
% 20.94/13.63 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(222,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[221])).
% 20.94/13.63 tff(223,plain,
% 20.94/13.63 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(224,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[223])).
% 20.94/13.63 tff(225,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(transitivity,[status(thm)],[224, 222])).
% 20.94/13.63 tff(226,plain,
% 20.94/13.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(227,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[226])).
% 20.94/13.63 tff(228,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 20.94/13.63 inference(rewrite,[status(thm)],[])).
% 20.94/13.63 tff(229,plain,
% 20.94/13.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 20.94/13.63 inference(bind,[status(th)],[])).
% 20.94/13.63 tff(230,plain,
% 20.94/13.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 20.94/13.63 inference(quant_intro,[status(thm)],[229])).
% 20.94/13.63 tff(231,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 20.94/13.63 tff(232,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[231, 230])).
% 20.94/13.63 tff(233,plain,
% 20.94/13.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[232, 228])).
% 20.94/13.63 tff(234,plain,(
% 20.94/13.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 20.94/13.63 inference(skolemize,[status(sab)],[233])).
% 20.94/13.63 tff(235,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[234, 227])).
% 20.94/13.63 tff(236,plain,
% 20.94/13.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 20.94/13.63 inference(modus_ponens,[status(thm)],[235, 225])).
% 20.94/13.63 tff(237,plain,
% 20.94/13.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(238,plain,
% 20.94/13.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 20.94/13.64 inference(quant_inst,[status(thm)],[])).
% 20.94/13.64 tff(239,plain,
% 20.94/13.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[238, 237])).
% 20.94/13.64 tff(240,plain,
% 20.94/13.64 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[239, 65, 129, 31, 236])).
% 20.94/13.64 tff(241,plain,
% 20.94/13.64 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(242,plain,
% 20.94/13.64 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 20.94/13.64 inference(quant_inst,[status(thm)],[])).
% 20.94/13.64 tff(243,plain,
% 20.94/13.64 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[242, 241])).
% 20.94/13.64 tff(244,plain,
% 20.94/13.64 (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[243, 240, 220])).
% 20.94/13.64 tff(245,plain,
% 20.94/13.64 ((v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))) | m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 20.94/13.64 inference(tautology,[status(thm)],[])).
% 20.94/13.64 tff(246,plain,
% 20.94/13.64 (m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[245, 244])).
% 20.94/13.64 tff(247,plain,
% 20.94/13.64 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[246, 200])).
% 20.94/13.64 tff(248,plain,
% 20.94/13.64 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(249,plain,
% 20.94/13.64 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.64 inference(quant_inst,[status(thm)],[])).
% 20.94/13.64 tff(250,plain,
% 20.94/13.64 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[249, 248])).
% 20.94/13.64 tff(251,plain,
% 20.94/13.64 ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[250, 162])).
% 20.94/13.64 tff(252,plain,
% 20.94/13.64 (m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[251, 247])).
% 20.94/13.64 tff(253,plain,
% 20.94/13.64 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(254,plain,
% 20.94/13.64 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))))))),
% 20.94/13.64 inference(quant_inst,[status(thm)],[])).
% 20.94/13.64 tff(255,plain,
% 20.94/13.64 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(C, k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[254, 253])).
% 20.94/13.64 tff(256,plain,
% 20.94/13.64 (~((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[255, 252, 170])).
% 20.94/13.64 tff(257,plain,
% 20.94/13.64 (((~((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(D, a_2_0_filter_2(A!0, B!1)))))) | (~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))))) | (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))),
% 20.94/13.64 inference(tautology,[status(thm)],[])).
% 20.94/13.64 tff(258,plain,
% 20.94/13.64 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[257, 256])).
% 20.94/13.64 tff(259,plain,
% 20.94/13.64 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))),
% 20.94/13.64 inference(monotonicity,[status(thm)],[198])).
% 20.94/13.64 tff(260,plain,
% 20.94/13.64 (r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1)) <=> r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.64 inference(symmetry,[status(thm)],[259])).
% 20.94/13.64 tff(261,plain,
% 20.94/13.64 ((~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) <=> (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.64 inference(monotonicity,[status(thm)],[260])).
% 20.94/13.64 tff(262,plain,
% 20.94/13.64 (m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.64 inference(monotonicity,[status(thm)],[198])).
% 20.94/13.64 tff(263,plain,
% 20.94/13.64 (m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[252, 262])).
% 20.94/13.64 tff(264,plain,
% 20.94/13.64 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))))),
% 20.94/13.64 inference(bind,[status(th)],[])).
% 20.94/13.64 tff(265,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 20.94/13.64 inference(quant_intro,[status(thm)],[264])).
% 20.94/13.64 tff(266,plain,
% 20.94/13.64 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))))), rewrite((r1_filter_2(A, C, B) | (v1_xboole_0(A) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~m1_subset_1(B, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))), ((r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))))),
% 20.94/13.64 inference(bind,[status(th)],[])).
% 20.94/13.64 tff(267,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 20.94/13.64 inference(quant_intro,[status(thm)],[266])).
% 20.94/13.64 tff(268,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(269,plain,
% 20.94/13.64 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), rewrite((r1_filter_2(A, B, C) => r1_filter_2(A, C, B)) <=> ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => ((~r1_filter_2(A, B, C)) | r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))))),
% 20.94/13.64 inference(bind,[status(th)],[])).
% 20.94/13.64 tff(270,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 20.94/13.64 inference(quant_intro,[status(thm)],[269])).
% 20.94/13.64 tff(271,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) => r1_filter_2(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','symmetry_r1_filter_2')).
% 20.94/13.64 tff(272,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[271, 270])).
% 20.94/13.64 tff(273,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[272, 268])).
% 20.94/13.64 tff(274,plain,(
% 20.94/13.64 ![A: $i, B: $i, C: $i] : (r1_filter_2(A, C, B) | (~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (~r1_filter_2(A, B, C)))),
% 20.94/13.64 inference(skolemize,[status(sab)],[273])).
% 20.94/13.64 tff(275,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[274, 267])).
% 20.94/13.64 tff(276,plain,
% 20.94/13.64 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[275, 265])).
% 20.94/13.64 tff(277,plain,
% 20.94/13.64 (~r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 20.94/13.64 inference(or_elim,[status(thm)],[127])).
% 20.94/13.64 tff(278,plain,
% 20.94/13.64 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(279,plain,
% 20.94/13.64 ((v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.64 inference(rewrite,[status(thm)],[])).
% 20.94/13.64 tff(280,plain,
% 20.94/13.64 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 20.94/13.64 inference(monotonicity,[status(thm)],[279])).
% 20.94/13.64 tff(281,plain,
% 20.94/13.64 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.64 inference(transitivity,[status(thm)],[280, 278])).
% 20.94/13.64 tff(282,plain,
% 20.94/13.64 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 20.94/13.64 inference(quant_inst,[status(thm)],[])).
% 20.94/13.64 tff(283,plain,
% 20.94/13.64 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | r1_filter_2(A, C, B) | (~m1_subset_1(C, k1_zfmisc_1(A))) | (~r1_filter_2(A, B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))))) | r1_filter_2(u1_struct_0(A!0), k18_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[282, 281])).
% 20.94/13.64 tff(284,plain,
% 20.94/13.64 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))) | (~m1_subset_1(k22_filter_2(A!0, k5_lattices(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[283, 277, 276])).
% 20.94/13.64 tff(285,plain,
% 20.94/13.64 (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), k18_filter_2(A!0, B!1))),
% 20.94/13.64 inference(unit_resolution,[status(thm)],[284, 263, 73, 166])).
% 20.94/13.64 tff(286,plain,
% 20.94/13.64 (~r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.64 inference(modus_ponens,[status(thm)],[285, 261])).
% 20.94/13.64 tff(287,plain,
% 20.94/13.64 ((~(r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))))) | r1_filter_2(u1_struct_0(A!0), k22_filter_2(A!0, k5_lattices(A!0), B!1), a_2_0_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))))),
% 20.94/13.65 inference(tautology,[status(thm)],[])).
% 20.94/13.65 tff(288,plain,
% 20.94/13.65 (~((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 20.94/13.65 inference(unit_resolution,[status(thm)],[287, 286, 258])).
% 20.94/13.65 tff(289,plain,
% 20.94/13.65 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 20.94/13.65 inference(tautology,[status(thm)],[])).
% 20.94/13.65 tff(290,plain,
% 20.94/13.65 (m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 20.94/13.65 inference(unit_resolution,[status(thm)],[289, 288])).
% 20.94/13.65 tff(291,plain,
% 20.94/13.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(292,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[291])).
% 20.94/13.65 tff(293,plain,
% 20.94/13.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(294,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[293])).
% 20.94/13.65 tff(295,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(transitivity,[status(thm)],[294, 292])).
% 20.94/13.65 tff(296,plain,
% 20.94/13.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(297,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[296])).
% 20.94/13.65 tff(298,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(299,plain,
% 20.94/13.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))) <=> ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(300,plain,
% 20.94/13.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[299])).
% 20.94/13.65 tff(301,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_filter_2')).
% 20.94/13.65 tff(302,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[301, 300])).
% 20.94/13.65 tff(303,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[302, 298])).
% 20.94/13.65 tff(304,plain,(
% 20.94/13.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 20.94/13.65 inference(skolemize,[status(sab)],[303])).
% 20.94/13.65 tff(305,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[304, 297])).
% 20.94/13.65 tff(306,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[305, 295])).
% 20.94/13.65 tff(307,plain,
% 20.94/13.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(308,plain,
% 20.94/13.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C)))))))))),
% 20.94/13.65 inference(quant_inst,[status(thm)],[])).
% 20.94/13.65 tff(309,plain,
% 20.94/13.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (~((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[308, 307])).
% 20.94/13.65 tff(310,plain,
% 20.94/13.65 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))),
% 20.94/13.65 inference(unit_resolution,[status(thm)],[309, 65, 129, 31, 306])).
% 20.94/13.65 tff(311,plain,
% 20.94/13.65 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(312,plain,
% 20.94/13.65 (((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C)))))))) <=> ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(313,plain,
% 20.94/13.65 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))))),
% 20.94/13.65 inference(monotonicity,[status(thm)],[312])).
% 20.94/13.65 tff(314,plain,
% 20.94/13.65 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))))),
% 20.94/13.65 inference(transitivity,[status(thm)],[313, 311])).
% 20.94/13.65 tff(315,plain,
% 20.94/13.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | ((~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, k5_lattices(A!0), C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), D)) | (~r3_lattices(A!0, D, C))))))))),
% 20.94/13.65 inference(quant_inst,[status(thm)],[])).
% 20.94/13.65 tff(316,plain,
% 20.94/13.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k22_filter_2(A!0, B, C)) <=> (~((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))))))))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[315, 314])).
% 20.94/13.65 tff(317,plain,
% 20.94/13.65 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))),
% 20.94/13.65 inference(unit_resolution,[status(thm)],[316, 310, 113])).
% 20.94/13.65 tff(318,plain,
% 20.94/13.65 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(319,plain,
% 20.94/13.65 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))),
% 20.94/13.65 inference(quant_inst,[status(thm)],[])).
% 20.94/13.65 tff(320,plain,
% 20.94/13.65 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), C)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), C)) <=> (~((~r3_lattices(A!0, D, C)) | (~r3_lattices(A!0, k5_lattices(A!0), D)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[319, 318])).
% 20.94/13.65 tff(321,plain,
% 20.94/13.65 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))),
% 20.94/13.65 inference(unit_resolution,[status(thm)],[320, 128, 317])).
% 20.94/13.65 tff(322,plain,
% 20.94/13.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(323,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[322])).
% 20.94/13.65 tff(324,plain,
% 20.94/13.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(325,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[324])).
% 20.94/13.65 tff(326,plain,
% 20.94/13.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(327,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[326])).
% 20.94/13.65 tff(328,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(transitivity,[status(thm)],[327, 325])).
% 20.94/13.65 tff(329,plain,
% 20.94/13.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(330,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[329])).
% 20.94/13.65 tff(331,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(332,plain,
% 20.94/13.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))))),
% 20.94/13.65 inference(bind,[status(th)],[])).
% 20.94/13.65 tff(333,plain,
% 20.94/13.65 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(quant_intro,[status(thm)],[332])).
% 20.94/13.65 tff(334,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, k5_lattices(A), B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t41_lattices')).
% 20.94/13.65 tff(335,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[334, 333])).
% 20.94/13.65 tff(336,plain,
% 20.94/13.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[335, 331])).
% 20.94/13.65 tff(337,plain,(
% 20.94/13.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(skolemize,[status(sab)],[336])).
% 20.94/13.65 tff(338,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[337, 330])).
% 20.94/13.65 tff(339,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[338, 328])).
% 20.94/13.65 tff(340,plain,
% 20.94/13.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))),
% 20.94/13.65 inference(modus_ponens,[status(thm)],[339, 323])).
% 20.94/13.65 tff(341,plain,
% 20.94/13.65 (v13_lattices(A!0)),
% 20.94/13.65 inference(or_elim,[status(thm)],[127])).
% 20.94/13.65 tff(342,plain,
% 20.94/13.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))),
% 20.94/13.65 inference(rewrite,[status(thm)],[])).
% 20.94/13.65 tff(343,plain,
% 20.94/13.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B)))),
% 20.94/13.66 inference(quant_inst,[status(thm)],[])).
% 20.94/13.66 tff(344,plain,
% 20.94/13.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, k5_lattices(A), B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v13_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))),
% 20.94/13.66 inference(modus_ponens,[status(thm)],[343, 342])).
% 20.94/13.66 tff(345,plain,
% 20.94/13.66 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[344, 65, 129, 31, 341, 340])).
% 20.94/13.66 tff(346,plain,
% 20.94/13.66 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))),
% 20.94/13.66 inference(rewrite,[status(thm)],[])).
% 20.94/13.66 tff(347,plain,
% 20.94/13.66 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1))),
% 20.94/13.66 inference(quant_inst,[status(thm)],[])).
% 20.94/13.66 tff(348,plain,
% 20.94/13.66 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B!1)),
% 20.94/13.66 inference(modus_ponens,[status(thm)],[347, 346])).
% 20.94/13.66 tff(349,plain,
% 20.94/13.66 (r3_lattices(A!0, k5_lattices(A!0), B!1)),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[348, 128, 345])).
% 20.94/13.66 tff(350,plain,
% 20.94/13.66 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))),
% 20.94/13.66 inference(rewrite,[status(thm)],[])).
% 20.94/13.66 tff(351,plain,
% 20.94/13.66 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))) <=> ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))),
% 20.94/13.66 inference(rewrite,[status(thm)],[])).
% 20.94/13.66 tff(352,plain,
% 20.94/13.66 ((r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))))) <=> (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))),
% 20.94/13.66 inference(rewrite,[status(thm)],[])).
% 20.94/13.66 tff(353,plain,
% 20.94/13.66 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))))))) <=> ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))),
% 20.94/13.66 inference(monotonicity,[status(thm)],[352])).
% 20.94/13.66 tff(354,plain,
% 20.94/13.66 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))))))) <=> ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))),
% 20.94/13.66 inference(transitivity,[status(thm)],[353, 351])).
% 20.94/13.66 tff(355,plain,
% 20.94/13.66 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | ((~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))))),
% 20.94/13.66 inference(monotonicity,[status(thm)],[354])).
% 20.94/13.66 tff(356,plain,
% 20.94/13.66 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))))),
% 20.94/13.66 inference(transitivity,[status(thm)],[355, 350])).
% 20.94/13.66 tff(357,plain,
% 20.94/13.66 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))))))),
% 20.94/13.66 inference(quant_inst,[status(thm)],[])).
% 20.94/13.66 tff(358,plain,
% 20.94/13.66 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (r2_hidden(D, k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, D, B!1)) | (~r3_lattices(A!0, k5_lattices(A!0), D))))))) | (~r3_lattices(A!0, k5_lattices(A!0), B!1)) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))),
% 20.94/13.66 inference(modus_ponens,[status(thm)],[357, 356])).
% 20.94/13.66 tff(359,plain,
% 20.94/13.66 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[358, 349, 321, 290])).
% 20.94/13.66 tff(360,plain,
% 20.94/13.66 ((~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))) | (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))),
% 20.94/13.66 inference(tautology,[status(thm)],[])).
% 20.94/13.66 tff(361,plain,
% 20.94/13.66 ((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[360, 359])).
% 20.94/13.66 tff(362,plain,
% 20.94/13.66 (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[361, 1])).
% 20.94/13.66 tff(363,plain,
% 20.94/13.66 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))))),
% 20.94/13.66 inference(tautology,[status(thm)],[])).
% 20.94/13.66 tff(364,plain,
% 20.94/13.66 (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[363, 288])).
% 20.94/13.66 tff(365,plain,
% 20.94/13.66 ((r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.66 inference(tautology,[status(thm)],[])).
% 20.94/13.66 tff(366,plain,
% 20.94/13.66 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[365, 364])).
% 20.94/13.66 tff(367,plain,
% 20.94/13.66 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.66 inference(unit_resolution,[status(thm)],[366, 362])).
% 20.94/13.66 tff(368,plain,
% 20.94/13.66 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))),
% 20.94/13.66 inference(bind,[status(th)],[])).
% 20.94/13.66 tff(369,plain,
% 20.94/13.66 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.66 inference(quant_intro,[status(thm)],[368])).
% 20.94/13.66 tff(370,plain,
% 20.94/13.66 (^[A: $i, B: $i, C: $i] : rewrite((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))),
% 20.94/13.66 inference(bind,[status(th)],[])).
% 20.94/13.66 tff(371,plain,
% 20.94/13.66 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.66 inference(quant_intro,[status(thm)],[370])).
% 20.94/13.66 tff(372,plain,
% 20.94/13.66 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.66 inference(transitivity,[status(thm)],[371, 369])).
% 20.94/13.66 tff(373,plain,
% 20.94/13.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), trans(monotonicity(rewrite(((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) <=> ((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))), ((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))) <=> (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C))))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))), rewrite((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C))))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))), ((((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))) <=> (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> ((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))))), rewrite(((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C)))))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))))),
% 20.94/13.66 inference(bind,[status(th)],[])).
% 20.94/13.66 tff(374,plain,
% 20.94/13.66 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.66 inference(quant_intro,[status(thm)],[373])).
% 20.94/13.66 tff(375,plain,
% 20.94/13.66 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 20.94/13.66 inference(rewrite,[status(thm)],[])).
% 20.94/13.66 tff(376,plain,
% 20.94/13.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))))),
% 20.94/13.67 inference(bind,[status(th)],[])).
% 20.94/13.67 tff(377,plain,
% 20.94/13.67 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 20.94/13.67 inference(quant_intro,[status(thm)],[376])).
% 20.94/13.67 tff(378,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fraenkel_a_2_0_filter_2')).
% 20.94/13.67 tff(379,plain,
% 20.94/13.67 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 20.94/13.67 inference(modus_ponens,[status(thm)],[378, 377])).
% 20.94/13.67 tff(380,plain,
% 20.94/13.67 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : (m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))),
% 20.94/13.67 inference(modus_ponens,[status(thm)],[379, 375])).
% 20.94/13.67 tff(381,plain,(
% 20.94/13.67 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (((~r2_hidden(A, a_2_0_filter_2(B, C))) | (m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B)) & (A = tptp_fun_D_10(C, B, A)) & r3_lattices(B, tptp_fun_D_10(C, B, A), C))) & (r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : (~(m1_subset_1(D, u1_struct_0(B)) & (A = D) & r3_lattices(B, D, C))))))),
% 20.94/13.67 inference(skolemize,[status(sab)],[380])).
% 20.94/13.67 tff(382,plain,
% 20.94/13.67 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.67 inference(modus_ponens,[status(thm)],[381, 374])).
% 20.94/13.67 tff(383,plain,
% 20.94/13.67 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))),
% 20.94/13.67 inference(modus_ponens,[status(thm)],[382, 372])).
% 20.94/13.67 tff(384,plain,
% 20.94/13.67 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))),
% 20.94/13.67 inference(rewrite,[status(thm)],[])).
% 20.94/13.67 tff(385,plain,
% 20.94/13.67 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))),
% 20.94/13.67 inference(rewrite,[status(thm)],[])).
% 20.94/13.67 tff(386,plain,
% 20.94/13.67 ((~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1))))))) <=> (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))))),
% 20.94/13.67 inference(rewrite,[status(thm)],[])).
% 20.94/13.67 tff(387,plain,
% 20.94/13.67 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))),
% 20.94/13.67 inference(monotonicity,[status(thm)],[386])).
% 20.94/13.67 tff(388,plain,
% 20.94/13.67 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1)))))))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))),
% 20.94/13.67 inference(transitivity,[status(thm)],[387, 385])).
% 20.94/13.67 tff(389,plain,
% 20.94/13.67 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))))))),
% 20.94/13.67 inference(monotonicity,[status(thm)],[388])).
% 20.94/13.67 tff(390,plain,
% 20.94/13.67 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1))))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))))),
% 20.94/13.67 inference(transitivity,[status(thm)],[389, 384])).
% 20.94/13.67 tff(391,plain,
% 20.94/13.67 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)) | (~r3_lattices(A!0, D, B!1))))))))),
% 20.94/13.67 inference(quant_inst,[status(thm)],[])).
% 20.94/13.67 tff(392,plain,
% 20.94/13.67 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~((~((~r2_hidden(A, a_2_0_filter_2(B, C))) | (~((~m1_subset_1(tptp_fun_D_10(C, B, A), u1_struct_0(B))) | (~(A = tptp_fun_D_10(C, B, A))) | (~r3_lattices(B, tptp_fun_D_10(C, B, A), C)))))) | (~(r2_hidden(A, a_2_0_filter_2(B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~(A = D)) | (~r3_lattices(B, D, C))))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))))),
% 20.94/13.68 inference(modus_ponens,[status(thm)],[391, 390])).
% 20.94/13.68 tff(393,plain,
% 20.94/13.68 (~((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[392, 65, 129, 31, 128, 383])).
% 20.94/13.68 tff(394,plain,
% 20.94/13.68 (((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))) | ((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(395,plain,
% 20.94/13.68 ((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[394, 393])).
% 20.94/13.68 tff(396,plain,
% 20.94/13.68 ((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(397,plain,
% 20.94/13.68 ((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[396, 395])).
% 20.94/13.68 tff(398,plain,
% 20.94/13.68 (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[397, 367])).
% 20.94/13.68 tff(399,plain,
% 20.94/13.68 (((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))) | (tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(400,plain,
% 20.94/13.68 (tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[399, 398])).
% 20.94/13.68 tff(401,plain,
% 20.94/13.68 (tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))),
% 20.94/13.68 inference(symmetry,[status(thm)],[400])).
% 20.94/13.68 tff(402,plain,
% 20.94/13.68 (r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1) <=> r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)),
% 20.94/13.68 inference(monotonicity,[status(thm)],[401])).
% 20.94/13.68 tff(403,plain,
% 20.94/13.68 (r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1) <=> r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)),
% 20.94/13.68 inference(symmetry,[status(thm)],[402])).
% 20.94/13.68 tff(404,plain,
% 20.94/13.68 ((~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) <=> (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))),
% 20.94/13.68 inference(monotonicity,[status(thm)],[403])).
% 20.94/13.68 tff(405,plain,
% 20.94/13.68 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))),
% 20.94/13.68 inference(rewrite,[status(thm)],[])).
% 20.94/13.68 tff(406,plain,
% 20.94/13.68 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))),
% 20.94/13.68 inference(quant_inst,[status(thm)],[])).
% 20.94/13.68 tff(407,plain,
% 20.94/13.68 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), B))) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))),
% 20.94/13.68 inference(modus_ponens,[status(thm)],[406, 405])).
% 20.94/13.68 tff(408,plain,
% 20.94/13.68 (r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[407, 345, 290])).
% 20.94/13.68 tff(409,plain,
% 20.94/13.68 ((~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))) | (~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(410,plain,
% 20.94/13.68 ((~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[409, 408])).
% 20.94/13.68 tff(411,plain,
% 20.94/13.68 (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[410, 1])).
% 20.94/13.68 tff(412,plain,
% 20.94/13.68 (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)),
% 20.94/13.68 inference(modus_ponens,[status(thm)],[411, 404])).
% 20.94/13.68 tff(413,plain,
% 20.94/13.68 (((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1))) | r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(414,plain,
% 20.94/13.68 (r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[413, 398])).
% 20.94/13.68 tff(415,plain,
% 20.94/13.68 ($false),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[414, 412])).
% 20.94/13.68 tff(416,plain,(~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))), inference(lemma,lemma(discharge,[]))).
% 20.94/13.68 tff(417,plain,
% 20.94/13.68 ((~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> (~((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))))) | r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | ((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(418,plain,
% 20.94/13.68 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) | ((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[417, 359])).
% 20.94/13.68 tff(419,plain,
% 20.94/13.68 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[418, 416])).
% 20.94/13.68 tff(420,plain,
% 20.94/13.68 ((r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1)) <=> r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(421,plain,
% 20.94/13.68 ((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), k22_filter_2(A!0, k5_lattices(A!0), B!1))) | (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[420, 364])).
% 20.94/13.68 tff(422,plain,
% 20.94/13.68 (~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[421, 419])).
% 20.94/13.68 tff(423,plain,
% 20.94/13.68 (((~((~r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1))) | (~((~m1_subset_1(tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), u1_struct_0(A!0))) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) | (~r3_lattices(A!0, tptp_fun_D_10(B!1, A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))), B!1)))))) | (~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))))) | (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(424,plain,
% 20.94/13.68 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))),
% 20.94/13.68 inference(unit_resolution,[status(thm)],[423, 393])).
% 20.94/13.68 tff(425,plain,
% 20.94/13.68 ((~(r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D))))) | r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))),
% 20.94/13.68 inference(tautology,[status(thm)],[])).
% 20.94/13.68 tff(426,plain,
% 20.94/13.68 (r2_hidden(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), a_2_0_filter_2(A!0, B!1)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))),
% 20.94/13.69 inference(unit_resolution,[status(thm)],[425, 424])).
% 20.94/13.69 tff(427,plain,
% 20.94/13.69 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))),
% 20.94/13.69 inference(unit_resolution,[status(thm)],[426, 422])).
% 20.94/13.69 tff(428,plain,
% 20.94/13.69 (((~r3_lattices(A!0, k5_lattices(A!0), tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))) | r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)),
% 20.94/13.69 inference(tautology,[status(thm)],[])).
% 20.94/13.69 tff(429,plain,
% 20.94/13.69 (r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)),
% 20.94/13.69 inference(unit_resolution,[status(thm)],[428, 416])).
% 20.94/13.69 tff(430,plain,
% 20.94/13.69 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.69 inference(rewrite,[status(thm)],[])).
% 20.94/13.69 tff(431,plain,
% 20.94/13.69 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | $false) <=> ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.69 inference(rewrite,[status(thm)],[])).
% 20.94/13.69 tff(432,plain,
% 20.94/13.69 ((~$true) <=> $false),
% 20.94/13.69 inference(rewrite,[status(thm)],[])).
% 20.94/13.69 tff(433,plain,
% 20.94/13.69 ((tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))) <=> $true),
% 20.94/13.69 inference(rewrite,[status(thm)],[])).
% 20.94/13.69 tff(434,plain,
% 20.94/13.69 ((~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) <=> (~$true)),
% 20.94/13.69 inference(monotonicity,[status(thm)],[433])).
% 20.94/13.69 tff(435,plain,
% 20.94/13.69 ((~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))) <=> $false),
% 20.94/13.69 inference(transitivity,[status(thm)],[434, 432])).
% 20.94/13.69 tff(436,plain,
% 20.94/13.69 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) <=> ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | $false)),
% 20.94/13.69 inference(monotonicity,[status(thm)],[435])).
% 20.94/13.69 tff(437,plain,
% 20.94/13.69 (((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0))))) <=> ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.69 inference(transitivity,[status(thm)],[436, 431])).
% 20.94/13.69 tff(438,plain,
% 20.94/13.69 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))))),
% 20.94/13.69 inference(monotonicity,[status(thm)],[437])).
% 20.94/13.69 tff(439,plain,
% 20.94/13.69 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)))),
% 20.94/13.69 inference(transitivity,[status(thm)],[438, 430])).
% 20.94/13.69 tff(440,plain,
% 20.94/13.69 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | ((~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)))))),
% 21.01/13.71 inference(quant_inst,[status(thm)],[])).
% 21.01/13.71 tff(441,plain,
% 21.01/13.71 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, D, B!1)) | (~(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)) = D)))) | (~m1_subset_1(tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, tptp_fun_D_2(a_2_0_filter_2(A!0, B!1), k22_filter_2(A!0, k5_lattices(A!0), B!1), u1_struct_0(A!0)), B!1))),
% 21.01/13.71 inference(modus_ponens,[status(thm)],[440, 439])).
% 21.01/13.71 tff(442,plain,
% 21.01/13.71 ($false),
% 21.01/13.71 inference(unit_resolution,[status(thm)],[441, 290, 429, 427])).
% 21.01/13.71 % SZS output end Proof
%------------------------------------------------------------------------------