TSTP Solution File: LAT324+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT324+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 18:33:05 EDT 2022
% Result : Theorem 53.76s 34.44s
% Output : Proof 54.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : LAT324+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n003.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 14:31:24 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 53.76/34.44 % SZS status Theorem
% 53.76/34.44 % SZS output start Proof
% 53.76/34.44 tff(v1_filter_0_type, type, (
% 53.76/34.44 v1_filter_0: ( $i * $i ) > $o)).
% 53.76/34.44 tff(k1_lattice2_type, type, (
% 53.76/34.44 k1_lattice2: $i > $i)).
% 53.76/34.44 tff(tptp_fun_A_0_type, type, (
% 53.76/34.44 tptp_fun_A_0: $i)).
% 53.76/34.44 tff(k15_filter_2_type, type, (
% 53.76/34.44 k15_filter_2: ( $i * $i ) > $i)).
% 53.76/34.44 tff(tptp_fun_D_31_type, type, (
% 53.76/34.44 tptp_fun_D_31: ( $i * $i * $i ) > $i)).
% 53.76/34.44 tff(g3_lattices_type, type, (
% 53.76/34.44 g3_lattices: ( $i * $i * $i ) > $i)).
% 53.76/34.44 tff(u2_lattices_type, type, (
% 53.76/34.44 u2_lattices: $i > $i)).
% 53.76/34.44 tff(u1_lattices_type, type, (
% 53.76/34.44 u1_lattices: $i > $i)).
% 53.76/34.44 tff(u1_struct_0_type, type, (
% 53.76/34.44 u1_struct_0: $i > $i)).
% 53.76/34.44 tff(tptp_fun_B_1_type, type, (
% 53.76/34.44 tptp_fun_B_1: $i)).
% 53.76/34.44 tff(tptp_fun_C_2_type, type, (
% 53.76/34.44 tptp_fun_C_2: $i)).
% 53.76/34.44 tff(l3_lattices_type, type, (
% 53.76/34.44 l3_lattices: $i > $o)).
% 53.76/34.44 tff(r2_hidden_type, type, (
% 53.76/34.44 r2_hidden: ( $i * $i ) > $o)).
% 53.76/34.44 tff(r2_filter_2_type, type, (
% 53.76/34.44 r2_filter_2: ( $i * $i ) > $o)).
% 53.76/34.44 tff(m2_filter_2_type, type, (
% 53.76/34.44 m2_filter_2: ( $i * $i ) > $o)).
% 53.76/34.44 tff(m1_subset_1_type, type, (
% 53.76/34.44 m1_subset_1: ( $i * $i ) > $o)).
% 53.76/34.44 tff(v17_lattices_type, type, (
% 53.76/34.44 v17_lattices: $i > $o)).
% 53.76/34.44 tff(v10_lattices_type, type, (
% 53.76/34.44 v10_lattices: $i > $o)).
% 53.76/34.44 tff(v3_struct_0_type, type, (
% 53.76/34.44 v3_struct_0: $i > $o)).
% 53.76/34.44 tff(k7_filter_2_type, type, (
% 53.76/34.44 k7_filter_2: ( $i * $i ) > $i)).
% 53.76/34.44 tff(k1_zfmisc_1_type, type, (
% 53.76/34.44 k1_zfmisc_1: $i > $i)).
% 53.76/34.44 tff(v3_lattices_type, type, (
% 53.76/34.44 v3_lattices: $i > $o)).
% 53.76/34.44 tff(m1_relset_1_type, type, (
% 53.76/34.44 m1_relset_1: ( $i * $i * $i ) > $o)).
% 53.76/34.44 tff(k2_zfmisc_1_type, type, (
% 53.76/34.44 k2_zfmisc_1: ( $i * $i ) > $i)).
% 53.76/34.44 tff(m2_relset_1_type, type, (
% 53.76/34.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 53.76/34.44 tff(v1_funct_2_type, type, (
% 53.76/34.44 v1_funct_2: ( $i * $i * $i ) > $o)).
% 53.76/34.44 tff(v1_funct_1_type, type, (
% 53.76/34.44 v1_funct_1: $i > $o)).
% 53.76/34.44 tff(l1_lattices_type, type, (
% 53.76/34.44 l1_lattices: $i > $o)).
% 53.76/34.44 tff(l2_lattices_type, type, (
% 53.76/34.44 l2_lattices: $i > $o)).
% 53.76/34.44 tff(v1_xboole_0_type, type, (
% 53.76/34.44 v1_xboole_0: $i > $o)).
% 53.76/34.44 tff(m1_filter_0_type, type, (
% 53.76/34.44 m1_filter_0: ( $i * $i ) > $o)).
% 53.76/34.44 tff(k5_filter_2_type, type, (
% 53.76/34.44 k5_filter_2: ( $i * $i ) > $i)).
% 53.76/34.44 tff(v9_lattices_type, type, (
% 53.76/34.44 v9_lattices: $i > $o)).
% 53.76/34.44 tff(v8_lattices_type, type, (
% 53.76/34.44 v8_lattices: $i > $o)).
% 53.76/34.44 tff(v7_lattices_type, type, (
% 53.76/34.44 v7_lattices: $i > $o)).
% 53.76/34.44 tff(v6_lattices_type, type, (
% 53.76/34.44 v6_lattices: $i > $o)).
% 53.76/34.44 tff(v5_lattices_type, type, (
% 53.76/34.44 v5_lattices: $i > $o)).
% 53.76/34.44 tff(v4_lattices_type, type, (
% 53.76/34.44 v4_lattices: $i > $o)).
% 53.76/34.44 tff(v16_lattices_type, type, (
% 53.76/34.44 v16_lattices: $i > $o)).
% 53.76/34.44 tff(v15_lattices_type, type, (
% 53.76/34.44 v15_lattices: $i > $o)).
% 53.76/34.44 tff(v14_lattices_type, type, (
% 53.76/34.44 v14_lattices: $i > $o)).
% 53.76/34.44 tff(v13_lattices_type, type, (
% 53.76/34.44 v13_lattices: $i > $o)).
% 53.76/34.44 tff(v12_lattices_type, type, (
% 53.76/34.44 v12_lattices: $i > $o)).
% 53.76/34.44 tff(v11_lattices_type, type, (
% 53.76/34.44 v11_lattices: $i > $o)).
% 53.76/34.44 tff(k14_filter_2_type, type, (
% 53.76/34.44 k14_filter_2: ( $i * $i ) > $i)).
% 53.76/34.44 tff(k8_filter_2_type, type, (
% 53.76/34.44 k8_filter_2: ( $i * $i ) > $i)).
% 53.76/34.44 tff(1,plain,
% 53.76/34.44 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 53.76/34.44 inference(bind,[status(th)],[])).
% 53.76/34.44 tff(2,plain,
% 53.76/34.44 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.44 inference(quant_intro,[status(thm)],[1])).
% 53.76/34.44 tff(3,plain,
% 53.76/34.44 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.44 inference(rewrite,[status(thm)],[])).
% 53.76/34.44 tff(4,plain,
% 53.76/34.44 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 53.76/34.44 inference(bind,[status(th)],[])).
% 53.76/34.44 tff(5,plain,
% 53.76/34.44 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[4])).
% 53.76/34.45 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 53.76/34.45 tff(7,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[6, 5])).
% 53.76/34.45 tff(8,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[7, 3])).
% 53.76/34.45 tff(9,plain,(
% 53.76/34.45 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.45 inference(skolemize,[status(sab)],[8])).
% 53.76/34.45 tff(10,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[9, 2])).
% 53.76/34.45 tff(11,plain,
% 53.76/34.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(12,plain,
% 53.76/34.45 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(13,plain,
% 53.76/34.45 ((m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(14,plain,
% 53.76/34.45 (((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))) <=> ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(15,plain,
% 53.76/34.45 ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> m1_subset_1(C!2, u1_struct_0(A!0))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(16,plain,
% 53.76/34.45 (((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[15, 14])).
% 53.76/34.45 tff(17,plain,
% 53.76/34.45 (((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(transitivity,[status(thm)],[16, 13])).
% 53.76/34.45 tff(18,plain,
% 53.76/34.45 ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> m1_subset_1(B!1, u1_struct_0(A!0))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(19,plain,
% 53.76/34.45 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[18, 17])).
% 53.76/34.45 tff(20,plain,
% 53.76/34.45 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(transitivity,[status(thm)],[19, 12])).
% 53.76/34.45 tff(21,plain,
% 53.76/34.45 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(22,plain,
% 53.76/34.45 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[21, 20])).
% 53.76/34.45 tff(23,plain,
% 53.76/34.45 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & ((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 53.76/34.45 inference(transitivity,[status(thm)],[22, 11])).
% 53.76/34.45 tff(24,plain,
% 53.76/34.45 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(25,plain,
% 53.76/34.45 ((~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m2_filter_2(D, A) => (~(r2_filter_2(A, D) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(26,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m2_filter_2(D, A) => (~(r2_filter_2(A, D) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_filter_2')).
% 53.76/34.45 tff(27,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[26, 25])).
% 53.76/34.45 tff(28,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[27, 24])).
% 53.76/34.45 tff(29,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 53.76/34.45 tff(30,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[29, 24])).
% 53.76/34.45 tff(31,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[30, 24])).
% 53.76/34.45 tff(32,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[31, 24])).
% 53.76/34.45 tff(33,plain,
% 53.76/34.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[32, 24])).
% 53.76/34.45 tff(34,plain,
% 53.76/34.45 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[33, 23])).
% 53.76/34.45 tff(35,plain,
% 53.76/34.45 (l3_lattices(A!0)),
% 53.76/34.45 inference(and_elim,[status(thm)],[34])).
% 53.76/34.45 tff(36,plain,
% 53.76/34.45 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(37,plain,
% 53.76/34.45 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(38,plain,
% 53.76/34.45 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[37, 36])).
% 53.76/34.45 tff(39,plain,
% 53.76/34.45 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[38, 35, 10])).
% 53.76/34.45 tff(40,plain,
% 53.76/34.45 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 53.76/34.45 inference(symmetry,[status(thm)],[39])).
% 53.76/34.45 tff(41,plain,
% 53.76/34.45 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[40])).
% 53.76/34.45 tff(42,plain,
% 53.76/34.45 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[41])).
% 53.76/34.45 tff(43,plain,
% 53.76/34.45 (k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.76/34.45 inference(symmetry,[status(thm)],[42])).
% 53.76/34.45 tff(44,plain,
% 53.76/34.45 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.76/34.45 inference(symmetry,[status(thm)],[41])).
% 53.76/34.45 tff(45,plain,
% 53.76/34.45 (g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.76/34.45 inference(monotonicity,[status(thm)],[44])).
% 53.76/34.45 tff(46,plain,
% 53.76/34.45 (g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.76/34.45 inference(symmetry,[status(thm)],[45])).
% 53.76/34.45 tff(47,plain,
% 53.76/34.45 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(48,plain,
% 53.76/34.45 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[47])).
% 53.76/34.45 tff(49,plain,
% 53.76/34.45 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(50,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 53.76/34.45 tff(51,plain,
% 53.76/34.45 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[50, 49])).
% 53.76/34.45 tff(52,plain,(
% 53.76/34.45 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.76/34.45 inference(skolemize,[status(sab)],[51])).
% 53.76/34.45 tff(53,plain,
% 53.76/34.45 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[52, 48])).
% 53.76/34.45 tff(54,plain,
% 53.76/34.45 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(55,plain,
% 53.76/34.45 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[54, 53])).
% 53.76/34.45 tff(56,plain,
% 53.76/34.45 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(57,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[56])).
% 53.76/34.45 tff(58,plain,
% 53.76/34.45 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(59,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[58])).
% 53.76/34.45 tff(60,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(61,plain,
% 53.76/34.45 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(62,plain,
% 53.76/34.45 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[61])).
% 53.76/34.45 tff(63,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 53.76/34.45 tff(64,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[63, 62])).
% 53.76/34.45 tff(65,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[64, 60])).
% 53.76/34.45 tff(66,plain,(
% 53.76/34.45 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.76/34.45 inference(skolemize,[status(sab)],[65])).
% 53.76/34.45 tff(67,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[66, 59])).
% 53.76/34.45 tff(68,plain,
% 53.76/34.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[67, 57])).
% 53.76/34.45 tff(69,plain,
% 53.76/34.45 (((~![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)))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(70,plain,
% 53.76/34.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(71,plain,
% 53.76/34.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 53.76/34.45 tff(72,plain,
% 53.76/34.45 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[71, 35, 68])).
% 53.76/34.45 tff(73,plain,
% 53.76/34.45 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 53.76/34.45 inference(tautology,[status(thm)],[])).
% 53.76/34.45 tff(74,plain,
% 53.76/34.45 (l1_lattices(A!0)),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[73, 72])).
% 53.76/34.45 tff(75,plain,
% 53.76/34.45 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(76,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[75])).
% 53.76/34.45 tff(77,plain,
% 53.76/34.45 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(78,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[77])).
% 53.76/34.45 tff(79,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(80,plain,
% 53.76/34.45 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(81,plain,
% 53.76/34.45 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[80])).
% 53.76/34.45 tff(82,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 53.76/34.45 tff(83,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[82, 81])).
% 53.76/34.45 tff(84,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[83, 79])).
% 53.76/34.45 tff(85,plain,(
% 53.76/34.45 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(skolemize,[status(sab)],[84])).
% 53.76/34.45 tff(86,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[85, 78])).
% 53.76/34.45 tff(87,plain,
% 53.76/34.45 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[86, 76])).
% 53.76/34.45 tff(88,plain,
% 53.76/34.45 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(89,plain,
% 53.76/34.45 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(90,plain,
% 53.76/34.45 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[89, 88])).
% 53.76/34.45 tff(91,plain,
% 53.76/34.45 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[90, 87])).
% 53.76/34.45 tff(92,plain,
% 53.76/34.45 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[91, 74])).
% 53.76/34.45 tff(93,plain,
% 53.76/34.45 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(tautology,[status(thm)],[])).
% 53.76/34.45 tff(94,plain,
% 53.76/34.45 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[93, 92])).
% 53.76/34.45 tff(95,plain,
% 53.76/34.45 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(tautology,[status(thm)],[])).
% 53.76/34.45 tff(96,plain,
% 53.76/34.45 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[95, 94])).
% 53.76/34.45 tff(97,plain,
% 53.76/34.45 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[96, 55])).
% 53.76/34.45 tff(98,plain,
% 53.76/34.45 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(99,plain,
% 53.76/34.45 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[98, 53])).
% 53.76/34.45 tff(100,plain,
% 53.76/34.45 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 53.76/34.45 inference(tautology,[status(thm)],[])).
% 53.76/34.45 tff(101,plain,
% 53.76/34.45 (l2_lattices(A!0)),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[100, 72])).
% 53.76/34.45 tff(102,plain,
% 53.76/34.45 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(103,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[102])).
% 53.76/34.45 tff(104,plain,
% 53.76/34.45 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(105,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[104])).
% 53.76/34.45 tff(106,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(107,plain,
% 53.76/34.45 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(bind,[status(th)],[])).
% 53.76/34.45 tff(108,plain,
% 53.76/34.45 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(quant_intro,[status(thm)],[107])).
% 53.76/34.45 tff(109,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 53.76/34.45 tff(110,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[109, 108])).
% 53.76/34.45 tff(111,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[110, 106])).
% 53.76/34.45 tff(112,plain,(
% 53.76/34.45 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.76/34.45 inference(skolemize,[status(sab)],[111])).
% 53.76/34.45 tff(113,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[112, 105])).
% 53.76/34.45 tff(114,plain,
% 53.76/34.45 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[113, 103])).
% 53.76/34.45 tff(115,plain,
% 53.76/34.45 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 53.76/34.45 inference(rewrite,[status(thm)],[])).
% 53.76/34.45 tff(116,plain,
% 53.76/34.45 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 53.76/34.45 inference(quant_inst,[status(thm)],[])).
% 53.76/34.45 tff(117,plain,
% 53.76/34.45 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 53.76/34.45 inference(modus_ponens,[status(thm)],[116, 115])).
% 53.76/34.45 tff(118,plain,
% 53.76/34.45 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[117, 114])).
% 53.76/34.45 tff(119,plain,
% 53.76/34.45 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 53.76/34.45 inference(unit_resolution,[status(thm)],[118, 101])).
% 53.76/34.45 tff(120,plain,
% 53.76/34.45 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.45 inference(tautology,[status(thm)],[])).
% 53.76/34.45 tff(121,plain,
% 53.76/34.45 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[120, 119])).
% 53.76/34.46 tff(122,plain,
% 53.76/34.46 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(tautology,[status(thm)],[])).
% 53.76/34.46 tff(123,plain,
% 53.76/34.46 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[122, 121])).
% 53.76/34.46 tff(124,plain,
% 53.76/34.46 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[123, 99])).
% 53.76/34.46 tff(125,plain,
% 53.76/34.46 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(tautology,[status(thm)],[])).
% 53.76/34.46 tff(126,plain,
% 53.76/34.46 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[125, 119])).
% 53.76/34.46 tff(127,plain,
% 53.76/34.46 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 53.76/34.46 inference(tautology,[status(thm)],[])).
% 53.76/34.46 tff(128,plain,
% 53.76/34.46 (v1_funct_1(u2_lattices(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[127, 119])).
% 53.76/34.46 tff(129,plain,
% 53.76/34.46 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(tautology,[status(thm)],[])).
% 53.76/34.46 tff(130,plain,
% 53.76/34.46 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[129, 92])).
% 53.76/34.46 tff(131,plain,
% 53.76/34.46 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 53.76/34.46 inference(tautology,[status(thm)],[])).
% 53.76/34.46 tff(132,plain,
% 53.76/34.46 (v1_funct_1(u1_lattices(A!0))),
% 53.76/34.46 inference(unit_resolution,[status(thm)],[131, 92])).
% 53.76/34.46 tff(133,plain,
% 53.76/34.46 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 53.76/34.46 inference(bind,[status(th)],[])).
% 53.76/34.46 tff(134,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 53.76/34.46 inference(quant_intro,[status(thm)],[133])).
% 53.76/34.46 tff(135,plain,
% 53.76/34.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 53.76/34.46 inference(bind,[status(th)],[])).
% 53.76/34.46 tff(136,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 53.76/34.46 inference(quant_intro,[status(thm)],[135])).
% 53.76/34.46 tff(137,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 53.76/34.46 inference(rewrite,[status(thm)],[])).
% 53.76/34.46 tff(138,plain,
% 53.76/34.46 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 53.76/34.46 inference(bind,[status(th)],[])).
% 53.76/34.46 tff(139,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 53.76/34.46 inference(quant_intro,[status(thm)],[138])).
% 53.76/34.46 tff(140,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 53.76/34.46 tff(141,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 53.76/34.46 inference(modus_ponens,[status(thm)],[140, 139])).
% 53.76/34.46 tff(142,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 53.76/34.46 inference(modus_ponens,[status(thm)],[141, 137])).
% 53.76/34.46 tff(143,plain,(
% 53.76/34.46 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 53.76/34.46 inference(skolemize,[status(sab)],[142])).
% 53.76/34.46 tff(144,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 53.76/34.46 inference(modus_ponens,[status(thm)],[143, 136])).
% 53.76/34.46 tff(145,plain,
% 53.76/34.46 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 53.76/34.46 inference(modus_ponens,[status(thm)],[144, 134])).
% 53.76/34.46 tff(146,plain,
% 53.76/34.46 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.76/34.46 inference(rewrite,[status(thm)],[])).
% 53.76/34.46 tff(147,plain,
% 53.76/34.46 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.76/34.46 inference(rewrite,[status(thm)],[])).
% 53.76/34.46 tff(148,plain,
% 53.76/34.46 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.76/34.46 inference(rewrite,[status(thm)],[])).
% 53.76/34.46 tff(149,plain,
% 53.76/34.46 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.76/34.46 inference(monotonicity,[status(thm)],[148])).
% 53.76/34.46 tff(150,plain,
% 53.76/34.46 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.76/34.46 inference(transitivity,[status(thm)],[149, 147])).
% 53.76/34.46 tff(151,plain,
% 53.76/34.46 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 53.76/34.46 inference(monotonicity,[status(thm)],[150])).
% 53.76/34.46 tff(152,plain,
% 53.76/34.46 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.76/34.46 inference(transitivity,[status(thm)],[151, 146])).
% 53.76/34.46 tff(153,plain,
% 53.76/34.46 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.89/34.46 inference(quant_inst,[status(thm)],[])).
% 53.89/34.46 tff(154,plain,
% 53.89/34.46 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.46 inference(modus_ponens,[status(thm)],[153, 152])).
% 53.89/34.46 tff(155,plain,
% 53.89/34.46 ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.46 inference(unit_resolution,[status(thm)],[154, 145, 132, 130, 128, 126])).
% 53.89/34.46 tff(156,plain,
% 53.89/34.46 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.89/34.46 inference(unit_resolution,[status(thm)],[155, 124, 97])).
% 53.89/34.46 tff(157,plain,
% 53.89/34.46 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.89/34.46 inference(tautology,[status(thm)],[])).
% 53.89/34.46 tff(158,plain,
% 53.89/34.46 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.89/34.46 inference(unit_resolution,[status(thm)],[157, 156])).
% 53.89/34.46 tff(159,plain,
% 53.89/34.46 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.89/34.46 inference(tautology,[status(thm)],[])).
% 53.89/34.46 tff(160,plain,
% 53.89/34.46 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.89/34.46 inference(unit_resolution,[status(thm)],[159, 156])).
% 53.89/34.46 tff(161,plain,
% 53.89/34.46 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 53.89/34.46 inference(bind,[status(th)],[])).
% 53.89/34.46 tff(162,plain,
% 53.89/34.46 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(quant_intro,[status(thm)],[161])).
% 53.89/34.46 tff(163,plain,
% 53.89/34.46 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(rewrite,[status(thm)],[])).
% 53.89/34.46 tff(164,plain,
% 53.89/34.46 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 53.89/34.46 inference(bind,[status(th)],[])).
% 53.89/34.46 tff(165,plain,
% 53.89/34.46 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(quant_intro,[status(thm)],[164])).
% 53.89/34.46 tff(166,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 53.89/34.46 tff(167,plain,
% 53.89/34.46 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(modus_ponens,[status(thm)],[166, 165])).
% 53.89/34.46 tff(168,plain,
% 53.89/34.46 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(modus_ponens,[status(thm)],[167, 163])).
% 53.89/34.46 tff(169,plain,(
% 53.89/34.46 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(skolemize,[status(sab)],[168])).
% 53.89/34.46 tff(170,plain,
% 53.89/34.46 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.46 inference(modus_ponens,[status(thm)],[169, 162])).
% 53.89/34.46 tff(171,plain,
% 53.89/34.46 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.46 inference(rewrite,[status(thm)],[])).
% 53.89/34.46 tff(172,plain,
% 53.89/34.46 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.46 inference(rewrite,[status(thm)],[])).
% 53.89/34.46 tff(173,plain,
% 53.89/34.46 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.89/34.46 inference(monotonicity,[status(thm)],[172])).
% 53.89/34.46 tff(174,plain,
% 53.89/34.46 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.46 inference(transitivity,[status(thm)],[173, 171])).
% 53.89/34.46 tff(175,plain,
% 53.89/34.46 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.89/34.46 inference(quant_inst,[status(thm)],[])).
% 53.89/34.46 tff(176,plain,
% 53.89/34.46 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.89/34.46 inference(modus_ponens,[status(thm)],[175, 174])).
% 53.89/34.47 tff(177,plain,
% 53.89/34.47 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.89/34.47 inference(unit_resolution,[status(thm)],[176, 170])).
% 53.89/34.47 tff(178,plain,
% 53.89/34.47 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.47 inference(unit_resolution,[status(thm)],[177, 160, 158])).
% 53.89/34.47 tff(179,plain,
% 53.89/34.47 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.47 inference(transitivity,[status(thm)],[178, 46])).
% 53.89/34.47 tff(180,plain,
% 53.89/34.47 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 53.89/34.47 inference(bind,[status(th)],[])).
% 53.89/34.47 tff(181,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(quant_intro,[status(thm)],[180])).
% 53.89/34.47 tff(182,plain,
% 53.89/34.47 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 53.89/34.47 inference(bind,[status(th)],[])).
% 53.89/34.47 tff(183,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(quant_intro,[status(thm)],[182])).
% 53.89/34.47 tff(184,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(transitivity,[status(thm)],[183, 181])).
% 53.89/34.47 tff(185,plain,
% 53.89/34.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 53.89/34.47 inference(bind,[status(th)],[])).
% 53.89/34.47 tff(186,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(quant_intro,[status(thm)],[185])).
% 53.89/34.47 tff(187,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.89/34.47 inference(rewrite,[status(thm)],[])).
% 53.89/34.47 tff(188,plain,
% 53.89/34.47 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 53.89/34.47 inference(bind,[status(th)],[])).
% 53.89/34.47 tff(189,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.89/34.47 inference(quant_intro,[status(thm)],[188])).
% 53.89/34.47 tff(190,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 53.89/34.47 tff(191,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.89/34.47 inference(modus_ponens,[status(thm)],[190, 189])).
% 53.89/34.47 tff(192,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.89/34.47 inference(modus_ponens,[status(thm)],[191, 187])).
% 53.89/34.47 tff(193,plain,(
% 53.89/34.47 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.89/34.47 inference(skolemize,[status(sab)],[192])).
% 53.89/34.47 tff(194,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(modus_ponens,[status(thm)],[193, 186])).
% 53.89/34.47 tff(195,plain,
% 53.89/34.47 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.89/34.47 inference(modus_ponens,[status(thm)],[194, 184])).
% 53.89/34.47 tff(196,plain,
% 53.89/34.47 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 53.89/34.47 inference(rewrite,[status(thm)],[])).
% 53.89/34.47 tff(197,plain,
% 53.89/34.47 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 53.89/34.47 inference(rewrite,[status(thm)],[])).
% 53.89/34.47 tff(198,plain,
% 53.89/34.47 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))))),
% 53.89/34.47 inference(monotonicity,[status(thm)],[197])).
% 53.89/34.47 tff(199,plain,
% 53.89/34.47 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 53.89/34.47 inference(transitivity,[status(thm)],[198, 196])).
% 53.89/34.47 tff(200,plain,
% 53.89/34.47 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 53.89/34.47 inference(quant_inst,[status(thm)],[])).
% 53.89/34.47 tff(201,plain,
% 53.89/34.47 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 53.89/34.47 inference(modus_ponens,[status(thm)],[200, 199])).
% 53.89/34.47 tff(202,plain,
% 53.89/34.47 ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 53.89/34.47 inference(unit_resolution,[status(thm)],[201, 195, 132, 130, 128, 126])).
% 53.89/34.47 tff(203,plain,
% 53.89/34.47 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 53.89/34.47 inference(unit_resolution,[status(thm)],[202, 124, 97])).
% 53.89/34.47 tff(204,plain,
% 53.89/34.47 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 53.89/34.47 inference(rewrite,[status(thm)],[])).
% 53.89/34.47 tff(205,plain,
% 53.89/34.47 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(206,plain,
% 53.89/34.48 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[205, 204])).
% 53.89/34.48 tff(207,plain,
% 53.89/34.48 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[206, 203])).
% 53.89/34.48 tff(208,plain,
% 53.89/34.48 (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[207, 179])).
% 53.89/34.48 tff(209,plain,
% 53.89/34.48 (((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(tautology,[status(thm)],[])).
% 53.89/34.48 tff(210,plain,
% 53.89/34.48 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[209, 208])).
% 53.89/34.48 tff(211,plain,
% 53.89/34.48 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[210])).
% 53.89/34.48 tff(212,plain,
% 53.89/34.48 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(transitivity,[status(thm)],[211, 43])).
% 53.89/34.48 tff(213,plain,
% 53.89/34.48 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[212])).
% 53.89/34.48 tff(214,plain,
% 53.89/34.48 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 53.89/34.48 inference(symmetry,[status(thm)],[213])).
% 53.89/34.48 tff(215,plain,
% 53.89/34.48 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(216,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = 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))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[215])).
% 53.89/34.48 tff(217,plain,
% 53.89/34.48 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(218,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[217])).
% 53.89/34.48 tff(219,plain,
% 53.89/34.48 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(220,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[219])).
% 53.89/34.48 tff(221,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(transitivity,[status(thm)],[220, 218])).
% 53.89/34.48 tff(222,plain,
% 53.89/34.48 (^[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))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(223,plain,
% 53.89/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[222])).
% 53.89/34.48 tff(224,plain,
% 53.89/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(225,plain,
% 53.89/34.48 (^[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)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(226,plain,
% 53.89/34.48 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[225])).
% 53.89/34.48 tff(227,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_filter_2')).
% 53.89/34.48 tff(228,plain,
% 53.89/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[227, 226])).
% 53.89/34.48 tff(229,plain,
% 53.89/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[228, 224])).
% 53.89/34.48 tff(230,plain,(
% 53.89/34.48 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(skolemize,[status(sab)],[229])).
% 53.89/34.48 tff(231,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[230, 223])).
% 53.89/34.48 tff(232,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[231, 221])).
% 53.89/34.48 tff(233,plain,
% 53.89/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[232, 216])).
% 53.89/34.48 tff(234,plain,
% 53.89/34.48 (v10_lattices(A!0)),
% 53.89/34.48 inference(and_elim,[status(thm)],[34])).
% 53.89/34.48 tff(235,plain,
% 53.89/34.48 (~v3_struct_0(A!0)),
% 53.89/34.48 inference(and_elim,[status(thm)],[34])).
% 53.89/34.48 tff(236,plain,
% 53.89/34.48 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = 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))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = 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))) | (k5_filter_2(A!0, B) = B)))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(237,plain,
% 53.89/34.48 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = 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))) | (k5_filter_2(A!0, B) = B)))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(238,plain,
% 53.89/34.48 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = 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))) | (k5_filter_2(A!0, B) = B))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[237, 236])).
% 53.89/34.48 tff(239,plain,
% 53.89/34.48 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[238, 235, 234, 35, 233])).
% 53.89/34.48 tff(240,plain,
% 53.89/34.48 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 53.89/34.48 inference(and_elim,[status(thm)],[34])).
% 53.89/34.48 tff(241,plain,
% 53.89/34.48 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(242,plain,
% 53.89/34.48 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(243,plain,
% 53.89/34.48 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2)),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[242, 241])).
% 53.89/34.48 tff(244,plain,
% 53.89/34.48 (k5_filter_2(A!0, C!2) = C!2),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[243, 240, 239])).
% 53.89/34.48 tff(245,plain,
% 53.89/34.48 (C!2 = k5_filter_2(A!0, C!2)),
% 53.89/34.48 inference(symmetry,[status(thm)],[244])).
% 53.89/34.48 tff(246,plain,
% 53.89/34.48 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[245, 41])).
% 53.89/34.48 tff(247,plain,
% 53.89/34.48 (m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(symmetry,[status(thm)],[246])).
% 53.89/34.48 tff(248,plain,
% 53.89/34.48 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(249,plain,
% 53.89/34.48 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[248])).
% 53.89/34.48 tff(250,plain,
% 53.89/34.48 (^[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)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(251,plain,
% 53.89/34.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[250])).
% 53.89/34.48 tff(252,plain,
% 53.89/34.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(253,plain,
% 53.89/34.48 (^[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))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))))),
% 53.89/34.48 inference(bind,[status(th)],[])).
% 53.89/34.48 tff(254,plain,
% 53.89/34.48 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 53.89/34.48 inference(quant_intro,[status(thm)],[253])).
% 53.89/34.48 tff(255,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 53.89/34.48 tff(256,plain,
% 53.89/34.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[255, 254])).
% 53.89/34.48 tff(257,plain,
% 53.89/34.48 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[256, 252])).
% 53.89/34.48 tff(258,plain,(
% 53.89/34.48 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 53.89/34.48 inference(skolemize,[status(sab)],[257])).
% 53.89/34.48 tff(259,plain,
% 53.89/34.48 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[258, 251])).
% 53.89/34.48 tff(260,plain,
% 53.89/34.48 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[259, 249])).
% 53.89/34.48 tff(261,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(262,plain,
% 53.89/34.48 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(263,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[262])).
% 53.89/34.48 tff(264,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(transitivity,[status(thm)],[263, 261])).
% 53.89/34.48 tff(265,plain,
% 53.89/34.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(266,plain,
% 53.89/34.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[265, 264])).
% 53.89/34.48 tff(267,plain,
% 53.89/34.48 (m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[266, 235, 234, 35, 240, 260])).
% 53.89/34.48 tff(268,plain,
% 53.89/34.48 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[267, 247])).
% 53.89/34.48 tff(269,plain,
% 53.89/34.48 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 53.89/34.48 inference(and_elim,[status(thm)],[34])).
% 53.89/34.48 tff(270,plain,
% 53.89/34.48 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(271,plain,
% 53.89/34.48 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(272,plain,
% 53.89/34.48 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[271, 270])).
% 53.89/34.48 tff(273,plain,
% 53.89/34.48 (k5_filter_2(A!0, B!1) = B!1),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[272, 269, 239])).
% 53.89/34.48 tff(274,plain,
% 53.89/34.48 (B!1 = k5_filter_2(A!0, B!1)),
% 53.89/34.48 inference(symmetry,[status(thm)],[273])).
% 53.89/34.48 tff(275,plain,
% 53.89/34.48 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[274, 41])).
% 53.89/34.48 tff(276,plain,
% 53.89/34.48 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(symmetry,[status(thm)],[275])).
% 53.89/34.48 tff(277,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(278,plain,
% 53.89/34.48 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(rewrite,[status(thm)],[])).
% 53.89/34.48 tff(279,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[278])).
% 53.89/34.48 tff(280,plain,
% 53.89/34.48 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 53.89/34.48 inference(transitivity,[status(thm)],[279, 277])).
% 53.89/34.48 tff(281,plain,
% 53.89/34.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 53.89/34.48 inference(quant_inst,[status(thm)],[])).
% 53.89/34.48 tff(282,plain,
% 53.89/34.48 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(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)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[281, 280])).
% 53.89/34.48 tff(283,plain,
% 53.89/34.48 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 53.89/34.48 inference(unit_resolution,[status(thm)],[282, 235, 234, 35, 269, 260])).
% 53.89/34.48 tff(284,plain,
% 53.89/34.48 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(modus_ponens,[status(thm)],[283, 276])).
% 53.89/34.48 tff(285,plain,
% 53.89/34.48 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[40])).
% 53.89/34.48 tff(286,plain,
% 53.89/34.48 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.89/34.48 inference(symmetry,[status(thm)],[285])).
% 53.89/34.48 tff(287,plain,
% 53.89/34.48 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.89/34.48 inference(monotonicity,[status(thm)],[286])).
% 53.89/34.48 tff(288,plain,
% 53.89/34.48 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 53.91/34.48 inference(bind,[status(th)],[])).
% 53.91/34.48 tff(289,plain,
% 53.91/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 53.91/34.48 inference(quant_intro,[status(thm)],[288])).
% 53.91/34.48 tff(290,plain,
% 53.91/34.48 (^[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))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 53.91/34.48 inference(bind,[status(th)],[])).
% 53.91/34.48 tff(291,plain,
% 53.91/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 53.91/34.48 inference(quant_intro,[status(thm)],[290])).
% 53.91/34.48 tff(292,plain,
% 53.91/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 53.91/34.48 inference(rewrite,[status(thm)],[])).
% 53.91/34.48 tff(293,plain,
% 53.91/34.48 (^[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))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 53.91/34.48 inference(bind,[status(th)],[])).
% 53.91/34.48 tff(294,plain,
% 53.91/34.48 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 53.91/34.48 inference(quant_intro,[status(thm)],[293])).
% 53.91/34.48 tff(295,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 53.91/34.48 tff(296,plain,
% 53.91/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 53.91/34.48 inference(modus_ponens,[status(thm)],[295, 294])).
% 53.91/34.48 tff(297,plain,
% 53.91/34.48 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 53.91/34.48 inference(modus_ponens,[status(thm)],[296, 292])).
% 53.91/34.48 tff(298,plain,(
% 53.91/34.48 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 53.91/34.48 inference(skolemize,[status(sab)],[297])).
% 53.91/34.48 tff(299,plain,
% 53.91/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 53.91/34.48 inference(modus_ponens,[status(thm)],[298, 291])).
% 53.91/34.48 tff(300,plain,
% 53.91/34.48 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 53.91/34.48 inference(modus_ponens,[status(thm)],[299, 289])).
% 53.91/34.48 tff(301,plain,
% 53.91/34.48 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 53.91/34.49 inference(rewrite,[status(thm)],[])).
% 53.91/34.49 tff(302,plain,
% 53.91/34.49 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 53.91/34.49 inference(quant_inst,[status(thm)],[])).
% 53.91/34.49 tff(303,plain,
% 53.91/34.49 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[302, 301])).
% 53.91/34.49 tff(304,plain,
% 53.91/34.49 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 53.91/34.49 inference(unit_resolution,[status(thm)],[303, 235, 234, 35, 300])).
% 53.91/34.49 tff(305,plain,
% 53.91/34.49 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 53.91/34.49 inference(tautology,[status(thm)],[])).
% 53.91/34.49 tff(306,plain,
% 53.91/34.49 (~v3_struct_0(k1_lattice2(A!0))),
% 53.91/34.49 inference(unit_resolution,[status(thm)],[305, 304])).
% 53.91/34.49 tff(307,plain,
% 53.91/34.49 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[306, 287])).
% 53.91/34.49 tff(308,plain,
% 53.91/34.49 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v17_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(monotonicity,[status(thm)],[40])).
% 53.91/34.49 tff(309,plain,
% 53.91/34.49 (v17_lattices(k1_lattice2(A!0)) <=> v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.49 inference(symmetry,[status(thm)],[308])).
% 53.91/34.49 tff(310,plain,
% 53.91/34.49 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(311,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[310])).
% 53.91/34.49 tff(312,plain,
% 53.91/34.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(313,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[312])).
% 53.91/34.49 tff(314,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 53.91/34.49 inference(rewrite,[status(thm)],[])).
% 53.91/34.49 tff(315,plain,
% 53.91/34.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)))), (((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))))), ((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)))), ((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))))), (((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)))), (((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))))), ((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)))), ((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))))), (((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)))), (((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))))), ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)))), ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))))), (((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))), (((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(316,plain,
% 53.91/34.49 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[315])).
% 53.91/34.49 tff(317,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_filter_2')).
% 53.91/34.49 tff(318,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[317, 316])).
% 53.91/34.49 tff(319,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[318, 314])).
% 53.91/34.49 tff(320,plain,(
% 53.91/34.49 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 53.91/34.49 inference(skolemize,[status(sab)],[319])).
% 53.91/34.49 tff(321,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[320, 313])).
% 53.91/34.49 tff(322,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[321, 311])).
% 53.91/34.49 tff(323,plain,
% 53.91/34.49 (v17_lattices(A!0)),
% 53.91/34.49 inference(and_elim,[status(thm)],[34])).
% 53.91/34.49 tff(324,plain,
% 53.91/34.49 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))),
% 53.91/34.49 inference(rewrite,[status(thm)],[])).
% 53.91/34.49 tff(325,plain,
% 53.91/34.49 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))),
% 53.91/34.49 inference(quant_inst,[status(thm)],[])).
% 53.91/34.49 tff(326,plain,
% 53.91/34.49 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0)))))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[325, 324])).
% 53.91/34.49 tff(327,plain,
% 53.91/34.49 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))),
% 53.91/34.49 inference(unit_resolution,[status(thm)],[326, 235, 234, 323, 35, 322])).
% 53.91/34.49 tff(328,plain,
% 53.91/34.49 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0)))) | v17_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(tautology,[status(thm)],[])).
% 53.91/34.49 tff(329,plain,
% 53.91/34.49 (v17_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(unit_resolution,[status(thm)],[328, 327])).
% 53.91/34.49 tff(330,plain,
% 53.91/34.49 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[329, 309])).
% 53.91/34.49 tff(331,plain,
% 53.91/34.49 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(monotonicity,[status(thm)],[40])).
% 53.91/34.49 tff(332,plain,
% 53.91/34.49 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.49 inference(symmetry,[status(thm)],[331])).
% 53.91/34.49 tff(333,plain,
% 53.91/34.49 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(tautology,[status(thm)],[])).
% 53.91/34.49 tff(334,plain,
% 53.91/34.49 (v10_lattices(k1_lattice2(A!0))),
% 53.91/34.49 inference(unit_resolution,[status(thm)],[333, 304])).
% 53.91/34.49 tff(335,plain,
% 53.91/34.49 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.49 inference(modus_ponens,[status(thm)],[334, 332])).
% 53.91/34.49 tff(336,plain,
% 53.91/34.49 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(337,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[336])).
% 53.91/34.49 tff(338,plain,
% 53.91/34.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(339,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[338])).
% 53.91/34.49 tff(340,plain,
% 53.91/34.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.49 inference(transitivity,[status(thm)],[339, 337])).
% 53.91/34.49 tff(341,plain,
% 53.91/34.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(342,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[341])).
% 53.91/34.49 tff(343,plain,
% 53.91/34.49 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | ((~(~(B = C))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 53.91/34.49 inference(bind,[status(th)],[])).
% 53.91/34.49 tff(344,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | ((~(~(B = C))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 53.91/34.49 inference(quant_intro,[status(thm)],[343])).
% 53.91/34.49 tff(345,plain,
% 53.91/34.49 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.91/34.49 inference(rewrite,[status(thm)],[])).
% 53.91/34.49 tff(346,plain,
% 53.91/34.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))) <=> (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))), ((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))), ((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))))),
% 53.91/34.50 inference(bind,[status(th)],[])).
% 53.91/34.50 tff(347,plain,
% 53.91/34.50 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.91/34.50 inference(quant_intro,[status(thm)],[346])).
% 53.91/34.50 tff(348,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_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)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t60_filter_0')).
% 53.91/34.50 tff(349,plain,
% 53.91/34.50 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[348, 347])).
% 53.91/34.50 tff(350,plain,
% 53.91/34.50 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[349, 345])).
% 53.91/34.50 tff(351,plain,(
% 53.91/34.50 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_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))) | ((~(~(B = C))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 53.91/34.50 inference(skolemize,[status(sab)],[350])).
% 53.91/34.50 tff(352,plain,
% 53.91/34.50 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[351, 344])).
% 53.91/34.50 tff(353,plain,
% 53.91/34.50 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[352, 342])).
% 53.91/34.50 tff(354,plain,
% 53.91/34.50 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[353, 340])).
% 53.91/34.50 tff(355,plain,
% 53.91/34.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))))),
% 53.91/34.50 inference(rewrite,[status(thm)],[])).
% 53.91/34.50 tff(356,plain,
% 53.91/34.50 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))))),
% 53.91/34.50 inference(quant_inst,[status(thm)],[])).
% 53.91/34.50 tff(357,plain,
% 53.91/34.50 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[356, 355])).
% 53.91/34.50 tff(358,plain,
% 53.91/34.50 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 53.91/34.50 inference(unit_resolution,[status(thm)],[357, 354])).
% 53.91/34.50 tff(359,plain,
% 53.91/34.50 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 53.91/34.50 inference(unit_resolution,[status(thm)],[358, 335, 160, 330, 307])).
% 53.91/34.50 tff(360,plain,
% 53.91/34.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 53.91/34.50 inference(rewrite,[status(thm)],[])).
% 53.91/34.50 tff(361,plain,
% 53.91/34.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 53.91/34.50 inference(quant_inst,[status(thm)],[])).
% 53.91/34.50 tff(362,plain,
% 53.91/34.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 53.91/34.50 inference(modus_ponens,[status(thm)],[361, 360])).
% 53.91/34.50 tff(363,plain,
% 53.91/34.50 ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 53.91/34.50 inference(unit_resolution,[status(thm)],[362, 359])).
% 53.91/34.50 tff(364,plain,
% 53.91/34.50 (![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[363, 284])).
% 53.91/34.51 tff(365,plain,
% 53.91/34.51 (~(B!1 = C!2)),
% 53.91/34.51 inference(and_elim,[status(thm)],[34])).
% 53.91/34.51 tff(366,plain,
% 53.91/34.51 (((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | ((B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) <=> ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | (B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(367,plain,
% 53.91/34.51 ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | ((B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 53.91/34.51 inference(quant_inst,[status(thm)],[])).
% 53.91/34.51 tff(368,plain,
% 53.91/34.51 ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | (B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[367, 366])).
% 53.91/34.51 tff(369,plain,
% 53.91/34.51 (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[368, 365, 364, 268])).
% 53.91/34.51 tff(370,plain,
% 53.91/34.51 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.51 inference(tautology,[status(thm)],[])).
% 53.91/34.51 tff(371,plain,
% 53.91/34.51 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[370, 369])).
% 53.91/34.51 tff(372,plain,
% 53.91/34.51 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(373,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[372])).
% 53.91/34.51 tff(374,plain,
% 53.91/34.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(375,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[374])).
% 53.91/34.51 tff(376,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(transitivity,[status(thm)],[375, 373])).
% 53.91/34.51 tff(377,plain,
% 53.91/34.51 (^[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_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(378,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[377])).
% 53.91/34.51 tff(379,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & 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] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(380,plain,
% 53.91/34.51 (^[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_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(381,plain,
% 53.91/34.51 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & 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] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[380])).
% 53.91/34.51 tff(382,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 53.91/34.51 tff(383,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[382, 381])).
% 53.91/34.51 tff(384,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[383, 379])).
% 53.91/34.51 tff(385,plain,(
% 53.91/34.51 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.91/34.51 inference(skolemize,[status(sab)],[384])).
% 53.91/34.51 tff(386,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[385, 378])).
% 53.91/34.51 tff(387,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[386, 376])).
% 53.91/34.51 tff(388,plain,
% 53.91/34.51 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(389,plain,
% 53.91/34.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 53.91/34.51 inference(quant_inst,[status(thm)],[])).
% 53.91/34.51 tff(390,plain,
% 53.91/34.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[389, 388])).
% 53.91/34.51 tff(391,plain,
% 53.91/34.51 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[390, 387])).
% 53.91/34.51 tff(392,plain,
% 53.91/34.51 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[391, 335, 160, 307])).
% 53.91/34.51 tff(393,plain,
% 53.91/34.51 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(394,plain,
% 53.91/34.51 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.91/34.51 inference(quant_inst,[status(thm)],[])).
% 53.91/34.51 tff(395,plain,
% 53.91/34.51 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[394, 393])).
% 53.91/34.51 tff(396,plain,
% 53.91/34.51 (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[395, 392, 371])).
% 53.91/34.51 tff(397,plain,
% 53.91/34.51 ((v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.91/34.51 inference(tautology,[status(thm)],[])).
% 53.91/34.51 tff(398,plain,
% 53.91/34.51 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.91/34.51 inference(unit_resolution,[status(thm)],[397, 396])).
% 53.91/34.51 tff(399,plain,
% 53.91/34.51 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[398, 214])).
% 53.91/34.51 tff(400,plain,
% 53.91/34.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(401,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[400])).
% 53.91/34.51 tff(402,plain,
% 53.91/34.51 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(403,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[402])).
% 53.91/34.51 tff(404,plain,
% 53.91/34.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(405,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[404])).
% 53.91/34.51 tff(406,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(transitivity,[status(thm)],[405, 403])).
% 53.91/34.51 tff(407,plain,
% 53.91/34.51 (^[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, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(408,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[407])).
% 53.91/34.51 tff(409,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(410,plain,
% 53.91/34.51 (^[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, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 53.91/34.51 inference(bind,[status(th)],[])).
% 53.91/34.51 tff(411,plain,
% 53.91/34.51 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(quant_intro,[status(thm)],[410])).
% 53.91/34.51 tff(412,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_filter_2')).
% 53.91/34.51 tff(413,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[412, 411])).
% 53.91/34.51 tff(414,plain,
% 53.91/34.51 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[413, 409])).
% 53.91/34.51 tff(415,plain,(
% 53.91/34.51 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(skolemize,[status(sab)],[414])).
% 53.91/34.51 tff(416,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[415, 408])).
% 53.91/34.51 tff(417,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[416, 406])).
% 53.91/34.51 tff(418,plain,
% 53.91/34.51 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 53.91/34.51 inference(modus_ponens,[status(thm)],[417, 401])).
% 53.91/34.51 tff(419,plain,
% 53.91/34.51 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 53.91/34.51 inference(rewrite,[status(thm)],[])).
% 53.91/34.51 tff(420,plain,
% 53.91/34.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 53.94/34.52 inference(quant_inst,[status(thm)],[])).
% 53.94/34.52 tff(421,plain,
% 53.94/34.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[420, 419])).
% 53.94/34.52 tff(422,plain,
% 53.94/34.52 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[421, 235, 234, 35, 418])).
% 53.94/34.52 tff(423,plain,
% 53.94/34.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(424,plain,
% 53.94/34.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(quant_inst,[status(thm)],[])).
% 53.94/34.52 tff(425,plain,
% 53.94/34.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[424, 423])).
% 53.94/34.52 tff(426,plain,
% 53.94/34.52 ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[425, 422])).
% 53.94/34.52 tff(427,plain,
% 53.94/34.52 (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[426, 399])).
% 53.94/34.52 tff(428,plain,
% 53.94/34.52 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)) <=> m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.94/34.52 inference(monotonicity,[status(thm)],[39])).
% 53.94/34.52 tff(429,plain,
% 53.94/34.52 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 53.94/34.52 inference(symmetry,[status(thm)],[428])).
% 53.94/34.52 tff(430,plain,
% 53.94/34.52 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[371, 429])).
% 53.94/34.52 tff(431,plain,
% 53.94/34.52 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(432,plain,
% 53.94/34.52 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[431])).
% 53.94/34.52 tff(433,plain,
% 53.94/34.52 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(434,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[433])).
% 53.94/34.52 tff(435,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(436,plain,
% 53.94/34.52 (^[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_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(437,plain,
% 53.94/34.52 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[436])).
% 53.94/34.52 tff(438,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k14_filter_2')).
% 53.94/34.52 tff(439,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[438, 437])).
% 53.94/34.52 tff(440,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[439, 435])).
% 53.94/34.52 tff(441,plain,(
% 53.94/34.52 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 53.94/34.52 inference(skolemize,[status(sab)],[440])).
% 53.94/34.52 tff(442,plain,
% 53.94/34.52 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[441, 434])).
% 53.94/34.52 tff(443,plain,
% 53.94/34.52 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[442, 432])).
% 53.94/34.52 tff(444,plain,
% 53.94/34.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(445,plain,
% 53.94/34.52 ((v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(446,plain,
% 53.94/34.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.94/34.52 inference(monotonicity,[status(thm)],[445])).
% 53.94/34.52 tff(447,plain,
% 53.94/34.52 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.94/34.52 inference(transitivity,[status(thm)],[446, 444])).
% 53.94/34.52 tff(448,plain,
% 53.94/34.52 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 53.94/34.52 inference(quant_inst,[status(thm)],[])).
% 53.94/34.52 tff(449,plain,
% 53.94/34.52 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[448, 447])).
% 53.94/34.52 tff(450,plain,
% 53.94/34.52 ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[449, 235, 234, 35, 443])).
% 53.94/34.52 tff(451,plain,
% 53.94/34.52 (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[450, 430])).
% 53.94/34.52 tff(452,plain,
% 53.94/34.52 (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(symmetry,[status(thm)],[451])).
% 53.94/34.52 tff(453,plain,
% 53.94/34.52 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(monotonicity,[status(thm)],[43])).
% 53.94/34.52 tff(454,plain,
% 53.94/34.52 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 53.94/34.52 inference(symmetry,[status(thm)],[453])).
% 53.94/34.52 tff(455,plain,
% 53.94/34.52 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[398, 454])).
% 53.94/34.52 tff(456,plain,
% 53.94/34.52 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(457,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[456])).
% 53.94/34.52 tff(458,plain,
% 53.94/34.52 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(459,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[458])).
% 53.94/34.52 tff(460,plain,
% 53.94/34.52 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(461,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[460])).
% 53.94/34.52 tff(462,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(transitivity,[status(thm)],[461, 459])).
% 53.94/34.52 tff(463,plain,
% 53.94/34.52 (^[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, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(464,plain,
% 53.94/34.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[463])).
% 53.94/34.52 tff(465,plain,
% 53.94/34.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(466,plain,
% 53.94/34.52 (^[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, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(467,plain,
% 53.94/34.52 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[466])).
% 53.94/34.52 tff(468,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_filter_2')).
% 53.94/34.52 tff(469,plain,
% 53.94/34.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[468, 467])).
% 53.94/34.52 tff(470,plain,
% 53.94/34.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[469, 465])).
% 53.94/34.52 tff(471,plain,(
% 53.94/34.52 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(skolemize,[status(sab)],[470])).
% 53.94/34.52 tff(472,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[471, 464])).
% 53.94/34.52 tff(473,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[472, 462])).
% 53.94/34.52 tff(474,plain,
% 53.94/34.52 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[473, 457])).
% 53.94/34.52 tff(475,plain,
% 53.94/34.52 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(476,plain,
% 53.94/34.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 53.94/34.52 inference(quant_inst,[status(thm)],[])).
% 53.94/34.52 tff(477,plain,
% 53.94/34.52 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[476, 475])).
% 53.94/34.52 tff(478,plain,
% 53.94/34.52 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[477, 235, 234, 35, 474])).
% 53.94/34.52 tff(479,plain,
% 53.94/34.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(480,plain,
% 53.94/34.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.94/34.52 inference(quant_inst,[status(thm)],[])).
% 53.94/34.52 tff(481,plain,
% 53.94/34.52 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(modus_ponens,[status(thm)],[480, 479])).
% 53.94/34.52 tff(482,plain,
% 53.94/34.52 ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[481, 478])).
% 53.94/34.52 tff(483,plain,
% 53.94/34.52 (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.94/34.52 inference(unit_resolution,[status(thm)],[482, 455])).
% 53.94/34.52 tff(484,plain,
% 53.94/34.52 (tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(symmetry,[status(thm)],[483])).
% 53.94/34.52 tff(485,plain,
% 53.94/34.52 (tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.94/34.52 inference(transitivity,[status(thm)],[484, 452])).
% 53.94/34.52 tff(486,plain,
% 53.94/34.52 (m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0) <=> m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 53.94/34.52 inference(monotonicity,[status(thm)],[485])).
% 53.94/34.52 tff(487,plain,
% 53.94/34.52 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) <=> m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 53.94/34.52 inference(symmetry,[status(thm)],[486])).
% 53.94/34.52 tff(488,plain,
% 53.94/34.52 (^[A: $i, B: $i] : refl((m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(489,plain,
% 53.94/34.52 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[488])).
% 53.94/34.52 tff(490,plain,
% 53.94/34.52 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 53.94/34.52 inference(bind,[status(th)],[])).
% 53.94/34.52 tff(491,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.52 inference(quant_intro,[status(thm)],[490])).
% 53.94/34.52 tff(492,plain,
% 53.94/34.52 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 53.94/34.52 inference(rewrite,[status(thm)],[])).
% 53.94/34.52 tff(493,plain,
% 53.94/34.52 (^[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_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))))),
% 53.94/34.53 inference(bind,[status(th)],[])).
% 53.94/34.53 tff(494,plain,
% 53.94/34.53 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 53.94/34.53 inference(quant_intro,[status(thm)],[493])).
% 53.94/34.53 tff(495,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k14_filter_2')).
% 53.94/34.53 tff(496,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[495, 494])).
% 53.94/34.53 tff(497,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[496, 492])).
% 53.94/34.53 tff(498,plain,(
% 53.94/34.53 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 53.94/34.53 inference(skolemize,[status(sab)],[497])).
% 53.94/34.53 tff(499,plain,
% 53.94/34.53 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[498, 491])).
% 53.94/34.53 tff(500,plain,
% 53.94/34.53 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[499, 489])).
% 53.94/34.53 tff(501,plain,
% 53.94/34.53 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 53.94/34.53 inference(rewrite,[status(thm)],[])).
% 53.94/34.53 tff(502,plain,
% 53.94/34.53 ((m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 53.94/34.53 inference(rewrite,[status(thm)],[])).
% 53.94/34.53 tff(503,plain,
% 53.94/34.53 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))))),
% 53.94/34.53 inference(monotonicity,[status(thm)],[502])).
% 53.94/34.53 tff(504,plain,
% 53.94/34.53 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 53.94/34.53 inference(transitivity,[status(thm)],[503, 501])).
% 53.94/34.53 tff(505,plain,
% 53.94/34.53 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 53.94/34.53 inference(quant_inst,[status(thm)],[])).
% 53.94/34.53 tff(506,plain,
% 53.94/34.53 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[505, 504])).
% 53.94/34.53 tff(507,plain,
% 53.94/34.53 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 53.94/34.53 inference(unit_resolution,[status(thm)],[506, 235, 234, 35, 500])).
% 53.94/34.53 tff(508,plain,
% 53.94/34.53 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 53.94/34.53 inference(unit_resolution,[status(thm)],[507, 430])).
% 53.94/34.53 tff(509,plain,
% 53.94/34.53 (m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[508, 487])).
% 53.94/34.53 tff(510,plain,
% 53.94/34.53 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 53.94/34.53 inference(bind,[status(th)],[])).
% 53.94/34.53 tff(511,plain,
% 53.94/34.53 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.94/34.53 inference(quant_intro,[status(thm)],[510])).
% 53.94/34.53 tff(512,plain,
% 53.94/34.53 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 53.94/34.53 inference(bind,[status(th)],[])).
% 53.94/34.53 tff(513,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.94/34.53 inference(quant_intro,[status(thm)],[512])).
% 53.94/34.53 tff(514,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 53.94/34.53 inference(rewrite,[status(thm)],[])).
% 53.94/34.53 tff(515,plain,
% 53.94/34.53 (^[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)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 53.94/34.53 inference(bind,[status(th)],[])).
% 53.94/34.53 tff(516,plain,
% 53.94/34.53 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 53.94/34.53 inference(quant_intro,[status(thm)],[515])).
% 53.94/34.53 tff(517,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 53.94/34.53 tff(518,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[517, 516])).
% 53.94/34.53 tff(519,plain,
% 53.94/34.53 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[518, 514])).
% 53.94/34.53 tff(520,plain,(
% 53.94/34.53 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 53.94/34.53 inference(skolemize,[status(sab)],[519])).
% 53.94/34.53 tff(521,plain,
% 53.94/34.53 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[520, 513])).
% 53.94/34.53 tff(522,plain,
% 53.94/34.53 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 53.94/34.53 inference(modus_ponens,[status(thm)],[521, 511])).
% 53.94/34.53 tff(523,plain,
% 53.94/34.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.96/34.53 inference(rewrite,[status(thm)],[])).
% 53.96/34.53 tff(524,plain,
% 53.96/34.53 ((v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.96/34.53 inference(rewrite,[status(thm)],[])).
% 53.96/34.53 tff(525,plain,
% 53.96/34.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.96/34.53 inference(monotonicity,[status(thm)],[524])).
% 53.96/34.53 tff(526,plain,
% 53.96/34.53 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.96/34.53 inference(transitivity,[status(thm)],[525, 523])).
% 53.96/34.53 tff(527,plain,
% 53.96/34.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 53.96/34.53 inference(quant_inst,[status(thm)],[])).
% 53.96/34.53 tff(528,plain,
% 53.96/34.53 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[527, 526])).
% 53.96/34.53 tff(529,plain,
% 53.96/34.53 (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.96/34.53 inference(unit_resolution,[status(thm)],[528, 235, 234, 35, 522, 509])).
% 53.96/34.53 tff(530,plain,
% 53.96/34.53 (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.96/34.53 inference(transitivity,[status(thm)],[529, 427])).
% 53.96/34.53 tff(531,plain,
% 53.96/34.53 (v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)) <=> v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.96/34.53 inference(monotonicity,[status(thm)],[530, 39])).
% 53.96/34.53 tff(532,plain,
% 53.96/34.53 (v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 53.96/34.53 inference(symmetry,[status(thm)],[531])).
% 53.96/34.53 tff(533,plain,
% 53.96/34.53 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.96/34.53 inference(tautology,[status(thm)],[])).
% 53.96/34.53 tff(534,plain,
% 53.96/34.53 (v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 53.96/34.53 inference(unit_resolution,[status(thm)],[533, 369])).
% 53.96/34.53 tff(535,plain,
% 53.96/34.53 (v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[534, 532])).
% 53.96/34.53 tff(536,plain,
% 53.96/34.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))),
% 53.96/34.53 inference(bind,[status(th)],[])).
% 53.96/34.53 tff(537,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(quant_intro,[status(thm)],[536])).
% 53.96/34.53 tff(538,plain,
% 53.96/34.53 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 53.96/34.53 inference(bind,[status(th)],[])).
% 53.96/34.53 tff(539,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(quant_intro,[status(thm)],[538])).
% 53.96/34.53 tff(540,plain,
% 53.96/34.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 53.96/34.53 inference(bind,[status(th)],[])).
% 53.96/34.53 tff(541,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(quant_intro,[status(thm)],[540])).
% 53.96/34.53 tff(542,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(transitivity,[status(thm)],[541, 539])).
% 53.96/34.53 tff(543,plain,
% 53.96/34.53 (^[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_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))))),
% 53.96/34.53 inference(bind,[status(th)],[])).
% 53.96/34.53 tff(544,plain,
% 53.96/34.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(quant_intro,[status(thm)],[543])).
% 53.96/34.53 tff(545,plain,
% 53.96/34.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(rewrite,[status(thm)],[])).
% 53.96/34.53 tff(546,plain,
% 53.96/34.53 (^[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) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))))),
% 53.96/34.53 inference(bind,[status(th)],[])).
% 53.96/34.53 tff(547,plain,
% 53.96/34.53 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(quant_intro,[status(thm)],[546])).
% 53.96/34.53 tff(548,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_filter_2')).
% 53.96/34.53 tff(549,plain,
% 53.96/34.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[548, 547])).
% 53.96/34.53 tff(550,plain,
% 53.96/34.53 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[549, 545])).
% 53.96/34.53 tff(551,plain,(
% 53.96/34.53 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(skolemize,[status(sab)],[550])).
% 53.96/34.53 tff(552,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[551, 544])).
% 53.96/34.53 tff(553,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[552, 542])).
% 53.96/34.53 tff(554,plain,
% 53.96/34.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[553, 537])).
% 53.96/34.53 tff(555,plain,
% 53.96/34.53 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 53.96/34.53 inference(rewrite,[status(thm)],[])).
% 53.96/34.53 tff(556,plain,
% 53.96/34.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 53.96/34.53 inference(quant_inst,[status(thm)],[])).
% 53.96/34.53 tff(557,plain,
% 53.96/34.53 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 53.96/34.53 inference(modus_ponens,[status(thm)],[556, 555])).
% 53.96/34.53 tff(558,plain,
% 53.96/34.53 (![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 53.96/34.53 inference(unit_resolution,[status(thm)],[557, 235, 234, 35, 554])).
% 53.96/34.53 tff(559,plain,
% 53.96/34.53 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 53.96/34.53 inference(rewrite,[status(thm)],[])).
% 53.96/34.53 tff(560,plain,
% 53.96/34.53 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 53.96/34.54 inference(quant_inst,[status(thm)],[])).
% 53.96/34.54 tff(561,plain,
% 53.96/34.54 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 53.96/34.54 inference(modus_ponens,[status(thm)],[560, 559])).
% 53.96/34.54 tff(562,plain,
% 53.96/34.54 (r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 53.96/34.54 inference(unit_resolution,[status(thm)],[561, 558, 509])).
% 53.96/34.54 tff(563,plain,
% 53.96/34.54 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | ((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 53.96/34.54 inference(tautology,[status(thm)],[])).
% 53.96/34.54 tff(564,plain,
% 53.96/34.54 ((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 53.96/34.54 inference(unit_resolution,[status(thm)],[563, 369])).
% 53.96/34.54 tff(565,plain,
% 53.96/34.54 (^[D: $i] : refl(((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))),
% 53.96/34.54 inference(bind,[status(th)],[])).
% 53.96/34.54 tff(566,plain,
% 53.96/34.54 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))) <=> ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 53.96/34.54 inference(quant_intro,[status(thm)],[565])).
% 53.96/34.54 tff(567,plain,
% 53.96/34.54 (^[D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) <=> (~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D))))), rewrite((r2_hidden(B!1, D) & (~r2_hidden(C!2, D))) <=> (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))), ((((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))), rewrite(((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))), ((((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))), ((r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))) <=> (r2_filter_2(A!0, D) & ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), rewrite((r2_filter_2(A!0, D) & ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))) <=> (~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))), ((r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))) <=> (~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))), ((~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))) <=> (~(~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))))), rewrite((~(~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))) <=> ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), ((~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))) <=> ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))), (((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))), rewrite(((~m2_filter_2(D, A!0)) | ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), (((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))),
% 53.96/34.54 inference(bind,[status(th)],[])).
% 53.96/34.54 tff(568,plain,
% 53.96/34.54 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 53.96/34.54 inference(quant_intro,[status(thm)],[567])).
% 53.96/34.54 tff(569,plain,
% 53.96/34.54 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))),
% 53.96/34.54 inference(and_elim,[status(thm)],[34])).
% 53.96/34.54 tff(570,plain,
% 53.96/34.54 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 53.96/34.54 inference(modus_ponens,[status(thm)],[569, 568])).
% 53.96/34.54 tff(571,plain,
% 53.96/34.54 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 53.96/34.54 inference(modus_ponens,[status(thm)],[570, 566])).
% 53.96/34.54 tff(572,plain,
% 53.96/34.54 (((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.96/34.54 inference(rewrite,[status(thm)],[])).
% 53.96/34.54 tff(573,plain,
% 53.96/34.54 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 53.96/34.54 inference(quant_inst,[status(thm)],[])).
% 53.96/34.54 tff(574,plain,
% 53.96/34.54 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 53.96/34.54 inference(modus_ponens,[status(thm)],[573, 572])).
% 53.96/34.54 tff(575,plain,
% 53.96/34.54 (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 53.96/34.54 inference(unit_resolution,[status(thm)],[574, 571, 564, 509])).
% 53.96/34.54 tff(576,plain,
% 53.96/34.54 ((~(r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 54.04/34.63 inference(tautology,[status(thm)],[])).
% 54.04/34.63 tff(577,plain,
% 54.04/34.63 ((~(r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 54.04/34.63 inference(unit_resolution,[status(thm)],[576, 575])).
% 54.04/34.63 tff(578,plain,
% 54.04/34.63 (~v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 54.04/34.63 inference(unit_resolution,[status(thm)],[577, 562])).
% 54.04/34.63 tff(579,plain,
% 54.04/34.63 ($false),
% 54.04/34.63 inference(unit_resolution,[status(thm)],[578, 535])).
% 54.04/34.63 % SZS output end Proof
%------------------------------------------------------------------------------