%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT306+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:16 AM UTC 2025
% Result : Theorem 0.39s 0.58s
% Output : Proof 0.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : LAT306+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n015.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:09:26 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.39/0.58 % SZS status Theorem
% 0.39/0.58 % SZS output start Proof
% 0.39/0.58 tff(m1_subset_1_type, type, (
% 0.39/0.58 m1_subset_1: ( $i * $i ) > $o)).
% 0.39/0.58 tff(u1_struct_0_type, type, (
% 0.39/0.58 u1_struct_0: $i > $i)).
% 0.39/0.58 tff(g3_lattices_type, type, (
% 0.39/0.58 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.39/0.58 tff(u2_lattices_type, type, (
% 0.39/0.58 u2_lattices: $i > $i)).
% 0.39/0.58 tff(tptp_fun_A_0_type, type, (
% 0.39/0.58 tptp_fun_A_0: $i)).
% 0.39/0.58 tff(u1_lattices_type, type, (
% 0.39/0.58 u1_lattices: $i > $i)).
% 0.39/0.58 tff(k5_lattices_type, type, (
% 0.39/0.58 k5_lattices: $i > $i)).
% 0.39/0.58 tff(k1_lattice2_type, type, (
% 0.39/0.58 k1_lattice2: $i > $i)).
% 0.39/0.58 tff(l3_lattices_type, type, (
% 0.39/0.58 l3_lattices: $i > $o)).
% 0.39/0.58 tff(v10_lattices_type, type, (
% 0.39/0.58 v10_lattices: $i > $o)).
% 0.39/0.58 tff(v3_struct_0_type, type, (
% 0.39/0.58 v3_struct_0: $i > $o)).
% 0.39/0.58 tff(v14_lattices_type, type, (
% 0.39/0.58 v14_lattices: $i > $o)).
% 0.39/0.58 tff(r1_filter_2_type, type, (
% 0.39/0.58 r1_filter_2: ( $i * $i * $i ) > $o)).
% 0.39/0.58 tff(k18_filter_2_type, type, (
% 0.39/0.58 k18_filter_2: ( $i * $i ) > $i)).
% 0.39/0.58 tff(k6_lattices_type, type, (
% 0.39/0.58 k6_lattices: $i > $i)).
% 0.39/0.58 tff(k17_filter_2_type, type, (
% 0.39/0.58 k17_filter_2: $i > $i)).
% 0.39/0.58 tff(l1_lattices_type, type, (
% 0.39/0.58 l1_lattices: $i > $o)).
% 0.39/0.58 tff(l2_lattices_type, type, (
% 0.39/0.58 l2_lattices: $i > $o)).
% 0.39/0.58 tff(v3_lattices_type, type, (
% 0.39/0.58 v3_lattices: $i > $o)).
% 0.39/0.58 tff(m1_relset_1_type, type, (
% 0.39/0.58 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.39/0.58 tff(k2_zfmisc_1_type, type, (
% 0.39/0.58 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.39/0.58 tff(m2_relset_1_type, type, (
% 0.39/0.58 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.39/0.58 tff(v1_funct_2_type, type, (
% 0.39/0.58 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.39/0.58 tff(v1_funct_1_type, type, (
% 0.39/0.58 v1_funct_1: $i > $o)).
% 0.39/0.58 tff(v9_lattices_type, type, (
% 0.39/0.58 v9_lattices: $i > $o)).
% 0.39/0.58 tff(v8_lattices_type, type, (
% 0.39/0.58 v8_lattices: $i > $o)).
% 0.39/0.58 tff(v7_lattices_type, type, (
% 0.39/0.58 v7_lattices: $i > $o)).
% 0.39/0.58 tff(v6_lattices_type, type, (
% 0.39/0.58 v6_lattices: $i > $o)).
% 0.39/0.58 tff(v5_lattices_type, type, (
% 0.39/0.58 v5_lattices: $i > $o)).
% 0.39/0.58 tff(v4_lattices_type, type, (
% 0.39/0.58 v4_lattices: $i > $o)).
% 0.39/0.58 tff(k2_filter_0_type, type, (
% 0.39/0.58 k2_filter_0: ( $i * $i ) > $i)).
% 0.39/0.58 tff(k2_filter_2_type, type, (
% 0.39/0.58 k2_filter_2: ( $i * $i ) > $i)).
% 0.39/0.58 tff(k1_filter_0_type, type, (
% 0.39/0.58 k1_filter_0: $i > $i)).
% 0.39/0.58 tff(v13_lattices_type, type, (
% 0.39/0.58 v13_lattices: $i > $o)).
% 0.39/0.58 tff(k5_filter_2_type, type, (
% 0.39/0.58 k5_filter_2: ( $i * $i ) > $i)).
% 0.39/0.58 tff(k1_zfmisc_1_type, type, (
% 0.39/0.58 k1_zfmisc_1: $i > $i)).
% 0.39/0.58 tff(m2_lattice4_type, type, (
% 0.39/0.58 m2_lattice4: ( $i * $i ) > $o)).
% 0.39/0.58 tff(v1_xboole_0_type, type, (
% 0.39/0.58 v1_xboole_0: $i > $o)).
% 0.39/0.58 tff(m2_filter_2_type, type, (
% 0.39/0.58 m2_filter_2: ( $i * $i ) > $o)).
% 0.39/0.58 tff(l1_struct_0_type, type, (
% 0.39/0.58 l1_struct_0: $i > $o)).
% 0.39/0.58 tff(m1_filter_0_type, type, (
% 0.39/0.58 m1_filter_0: ( $i * $i ) > $o)).
% 0.39/0.58 tff(1,plain,
% 0.39/0.58 (^[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)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(2,plain,
% 0.39/0.58 (![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))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[1])).
% 0.39/0.58 tff(3,plain,
% 0.39/0.58 (![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))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(4,plain,
% 0.39/0.58 (^[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)))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(5,plain,
% 0.39/0.58 (![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))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[4])).
% 0.39/0.58 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')).
% 0.39/0.58 tff(7,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.39/0.58 tff(8,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.39/0.58 tff(9,plain,(
% 0.39/0.58 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.39/0.58 inference(skolemize,[status(sab)],[8])).
% 0.39/0.58 tff(10,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.39/0.58 tff(11,plain,
% 0.39/0.58 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))) <=> (~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(12,plain,
% 0.39/0.58 ((~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))) <=> (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(13,plain,
% 0.39/0.58 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A)))))) <=> (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(14,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t32_filter_2')).
% 0.39/0.58 tff(15,plain,
% 0.39/0.58 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.39/0.58 tff(16,plain,
% 0.39/0.58 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.39/0.58 tff(17,plain,
% 0.39/0.58 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.39/0.58 tff(18,plain,
% 0.39/0.58 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.39/0.58 tff(19,plain,(
% 0.39/0.58 ~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.39/0.58 inference(skolemize,[status(sab)],[18])).
% 0.39/0.58 tff(20,plain,
% 0.39/0.58 (~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.39/0.58 tff(21,plain,
% 0.39/0.58 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 0.39/0.58 inference(or_elim,[status(thm)],[20])).
% 0.39/0.58 tff(22,plain,
% 0.39/0.58 (l3_lattices(A!0)),
% 0.39/0.58 inference(and_elim,[status(thm)],[21])).
% 0.39/0.58 tff(23,plain,
% 0.39/0.58 (((~![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))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(24,plain,
% 0.39/0.58 ((~![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))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(25,plain,
% 0.39/0.58 ((~![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)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.39/0.58 tff(26,plain,
% 0.39/0.58 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[25, 22, 10])).
% 0.39/0.58 tff(27,plain,
% 0.39/0.58 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.39/0.58 inference(symmetry,[status(thm)],[26])).
% 0.39/0.58 tff(28,plain,
% 0.39/0.58 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[27])).
% 0.39/0.58 tff(29,plain,
% 0.39/0.58 (k5_lattices(k1_lattice2(A!0)) = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.58 inference(symmetry,[status(thm)],[28])).
% 0.39/0.58 tff(30,plain,
% 0.39/0.58 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.58 inference(monotonicity,[status(thm)],[29])).
% 0.39/0.58 tff(31,plain,
% 0.39/0.58 (m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.58 inference(symmetry,[status(thm)],[30])).
% 0.39/0.58 tff(32,plain,
% 0.39/0.58 (^[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)))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(33,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[32])).
% 0.39/0.58 tff(34,plain,
% 0.39/0.58 (![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))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(35,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')).
% 0.39/0.58 tff(36,plain,
% 0.39/0.58 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[35, 34])).
% 0.39/0.58 tff(37,plain,(
% 0.39/0.58 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.39/0.58 inference(skolemize,[status(sab)],[36])).
% 0.39/0.58 tff(38,plain,
% 0.39/0.58 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[37, 33])).
% 0.39/0.58 tff(39,plain,
% 0.39/0.58 ((~![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)))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(40,plain,
% 0.39/0.58 (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))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.39/0.58 tff(41,plain,
% 0.39/0.58 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(42,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[41])).
% 0.39/0.58 tff(43,plain,
% 0.39/0.58 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(44,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[43])).
% 0.39/0.58 tff(45,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(46,plain,
% 0.39/0.58 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.39/0.58 inference(bind,[status(th)],[])).
% 0.39/0.58 tff(47,plain,
% 0.39/0.58 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.39/0.58 inference(quant_intro,[status(thm)],[46])).
% 0.39/0.58 tff(48,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.39/0.58 tff(49,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.39/0.58 tff(50,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[49, 45])).
% 0.39/0.58 tff(51,plain,(
% 0.39/0.58 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.39/0.58 inference(skolemize,[status(sab)],[50])).
% 0.39/0.58 tff(52,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[51, 44])).
% 0.39/0.58 tff(53,plain,
% 0.39/0.58 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[52, 42])).
% 0.39/0.58 tff(54,plain,
% 0.39/0.58 (((~![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)))))),
% 0.39/0.58 inference(rewrite,[status(thm)],[])).
% 0.39/0.58 tff(55,plain,
% 0.39/0.58 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.39/0.58 inference(quant_inst,[status(thm)],[])).
% 0.39/0.58 tff(56,plain,
% 0.39/0.58 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.39/0.58 inference(modus_ponens,[status(thm)],[55, 54])).
% 0.39/0.58 tff(57,plain,
% 0.39/0.58 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[56, 22, 53])).
% 0.39/0.58 tff(58,plain,
% 0.39/0.58 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.39/0.58 inference(tautology,[status(thm)],[])).
% 0.39/0.58 tff(59,plain,
% 0.39/0.58 (l1_lattices(A!0)),
% 0.39/0.58 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.39/0.58 tff(60,plain,
% 0.39/0.58 (^[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)))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(61,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[60])).
% 0.39/0.59 tff(62,plain,
% 0.39/0.59 (^[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)))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(63,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[62])).
% 0.39/0.59 tff(64,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(65,plain,
% 0.39/0.59 (^[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))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(66,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[65])).
% 0.39/0.59 tff(67,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')).
% 0.39/0.59 tff(68,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.39/0.59 tff(69,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[68, 64])).
% 0.39/0.59 tff(70,plain,(
% 0.39/0.59 ![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))))),
% 0.39/0.59 inference(skolemize,[status(sab)],[69])).
% 0.39/0.59 tff(71,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[70, 63])).
% 0.39/0.59 tff(72,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[71, 61])).
% 0.39/0.59 tff(73,plain,
% 0.39/0.59 (((~![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))))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(74,plain,
% 0.39/0.59 ((~![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))))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(75,plain,
% 0.39/0.59 ((~![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)))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[74, 73])).
% 0.39/0.59 tff(76,plain,
% 0.39/0.59 ((~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)))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[75, 72])).
% 0.39/0.59 tff(77,plain,
% 0.39/0.59 (~((~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))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[76, 59])).
% 0.39/0.59 tff(78,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(79,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.39/0.59 tff(80,plain,
% 0.39/0.59 ((~(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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(81,plain,
% 0.39/0.59 ((~(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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.39/0.59 tff(82,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[81, 40])).
% 0.39/0.59 tff(83,plain,
% 0.39/0.59 ((~![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)))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(84,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[83, 38])).
% 0.39/0.59 tff(85,plain,
% 0.39/0.59 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(86,plain,
% 0.39/0.59 (l2_lattices(A!0)),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[85, 57])).
% 0.39/0.59 tff(87,plain,
% 0.39/0.59 (^[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)))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(88,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[87])).
% 0.39/0.59 tff(89,plain,
% 0.39/0.59 (^[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)))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(90,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[89])).
% 0.39/0.59 tff(91,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(92,plain,
% 0.39/0.59 (^[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))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(93,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[92])).
% 0.39/0.59 tff(94,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')).
% 0.39/0.59 tff(95,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.39/0.59 tff(96,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.39/0.59 tff(97,plain,(
% 0.39/0.59 ![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))))),
% 0.39/0.59 inference(skolemize,[status(sab)],[96])).
% 0.39/0.59 tff(98,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.39/0.59 tff(99,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[98, 88])).
% 0.39/0.59 tff(100,plain,
% 0.39/0.59 (((~![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))))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(101,plain,
% 0.39/0.59 ((~![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))))))),
% 0.39/0.59 inference(quant_inst,[status(thm)],[])).
% 0.39/0.59 tff(102,plain,
% 0.39/0.59 ((~![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)))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[101, 100])).
% 0.39/0.59 tff(103,plain,
% 0.39/0.59 ((~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)))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.39/0.59 tff(104,plain,
% 0.39/0.59 (~((~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))))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[103, 86])).
% 0.39/0.59 tff(105,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(106,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[105, 104])).
% 0.39/0.59 tff(107,plain,
% 0.39/0.59 ((~(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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(108,plain,
% 0.39/0.59 ((~(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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.39/0.59 tff(109,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[108, 84])).
% 0.39/0.59 tff(110,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(111,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[110, 104])).
% 0.39/0.59 tff(112,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(113,plain,
% 0.39/0.59 (v1_funct_1(u2_lattices(A!0))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[112, 104])).
% 0.39/0.59 tff(114,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(115,plain,
% 0.39/0.59 (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))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[114, 77])).
% 0.39/0.59 tff(116,plain,
% 0.39/0.59 (((~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))),
% 0.39/0.59 inference(tautology,[status(thm)],[])).
% 0.39/0.59 tff(117,plain,
% 0.39/0.59 (v1_funct_1(u1_lattices(A!0))),
% 0.39/0.59 inference(unit_resolution,[status(thm)],[116, 77])).
% 0.39/0.59 tff(118,plain,
% 0.39/0.59 (^[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)))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(119,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[118])).
% 0.39/0.59 tff(120,plain,
% 0.39/0.59 (^[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))))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(121,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[120])).
% 0.39/0.59 tff(122,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(rewrite,[status(thm)],[])).
% 0.39/0.59 tff(123,plain,
% 0.39/0.59 (^[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))))))),
% 0.39/0.59 inference(bind,[status(th)],[])).
% 0.39/0.59 tff(124,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(quant_intro,[status(thm)],[123])).
% 0.39/0.59 tff(125,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')).
% 0.39/0.59 tff(126,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.39/0.59 tff(127,plain,
% 0.39/0.59 (![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))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.39/0.59 tff(128,plain,(
% 0.39/0.59 ![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))))),
% 0.39/0.59 inference(skolemize,[status(sab)],[127])).
% 0.39/0.59 tff(129,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.39/0.59 tff(130,plain,
% 0.39/0.59 (![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))))))),
% 0.39/0.59 inference(modus_ponens,[status(thm)],[129, 119])).
% 0.39/0.59 tff(131,plain,
% 0.39/0.59 (((~![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(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))) | (~((~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(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))) | (~((~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)))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(132,plain,
% 0.39/0.60 (((~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(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))) | (~((~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)))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(133,plain,
% 0.39/0.60 ((~((~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))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(134,plain,
% 0.39/0.60 (((~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)))))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[133])).
% 0.39/0.60 tff(135,plain,
% 0.39/0.60 (((~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(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))) | (~((~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)))))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[134, 132])).
% 0.39/0.60 tff(136,plain,
% 0.39/0.60 (((~![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(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))) | (~((~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))))))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[135])).
% 0.39/0.60 tff(137,plain,
% 0.39/0.60 (((~![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(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))) | (~((~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)))))))),
% 0.39/0.60 inference(transitivity,[status(thm)],[136, 131])).
% 0.39/0.60 tff(138,plain,
% 0.39/0.60 ((~![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)))))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(139,plain,
% 0.39/0.60 ((~![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(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))) | (~((~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))))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.39/0.60 tff(140,plain,
% 0.39/0.60 ((~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(u1_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))))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[139, 130, 117, 115, 113, 111])).
% 0.39/0.60 tff(141,plain,
% 0.39/0.60 (~((~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)))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[140, 109, 82])).
% 0.39/0.60 tff(142,plain,
% 0.39/0.60 (((~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)))),
% 0.39/0.60 inference(tautology,[status(thm)],[])).
% 0.39/0.60 tff(143,plain,
% 0.39/0.60 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.39/0.60 tff(144,plain,
% 0.39/0.60 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(145,plain,
% 0.39/0.60 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(146,plain,
% 0.39/0.60 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.39/0.60 tff(147,plain,
% 0.39/0.60 (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[146, 53, 143])).
% 0.39/0.60 tff(148,plain,
% 0.39/0.60 (((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.60 inference(tautology,[status(thm)],[])).
% 0.39/0.60 tff(149,plain,
% 0.39/0.60 (l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.39/0.60 tff(150,plain,
% 0.39/0.60 (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))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[27])).
% 0.39/0.60 tff(151,plain,
% 0.39/0.60 (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)))),
% 0.39/0.60 inference(symmetry,[status(thm)],[150])).
% 0.39/0.60 tff(152,plain,
% 0.39/0.60 ((~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))))),
% 0.39/0.60 inference(monotonicity,[status(thm)],[151])).
% 0.39/0.60 tff(153,plain,
% 0.39/0.60 (^[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)))))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(154,plain,
% 0.39/0.60 (![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))))))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[153])).
% 0.39/0.60 tff(155,plain,
% 0.39/0.60 (^[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))))))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(156,plain,
% 0.39/0.60 (![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))))))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[155])).
% 0.39/0.60 tff(157,plain,
% 0.39/0.60 (![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))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(158,plain,
% 0.39/0.60 (^[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))))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(159,plain,
% 0.39/0.60 (![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))))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[158])).
% 0.39/0.60 tff(160,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')).
% 0.39/0.60 tff(161,plain,
% 0.39/0.60 (![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))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.39/0.60 tff(162,plain,
% 0.39/0.60 (![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))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[161, 157])).
% 0.39/0.60 tff(163,plain,(
% 0.39/0.60 ![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))))),
% 0.39/0.60 inference(skolemize,[status(sab)],[162])).
% 0.39/0.60 tff(164,plain,
% 0.39/0.60 (![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))))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[163, 156])).
% 0.39/0.60 tff(165,plain,
% 0.39/0.60 (![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))))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[164, 154])).
% 0.39/0.60 tff(166,plain,
% 0.39/0.60 (v10_lattices(A!0)),
% 0.39/0.60 inference(and_elim,[status(thm)],[21])).
% 0.39/0.60 tff(167,plain,
% 0.39/0.60 (~v3_struct_0(A!0)),
% 0.39/0.60 inference(and_elim,[status(thm)],[21])).
% 0.39/0.60 tff(168,plain,
% 0.39/0.60 (((~![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))))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(169,plain,
% 0.39/0.60 ((~![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))))))),
% 0.39/0.60 inference(quant_inst,[status(thm)],[])).
% 0.39/0.60 tff(170,plain,
% 0.39/0.60 ((~![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)))))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[169, 168])).
% 0.39/0.60 tff(171,plain,
% 0.39/0.60 (~(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))))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[170, 167, 166, 22, 165])).
% 0.39/0.60 tff(172,plain,
% 0.39/0.60 ((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)))),
% 0.39/0.60 inference(tautology,[status(thm)],[])).
% 0.39/0.60 tff(173,plain,
% 0.39/0.60 (~v3_struct_0(k1_lattice2(A!0))),
% 0.39/0.60 inference(unit_resolution,[status(thm)],[172, 171])).
% 0.39/0.60 tff(174,plain,
% 0.39/0.60 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[173, 152])).
% 0.39/0.60 tff(175,plain,
% 0.39/0.60 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(176,plain,
% 0.39/0.60 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[175])).
% 0.39/0.60 tff(177,plain,
% 0.39/0.60 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(178,plain,
% 0.39/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[177])).
% 0.39/0.60 tff(179,plain,
% 0.39/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(180,plain,
% 0.39/0.60 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))),
% 0.39/0.60 inference(bind,[status(th)],[])).
% 0.39/0.60 tff(181,plain,
% 0.39/0.60 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.39/0.60 inference(quant_intro,[status(thm)],[180])).
% 0.39/0.60 tff(182,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattices')).
% 0.39/0.60 tff(183,plain,
% 0.39/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.39/0.60 tff(184,plain,
% 0.39/0.60 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[183, 179])).
% 0.39/0.60 tff(185,plain,(
% 0.39/0.60 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.39/0.60 inference(skolemize,[status(sab)],[184])).
% 0.39/0.60 tff(186,plain,
% 0.39/0.60 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[185, 178])).
% 0.39/0.60 tff(187,plain,
% 0.39/0.60 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.39/0.60 inference(modus_ponens,[status(thm)],[186, 176])).
% 0.39/0.60 tff(188,plain,
% 0.39/0.60 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.60 inference(rewrite,[status(thm)],[])).
% 0.39/0.60 tff(189,plain,
% 0.39/0.60 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(190,plain,
% 0.39/0.61 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[189, 188])).
% 0.39/0.61 tff(191,plain,
% 0.39/0.61 (m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[190, 187, 174])).
% 0.39/0.61 tff(192,plain,
% 0.39/0.61 (m1_subset_1(k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[191, 149])).
% 0.39/0.61 tff(193,plain,
% 0.39/0.61 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[192, 31])).
% 0.39/0.61 tff(194,plain,
% 0.39/0.61 ((k18_filter_2(A!0, k6_lattices(A!0)) = k17_filter_2(A!0)) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.39/0.61 inference(commutativity,[status(thm)],[])).
% 0.39/0.61 tff(195,plain,
% 0.39/0.61 (^[A: $i] : refl((v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(196,plain,
% 0.39/0.61 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[195])).
% 0.39/0.61 tff(197,plain,
% 0.39/0.61 (^[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))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(198,plain,
% 0.39/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[197])).
% 0.39/0.61 tff(199,plain,
% 0.39/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(200,plain,
% 0.39/0.61 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(201,plain,
% 0.39/0.61 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[200])).
% 0.39/0.61 tff(202,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d8_filter_2')).
% 0.39/0.61 tff(203,plain,
% 0.39/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.39/0.61 tff(204,plain,
% 0.39/0.61 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.39/0.61 tff(205,plain,(
% 0.39/0.61 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.39/0.61 inference(skolemize,[status(sab)],[204])).
% 0.39/0.61 tff(206,plain,
% 0.39/0.61 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.39/0.61 tff(207,plain,
% 0.39/0.61 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[206, 196])).
% 0.39/0.61 tff(208,plain,
% 0.39/0.61 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(209,plain,
% 0.39/0.61 ((v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(210,plain,
% 0.39/0.61 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[209])).
% 0.39/0.61 tff(211,plain,
% 0.39/0.61 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.39/0.61 inference(transitivity,[status(thm)],[210, 208])).
% 0.39/0.61 tff(212,plain,
% 0.39/0.61 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(213,plain,
% 0.39/0.61 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.39/0.61 tff(214,plain,
% 0.39/0.61 (k17_filter_2(A!0) = u1_struct_0(A!0)),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[213, 167, 166, 22, 207])).
% 0.39/0.61 tff(215,plain,
% 0.39/0.61 (u1_struct_0(A!0) = k17_filter_2(A!0)),
% 0.39/0.61 inference(symmetry,[status(thm)],[214])).
% 0.39/0.61 tff(216,plain,
% 0.39/0.61 (((~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)))),
% 0.39/0.61 inference(tautology,[status(thm)],[])).
% 0.39/0.61 tff(217,plain,
% 0.39/0.61 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[216, 141])).
% 0.39/0.61 tff(218,plain,
% 0.39/0.61 (^[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))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(219,plain,
% 0.39/0.61 (![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)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[218])).
% 0.39/0.61 tff(220,plain,
% 0.39/0.61 (![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)))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(221,plain,
% 0.39/0.61 (^[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)))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(222,plain,
% 0.39/0.61 (![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)))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[221])).
% 0.39/0.61 tff(223,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')).
% 0.39/0.61 tff(224,plain,
% 0.39/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.39/0.61 tff(225,plain,
% 0.39/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.39/0.61 tff(226,plain,(
% 0.39/0.61 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.39/0.61 inference(skolemize,[status(sab)],[225])).
% 0.39/0.61 tff(227,plain,
% 0.39/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.39/0.61 tff(228,plain,
% 0.39/0.61 (((~![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))))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(229,plain,
% 0.39/0.61 (((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))))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(230,plain,
% 0.39/0.61 (((~![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)))))))),
% 0.39/0.61 inference(monotonicity,[status(thm)],[229])).
% 0.39/0.61 tff(231,plain,
% 0.39/0.61 (((~![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))))))),
% 0.39/0.61 inference(transitivity,[status(thm)],[230, 228])).
% 0.39/0.61 tff(232,plain,
% 0.39/0.61 ((~![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)))))),
% 0.39/0.61 inference(quant_inst,[status(thm)],[])).
% 0.39/0.61 tff(233,plain,
% 0.39/0.61 ((~![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)))))),
% 0.39/0.61 inference(modus_ponens,[status(thm)],[232, 231])).
% 0.39/0.61 tff(234,plain,
% 0.39/0.61 ((~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)))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[233, 227])).
% 0.39/0.61 tff(235,plain,
% 0.39/0.61 (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))))),
% 0.39/0.61 inference(unit_resolution,[status(thm)],[234, 143, 217])).
% 0.39/0.61 tff(236,plain,
% 0.39/0.61 (^[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)))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(237,plain,
% 0.39/0.61 (![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))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[236])).
% 0.39/0.61 tff(238,plain,
% 0.39/0.61 (^[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)))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(239,plain,
% 0.39/0.61 (![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))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[238])).
% 0.39/0.61 tff(240,plain,
% 0.39/0.61 (![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))))))),
% 0.39/0.61 inference(transitivity,[status(thm)],[239, 237])).
% 0.39/0.61 tff(241,plain,
% 0.39/0.61 (^[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))))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(242,plain,
% 0.39/0.61 (![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))))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[241])).
% 0.39/0.61 tff(243,plain,
% 0.39/0.61 (![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))))),
% 0.39/0.61 inference(rewrite,[status(thm)],[])).
% 0.39/0.61 tff(244,plain,
% 0.39/0.61 (^[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))))))),
% 0.39/0.61 inference(bind,[status(th)],[])).
% 0.39/0.61 tff(245,plain,
% 0.39/0.61 (![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))))),
% 0.39/0.61 inference(quant_intro,[status(thm)],[244])).
% 0.39/0.61 tff(246,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')).
% 0.39/0.61 tff(247,plain,
% 0.39/0.61 (![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))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.39/0.62 tff(248,plain,
% 0.39/0.62 (![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))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.39/0.62 tff(249,plain,(
% 0.39/0.62 ![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))))),
% 0.39/0.62 inference(skolemize,[status(sab)],[248])).
% 0.39/0.62 tff(250,plain,
% 0.39/0.62 (![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))))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.39/0.62 tff(251,plain,
% 0.39/0.62 (![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))))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[250, 240])).
% 0.39/0.62 tff(252,plain,
% 0.39/0.62 (((~![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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(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)) | ![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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(253,plain,
% 0.39/0.62 (((~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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(254,plain,
% 0.39/0.62 (((~![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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[253])).
% 0.39/0.62 tff(255,plain,
% 0.39/0.62 (((~![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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[254, 252])).
% 0.39/0.62 tff(256,plain,
% 0.39/0.62 ((~![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))))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(257,plain,
% 0.39/0.62 ((~![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))) | ![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[256, 255])).
% 0.39/0.62 tff(258,plain,
% 0.39/0.62 (![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))))) | (~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(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[257, 251, 117, 115, 113, 111])).
% 0.39/0.62 tff(259,plain,
% 0.39/0.62 (![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)))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[258, 109, 82])).
% 0.39/0.62 tff(260,plain,
% 0.39/0.62 (((~![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(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)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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(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)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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))))))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(261,plain,
% 0.39/0.62 ((~![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(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)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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))))))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(262,plain,
% 0.39/0.62 ((~![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(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)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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)))))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.39/0.62 tff(263,plain,
% 0.39/0.62 (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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))))))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[262, 259, 235])).
% 0.39/0.62 tff(264,plain,
% 0.39/0.62 (((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(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(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.62 inference(tautology,[status(thm)],[])).
% 0.39/0.62 tff(265,plain,
% 0.39/0.62 (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[264, 263])).
% 0.39/0.62 tff(266,plain,
% 0.39/0.62 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 0.39/0.62 inference(symmetry,[status(thm)],[265])).
% 0.39/0.62 tff(267,plain,
% 0.39/0.62 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[27])).
% 0.39/0.62 tff(268,plain,
% 0.39/0.62 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.62 inference(symmetry,[status(thm)],[267])).
% 0.39/0.62 tff(269,plain,
% 0.39/0.62 ((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))),
% 0.39/0.62 inference(tautology,[status(thm)],[])).
% 0.39/0.62 tff(270,plain,
% 0.39/0.62 (v10_lattices(k1_lattice2(A!0))),
% 0.39/0.62 inference(unit_resolution,[status(thm)],[269, 171])).
% 0.39/0.62 tff(271,plain,
% 0.39/0.62 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[270, 268])).
% 0.39/0.62 tff(272,plain,
% 0.39/0.62 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(273,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[272])).
% 0.39/0.62 tff(274,plain,
% 0.39/0.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(275,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[274])).
% 0.39/0.62 tff(276,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(277,plain,
% 0.39/0.62 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))))),
% 0.39/0.62 inference(bind,[status(th)],[])).
% 0.39/0.62 tff(278,plain,
% 0.39/0.62 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.39/0.62 inference(quant_intro,[status(thm)],[277])).
% 0.39/0.62 tff(279,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_filter_0')).
% 0.39/0.62 tff(280,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.39/0.62 tff(281,plain,
% 0.39/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[280, 276])).
% 0.39/0.62 tff(282,plain,(
% 0.39/0.62 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.39/0.62 inference(skolemize,[status(sab)],[281])).
% 0.39/0.62 tff(283,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[282, 275])).
% 0.39/0.62 tff(284,plain,
% 0.39/0.62 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[283, 273])).
% 0.39/0.62 tff(285,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(286,plain,
% 0.39/0.62 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_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))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.62 inference(rewrite,[status(thm)],[])).
% 0.39/0.62 tff(287,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_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)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.39/0.62 inference(monotonicity,[status(thm)],[286])).
% 0.39/0.62 tff(288,plain,
% 0.39/0.62 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_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)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.62 inference(transitivity,[status(thm)],[287, 285])).
% 0.39/0.62 tff(289,plain,
% 0.39/0.62 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_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)))))),
% 0.39/0.62 inference(quant_inst,[status(thm)],[])).
% 0.39/0.62 tff(290,plain,
% 0.39/0.62 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.62 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.39/0.63 tff(291,plain,
% 0.39/0.63 (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[290, 284, 143, 174, 271])).
% 0.39/0.63 tff(292,plain,
% 0.39/0.63 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v13_lattices(k1_lattice2(A!0))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[27])).
% 0.39/0.63 tff(293,plain,
% 0.39/0.63 (v13_lattices(k1_lattice2(A!0)) <=> v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.63 inference(symmetry,[status(thm)],[292])).
% 0.39/0.63 tff(294,plain,
% 0.39/0.63 (^[A: $i] : refl((v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(295,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[294])).
% 0.39/0.63 tff(296,plain,
% 0.39/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(297,plain,
% 0.39/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[296])).
% 0.39/0.63 tff(298,plain,
% 0.39/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(299,plain,
% 0.39/0.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(300,plain,
% 0.39/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[299])).
% 0.39/0.63 tff(301,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t64_lattice2')).
% 0.39/0.63 tff(302,plain,
% 0.39/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[301, 300])).
% 0.39/0.63 tff(303,plain,
% 0.39/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[302, 298])).
% 0.39/0.63 tff(304,plain,(
% 0.39/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.39/0.63 inference(skolemize,[status(sab)],[303])).
% 0.39/0.63 tff(305,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[304, 297])).
% 0.39/0.63 tff(306,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[305, 295])).
% 0.39/0.63 tff(307,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(308,plain,
% 0.39/0.63 ((v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(309,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[308])).
% 0.39/0.63 tff(310,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[309, 307])).
% 0.39/0.63 tff(311,plain,
% 0.39/0.63 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(312,plain,
% 0.39/0.63 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.39/0.63 tff(313,plain,
% 0.39/0.63 (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[312, 167, 166, 22, 306])).
% 0.39/0.63 tff(314,plain,
% 0.39/0.63 (v14_lattices(A!0)),
% 0.39/0.63 inference(or_elim,[status(thm)],[20])).
% 0.39/0.63 tff(315,plain,
% 0.39/0.63 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | (~v14_lattices(A!0)) | v13_lattices(k1_lattice2(A!0))),
% 0.39/0.63 inference(tautology,[status(thm)],[])).
% 0.39/0.63 tff(316,plain,
% 0.39/0.63 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | v13_lattices(k1_lattice2(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[315, 314])).
% 0.39/0.63 tff(317,plain,
% 0.39/0.63 (v13_lattices(k1_lattice2(A!0))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[316, 313])).
% 0.39/0.63 tff(318,plain,
% 0.39/0.63 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[317, 293])).
% 0.39/0.63 tff(319,plain,
% 0.39/0.63 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(320,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[319])).
% 0.39/0.63 tff(321,plain,
% 0.39/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), (((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))))), rewrite(((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), (((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(322,plain,
% 0.39/0.63 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[321])).
% 0.39/0.63 tff(323,plain,
% 0.39/0.63 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(324,plain,
% 0.39/0.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))))),
% 0.39/0.63 inference(bind,[status(th)],[])).
% 0.39/0.63 tff(325,plain,
% 0.39/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.39/0.63 inference(quant_intro,[status(thm)],[324])).
% 0.39/0.63 tff(326,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t20_filter_0')).
% 0.39/0.63 tff(327,plain,
% 0.39/0.63 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.39/0.63 tff(328,plain,
% 0.39/0.63 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[327, 323])).
% 0.39/0.63 tff(329,plain,(
% 0.39/0.63 ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.39/0.63 inference(skolemize,[status(sab)],[328])).
% 0.39/0.63 tff(330,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[329, 322])).
% 0.39/0.63 tff(331,plain,
% 0.39/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[330, 320])).
% 0.39/0.63 tff(332,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(333,plain,
% 0.39/0.63 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_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_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.63 inference(rewrite,[status(thm)],[])).
% 0.39/0.63 tff(334,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[333])).
% 0.39/0.63 tff(335,plain,
% 0.39/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.63 inference(transitivity,[status(thm)],[334, 332])).
% 0.39/0.63 tff(336,plain,
% 0.39/0.63 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.39/0.63 inference(quant_inst,[status(thm)],[])).
% 0.39/0.63 tff(337,plain,
% 0.39/0.63 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.63 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.39/0.63 tff(338,plain,
% 0.39/0.63 (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.63 inference(unit_resolution,[status(thm)],[337, 331, 143, 174, 271, 318])).
% 0.39/0.63 tff(339,plain,
% 0.39/0.63 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.39/0.63 inference(symmetry,[status(thm)],[338])).
% 0.39/0.63 tff(340,plain,
% 0.39/0.63 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.39/0.63 inference(monotonicity,[status(thm)],[29])).
% 0.39/0.63 tff(341,plain,
% 0.39/0.63 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k17_filter_2(A!0)),
% 0.47/0.63 inference(transitivity,[status(thm)],[340, 339, 291, 266, 215])).
% 0.47/0.63 tff(342,plain,
% 0.47/0.63 (^[A: $i] : refl((v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(343,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[342])).
% 0.47/0.63 tff(344,plain,
% 0.47/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(345,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[344])).
% 0.47/0.63 tff(346,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(347,plain,
% 0.47/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(348,plain,
% 0.47/0.63 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[347])).
% 0.47/0.63 tff(349,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t79_lattice2')).
% 0.47/0.63 tff(350,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[349, 348])).
% 0.47/0.63 tff(351,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[350, 346])).
% 0.47/0.63 tff(352,plain,(
% 0.47/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.47/0.63 inference(skolemize,[status(sab)],[351])).
% 0.47/0.63 tff(353,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[352, 345])).
% 0.47/0.63 tff(354,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[353, 343])).
% 0.47/0.63 tff(355,plain,
% 0.47/0.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(356,plain,
% 0.47/0.63 ((v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> ((~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(357,plain,
% 0.47/0.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[356])).
% 0.47/0.63 tff(358,plain,
% 0.47/0.63 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.63 inference(transitivity,[status(thm)],[357, 355])).
% 0.47/0.63 tff(359,plain,
% 0.47/0.63 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.47/0.63 inference(quant_inst,[status(thm)],[])).
% 0.47/0.63 tff(360,plain,
% 0.47/0.63 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v14_lattices(A!0)) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.47/0.63 tff(361,plain,
% 0.47/0.63 (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))),
% 0.47/0.63 inference(unit_resolution,[status(thm)],[360, 314, 167, 166, 22, 354])).
% 0.47/0.63 tff(362,plain,
% 0.47/0.63 (k5_lattices(k1_lattice2(A!0)) = k6_lattices(A!0)),
% 0.47/0.63 inference(symmetry,[status(thm)],[361])).
% 0.47/0.63 tff(363,plain,
% 0.47/0.63 (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k18_filter_2(A!0, k6_lattices(A!0))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[362])).
% 0.47/0.63 tff(364,plain,
% 0.47/0.63 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0)) <=> m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.47/0.63 inference(monotonicity,[status(thm)],[362])).
% 0.47/0.63 tff(365,plain,
% 0.47/0.63 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) <=> m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))),
% 0.47/0.63 inference(symmetry,[status(thm)],[364])).
% 0.47/0.63 tff(366,plain,
% 0.47/0.63 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(367,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[366])).
% 0.47/0.63 tff(368,plain,
% 0.47/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(369,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[368])).
% 0.47/0.63 tff(370,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(371,plain,
% 0.47/0.63 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))),
% 0.47/0.63 inference(bind,[status(th)],[])).
% 0.47/0.63 tff(372,plain,
% 0.47/0.63 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.47/0.63 inference(quant_intro,[status(thm)],[371])).
% 0.47/0.63 tff(373,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k6_lattices')).
% 0.47/0.63 tff(374,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[373, 372])).
% 0.47/0.63 tff(375,plain,
% 0.47/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[374, 370])).
% 0.47/0.63 tff(376,plain,(
% 0.47/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.47/0.63 inference(skolemize,[status(sab)],[375])).
% 0.47/0.63 tff(377,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[376, 369])).
% 0.47/0.63 tff(378,plain,
% 0.47/0.63 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.47/0.63 inference(modus_ponens,[status(thm)],[377, 367])).
% 0.47/0.63 tff(379,plain,
% 0.47/0.63 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.63 tff(380,plain,
% 0.47/0.63 ((v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.47/0.63 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(381,plain,
% 0.47/0.64 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[380])).
% 0.47/0.64 tff(382,plain,
% 0.47/0.64 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[381, 379])).
% 0.47/0.64 tff(383,plain,
% 0.47/0.64 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(384,plain,
% 0.47/0.64 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[383, 382])).
% 0.47/0.64 tff(385,plain,
% 0.47/0.64 ((~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[384, 167, 378])).
% 0.47/0.64 tff(386,plain,
% 0.47/0.64 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[385, 86])).
% 0.47/0.64 tff(387,plain,
% 0.47/0.64 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[386, 365])).
% 0.47/0.64 tff(388,plain,
% 0.47/0.64 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(389,plain,
% 0.47/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[388])).
% 0.47/0.64 tff(390,plain,
% 0.47/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(391,plain,
% 0.47/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[390])).
% 0.47/0.64 tff(392,plain,
% 0.47/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(transitivity,[status(thm)],[391, 389])).
% 0.47/0.64 tff(393,plain,
% 0.47/0.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(394,plain,
% 0.47/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[393])).
% 0.47/0.64 tff(395,plain,
% 0.47/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(396,plain,
% 0.47/0.64 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(397,plain,
% 0.47/0.64 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[396])).
% 0.47/0.64 tff(398,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t30_filter_2')).
% 0.47/0.64 tff(399,plain,
% 0.47/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.47/0.64 tff(400,plain,
% 0.47/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[399, 395])).
% 0.47/0.64 tff(401,plain,(
% 0.47/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.47/0.64 inference(skolemize,[status(sab)],[400])).
% 0.47/0.64 tff(402,plain,
% 0.47/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[401, 394])).
% 0.47/0.64 tff(403,plain,
% 0.47/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[402, 392])).
% 0.47/0.64 tff(404,plain,
% 0.47/0.64 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(405,plain,
% 0.47/0.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(406,plain,
% 0.47/0.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[405, 404])).
% 0.47/0.64 tff(407,plain,
% 0.47/0.64 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[406, 167, 166, 22, 403])).
% 0.47/0.64 tff(408,plain,
% 0.47/0.64 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(409,plain,
% 0.47/0.64 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(410,plain,
% 0.47/0.64 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.47/0.64 tff(411,plain,
% 0.47/0.64 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[410, 407])).
% 0.47/0.64 tff(412,plain,
% 0.47/0.64 (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[411, 387])).
% 0.47/0.64 tff(413,plain,
% 0.47/0.64 (((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.64 inference(tautology,[status(thm)],[])).
% 0.47/0.64 tff(414,plain,
% 0.47/0.64 (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[413, 412])).
% 0.47/0.64 tff(415,plain,
% 0.47/0.64 (k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))),
% 0.47/0.64 inference(symmetry,[status(thm)],[414])).
% 0.47/0.64 tff(416,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(417,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[416])).
% 0.47/0.64 tff(418,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(419,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[418])).
% 0.47/0.64 tff(420,plain,
% 0.47/0.64 (^[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))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(421,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[420])).
% 0.47/0.64 tff(422,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[421, 419])).
% 0.47/0.64 tff(423,plain,
% 0.47/0.64 (^[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)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(424,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[423])).
% 0.47/0.64 tff(425,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(426,plain,
% 0.47/0.64 (^[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)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(427,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[426])).
% 0.47/0.64 tff(428,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')).
% 0.47/0.64 tff(429,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[428, 427])).
% 0.47/0.64 tff(430,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[429, 425])).
% 0.47/0.64 tff(431,plain,(
% 0.47/0.64 ![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)))),
% 0.47/0.64 inference(skolemize,[status(sab)],[430])).
% 0.47/0.64 tff(432,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[431, 424])).
% 0.47/0.64 tff(433,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[432, 422])).
% 0.47/0.64 tff(434,plain,
% 0.47/0.64 (![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)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[433, 417])).
% 0.47/0.64 tff(435,plain,
% 0.47/0.64 (((~![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)))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(436,plain,
% 0.47/0.64 ((~![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)))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(437,plain,
% 0.47/0.64 ((~![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))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.47/0.64 tff(438,plain,
% 0.47/0.64 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[437, 167, 166, 22, 434])).
% 0.47/0.64 tff(439,plain,
% 0.47/0.64 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(440,plain,
% 0.47/0.64 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.64 inference(quant_inst,[status(thm)],[])).
% 0.47/0.64 tff(441,plain,
% 0.47/0.64 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.47/0.64 tff(442,plain,
% 0.47/0.64 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0)))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[441, 438])).
% 0.47/0.64 tff(443,plain,
% 0.47/0.64 (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 0.47/0.64 inference(unit_resolution,[status(thm)],[442, 387])).
% 0.47/0.64 tff(444,plain,
% 0.47/0.64 (k5_lattices(k1_lattice2(A!0)) = k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))),
% 0.47/0.64 inference(symmetry,[status(thm)],[443])).
% 0.47/0.64 tff(445,plain,
% 0.47/0.64 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[27, 444])).
% 0.47/0.64 tff(446,plain,
% 0.47/0.64 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k18_filter_2(A!0, k6_lattices(A!0))),
% 0.47/0.64 inference(transitivity,[status(thm)],[445, 415, 363])).
% 0.47/0.64 tff(447,plain,
% 0.47/0.64 ((k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) <=> (k18_filter_2(A!0, k6_lattices(A!0)) = k17_filter_2(A!0))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[446, 341])).
% 0.47/0.64 tff(448,plain,
% 0.47/0.64 ((k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.47/0.64 inference(transitivity,[status(thm)],[447, 194])).
% 0.47/0.64 tff(449,plain,
% 0.47/0.64 ((k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))) <=> (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.64 inference(symmetry,[status(thm)],[448])).
% 0.47/0.64 tff(450,plain,
% 0.47/0.64 ((~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) <=> (~(k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.64 inference(monotonicity,[status(thm)],[449])).
% 0.47/0.64 tff(451,plain,
% 0.47/0.64 (^[A: $i, B: $i] : refl((m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(452,plain,
% 0.47/0.64 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[451])).
% 0.47/0.64 tff(453,plain,
% 0.47/0.64 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(454,plain,
% 0.47/0.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[453])).
% 0.47/0.64 tff(455,plain,
% 0.47/0.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.47/0.64 inference(rewrite,[status(thm)],[])).
% 0.47/0.64 tff(456,plain,
% 0.47/0.64 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))))),
% 0.47/0.64 inference(bind,[status(th)],[])).
% 0.47/0.64 tff(457,plain,
% 0.47/0.64 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.47/0.64 inference(quant_intro,[status(thm)],[456])).
% 0.47/0.64 tff(458,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k18_filter_2')).
% 0.47/0.64 tff(459,plain,
% 0.47/0.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[458, 457])).
% 0.47/0.64 tff(460,plain,
% 0.47/0.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[459, 455])).
% 0.47/0.64 tff(461,plain,(
% 0.47/0.64 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.47/0.64 inference(skolemize,[status(sab)],[460])).
% 0.47/0.64 tff(462,plain,
% 0.47/0.64 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.64 inference(modus_ponens,[status(thm)],[461, 454])).
% 0.47/0.64 tff(463,plain,
% 0.47/0.64 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[462, 452])).
% 0.47/0.65 tff(464,plain,
% 0.47/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(465,plain,
% 0.47/0.65 ((m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(466,plain,
% 0.47/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[465])).
% 0.47/0.65 tff(467,plain,
% 0.47/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[466, 464])).
% 0.47/0.65 tff(468,plain,
% 0.47/0.65 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(469,plain,
% 0.47/0.65 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.47/0.65 tff(470,plain,
% 0.47/0.65 (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[469, 167, 166, 22, 463])).
% 0.47/0.65 tff(471,plain,
% 0.47/0.65 (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[470, 386])).
% 0.47/0.65 tff(472,plain,
% 0.47/0.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(473,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[472])).
% 0.47/0.65 tff(474,plain,
% 0.47/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(475,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[474])).
% 0.47/0.65 tff(476,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[475, 473])).
% 0.47/0.65 tff(477,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(478,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[477])).
% 0.47/0.65 tff(479,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(480,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(481,plain,
% 0.47/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[480])).
% 0.47/0.65 tff(482,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.47/0.65 tff(483,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[482, 481])).
% 0.47/0.65 tff(484,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[483, 479])).
% 0.47/0.65 tff(485,plain,(
% 0.47/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[484])).
% 0.47/0.65 tff(486,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[485, 478])).
% 0.47/0.65 tff(487,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[486, 476])).
% 0.47/0.65 tff(488,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(489,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(490,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[489, 488])).
% 0.47/0.65 tff(491,plain,
% 0.47/0.65 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[490, 167, 166, 22, 487])).
% 0.47/0.65 tff(492,plain,
% 0.47/0.65 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(493,plain,
% 0.47/0.65 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(494,plain,
% 0.47/0.65 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.47/0.65 tff(495,plain,
% 0.47/0.65 (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[494, 491, 471])).
% 0.47/0.65 tff(496,plain,
% 0.47/0.65 ((v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0))) | m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.47/0.65 inference(tautology,[status(thm)],[])).
% 0.47/0.65 tff(497,plain,
% 0.47/0.65 (m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[496, 495])).
% 0.47/0.65 tff(498,plain,
% 0.47/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(499,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[498])).
% 0.47/0.65 tff(500,plain,
% 0.47/0.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(501,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[500])).
% 0.47/0.65 tff(502,plain,
% 0.47/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(503,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[502])).
% 0.47/0.65 tff(504,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[503, 501])).
% 0.47/0.65 tff(505,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(506,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[505])).
% 0.47/0.65 tff(507,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(508,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(509,plain,
% 0.47/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[508])).
% 0.47/0.65 tff(510,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.47/0.65 tff(511,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[510, 509])).
% 0.47/0.65 tff(512,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[511, 507])).
% 0.47/0.65 tff(513,plain,(
% 0.47/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[512])).
% 0.47/0.65 tff(514,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[513, 506])).
% 0.47/0.65 tff(515,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[514, 504])).
% 0.47/0.65 tff(516,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[515, 499])).
% 0.47/0.65 tff(517,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(518,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(519,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[518, 517])).
% 0.47/0.65 tff(520,plain,
% 0.47/0.65 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[519, 167, 166, 22, 516])).
% 0.47/0.65 tff(521,plain,
% 0.47/0.65 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(522,plain,
% 0.47/0.65 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(523,plain,
% 0.47/0.65 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[522, 521])).
% 0.47/0.65 tff(524,plain,
% 0.47/0.65 (m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[523, 520, 497])).
% 0.47/0.65 tff(525,plain,
% 0.47/0.65 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(526,plain,
% 0.47/0.65 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[525])).
% 0.47/0.65 tff(527,plain,
% 0.47/0.65 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(528,plain,
% 0.47/0.65 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(529,plain,
% 0.47/0.65 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[528])).
% 0.47/0.65 tff(530,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.47/0.65 tff(531,plain,
% 0.47/0.65 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[530, 529])).
% 0.47/0.65 tff(532,plain,
% 0.47/0.65 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[531, 527])).
% 0.47/0.65 tff(533,plain,(
% 0.47/0.65 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(skolemize,[status(sab)],[532])).
% 0.47/0.65 tff(534,plain,
% 0.47/0.65 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[533, 526])).
% 0.47/0.65 tff(535,plain,
% 0.47/0.65 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(536,plain,
% 0.47/0.65 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(537,plain,
% 0.47/0.65 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[536, 535])).
% 0.47/0.65 tff(538,plain,
% 0.47/0.65 (l1_struct_0(A!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[537, 534, 86])).
% 0.47/0.65 tff(539,plain,
% 0.47/0.65 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(540,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[539])).
% 0.47/0.65 tff(541,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(542,plain,
% 0.47/0.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[541])).
% 0.47/0.65 tff(543,plain,
% 0.47/0.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(544,plain,
% 0.47/0.65 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(545,plain,
% 0.47/0.65 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[544])).
% 0.47/0.65 tff(546,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.47/0.65 tff(547,plain,
% 0.47/0.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.47/0.65 tff(548,plain,
% 0.47/0.65 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[547, 543])).
% 0.47/0.65 tff(549,plain,(
% 0.47/0.65 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.47/0.65 inference(skolemize,[status(sab)],[548])).
% 0.47/0.65 tff(550,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[549, 542])).
% 0.47/0.65 tff(551,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[550, 540])).
% 0.47/0.65 tff(552,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(553,plain,
% 0.47/0.65 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(554,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[553])).
% 0.47/0.65 tff(555,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.47/0.65 inference(transitivity,[status(thm)],[554, 552])).
% 0.47/0.65 tff(556,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(557,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.47/0.65 tff(558,plain,
% 0.47/0.65 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[557, 167, 551])).
% 0.47/0.65 tff(559,plain,
% 0.47/0.65 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[558, 538])).
% 0.47/0.65 tff(560,plain,
% 0.47/0.65 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[215])).
% 0.47/0.65 tff(561,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(562,plain,
% 0.47/0.65 ((v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(563,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))))),
% 0.47/0.65 inference(monotonicity,[status(thm)],[562])).
% 0.47/0.65 tff(564,plain,
% 0.47/0.65 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.47/0.65 inference(transitivity,[status(thm)],[563, 561])).
% 0.47/0.65 tff(565,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.47/0.65 inference(quant_inst,[status(thm)],[])).
% 0.47/0.65 tff(566,plain,
% 0.47/0.65 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[565, 564])).
% 0.47/0.65 tff(567,plain,
% 0.47/0.65 (k1_filter_0(A!0) = u1_struct_0(A!0)),
% 0.47/0.65 inference(unit_resolution,[status(thm)],[566, 167, 166, 22, 284])).
% 0.47/0.65 tff(568,plain,
% 0.47/0.65 (u1_struct_0(A!0) = k1_filter_0(A!0)),
% 0.47/0.65 inference(symmetry,[status(thm)],[567])).
% 0.47/0.65 tff(569,plain,
% 0.47/0.65 (m1_filter_0(u1_struct_0(A!0), A!0) <=> m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.47/0.65 inference(monotonicity,[status(thm)],[568])).
% 0.47/0.65 tff(570,plain,
% 0.47/0.65 (m1_filter_0(k1_filter_0(A!0), A!0) <=> m1_filter_0(u1_struct_0(A!0), A!0)),
% 0.47/0.65 inference(symmetry,[status(thm)],[569])).
% 0.47/0.65 tff(571,plain,
% 0.47/0.65 (^[A: $i] : refl((v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(572,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[571])).
% 0.47/0.65 tff(573,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(k1_filter_0(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(574,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[573])).
% 0.47/0.65 tff(575,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.47/0.65 inference(rewrite,[status(thm)],[])).
% 0.47/0.65 tff(576,plain,
% 0.47/0.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))))),
% 0.47/0.65 inference(bind,[status(th)],[])).
% 0.47/0.65 tff(577,plain,
% 0.47/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.47/0.65 inference(quant_intro,[status(thm)],[576])).
% 0.47/0.65 tff(578,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_filter_0')).
% 0.47/0.65 tff(579,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[578, 577])).
% 0.47/0.65 tff(580,plain,
% 0.47/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.47/0.65 inference(modus_ponens,[status(thm)],[579, 575])).
% 0.47/0.65 tff(581,plain,(
% 0.47/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.47/0.65 inference(skolemize,[status(sab)],[580])).
% 0.47/0.65 tff(582,plain,
% 0.47/0.65 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[581, 574])).
% 0.47/0.66 tff(583,plain,
% 0.47/0.66 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[582, 572])).
% 0.47/0.66 tff(584,plain,
% 0.47/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(585,plain,
% 0.47/0.66 ((v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(586,plain,
% 0.47/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0)))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[585])).
% 0.47/0.66 tff(587,plain,
% 0.47/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.47/0.66 inference(transitivity,[status(thm)],[586, 584])).
% 0.47/0.66 tff(588,plain,
% 0.47/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(589,plain,
% 0.47/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[588, 587])).
% 0.47/0.66 tff(590,plain,
% 0.47/0.66 (m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[589, 167, 166, 22, 583])).
% 0.47/0.66 tff(591,plain,
% 0.47/0.66 (m1_filter_0(u1_struct_0(A!0), A!0)),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[590, 570])).
% 0.47/0.66 tff(592,plain,
% 0.47/0.66 (^[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)))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(593,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[592])).
% 0.47/0.66 tff(594,plain,
% 0.47/0.66 (^[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)))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(595,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[594])).
% 0.47/0.66 tff(596,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[595, 593])).
% 0.47/0.66 tff(597,plain,
% 0.47/0.66 (^[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))))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(598,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[597])).
% 0.47/0.66 tff(599,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(600,plain,
% 0.47/0.66 (^[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))))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(601,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[600])).
% 0.47/0.66 tff(602,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')).
% 0.47/0.66 tff(603,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[602, 601])).
% 0.47/0.66 tff(604,plain,
% 0.47/0.66 (![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))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[603, 599])).
% 0.47/0.66 tff(605,plain,(
% 0.47/0.66 ![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))))))),
% 0.47/0.66 inference(skolemize,[status(sab)],[604])).
% 0.47/0.66 tff(606,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[605, 598])).
% 0.47/0.66 tff(607,plain,
% 0.47/0.66 (![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))))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[606, 596])).
% 0.47/0.66 tff(608,plain,
% 0.47/0.66 (((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(609,plain,
% 0.47/0.66 ((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(610,plain,
% 0.47/0.66 ((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.47/0.66 tff(611,plain,
% 0.47/0.66 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[610, 167, 166, 22, 607])).
% 0.47/0.66 tff(612,plain,
% 0.47/0.66 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(613,plain,
% 0.47/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(614,plain,
% 0.47/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.47/0.66 tff(615,plain,
% 0.47/0.66 (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[614, 611, 591])).
% 0.47/0.66 tff(616,plain,
% 0.47/0.66 ((v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(617,plain,
% 0.47/0.66 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[616, 615])).
% 0.47/0.66 tff(618,plain,
% 0.47/0.66 (m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[617, 560])).
% 0.47/0.66 tff(619,plain,
% 0.47/0.66 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(620,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[619])).
% 0.47/0.66 tff(621,plain,
% 0.47/0.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(622,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[621])).
% 0.47/0.66 tff(623,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(624,plain,
% 0.47/0.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(625,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[624])).
% 0.47/0.66 tff(626,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 0.47/0.66 tff(627,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[626, 625])).
% 0.47/0.66 tff(628,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[627, 623])).
% 0.47/0.66 tff(629,plain,(
% 0.47/0.66 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[628])).
% 0.47/0.66 tff(630,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[629, 622])).
% 0.47/0.66 tff(631,plain,
% 0.47/0.66 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[630, 620])).
% 0.47/0.66 tff(632,plain,
% 0.47/0.66 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(633,plain,
% 0.47/0.66 ((v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(634,plain,
% 0.47/0.66 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))))),
% 0.47/0.66 inference(monotonicity,[status(thm)],[633])).
% 0.47/0.66 tff(635,plain,
% 0.47/0.66 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.47/0.66 inference(transitivity,[status(thm)],[634, 632])).
% 0.47/0.66 tff(636,plain,
% 0.47/0.66 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.47/0.66 inference(quant_inst,[status(thm)],[])).
% 0.47/0.66 tff(637,plain,
% 0.47/0.66 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[636, 635])).
% 0.47/0.66 tff(638,plain,
% 0.47/0.66 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[637, 631])).
% 0.47/0.66 tff(639,plain,
% 0.47/0.66 (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[638, 618, 559, 524])).
% 0.47/0.66 tff(640,plain,
% 0.47/0.66 (~r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.47/0.66 inference(or_elim,[status(thm)],[20])).
% 0.47/0.66 tff(641,plain,
% 0.47/0.66 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))) | r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.47/0.66 inference(tautology,[status(thm)],[])).
% 0.47/0.66 tff(642,plain,
% 0.47/0.66 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))) | (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[641, 640])).
% 0.47/0.66 tff(643,plain,
% 0.47/0.66 (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.47/0.66 inference(unit_resolution,[status(thm)],[642, 639])).
% 0.47/0.66 tff(644,plain,
% 0.47/0.66 (~(k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[643, 450])).
% 0.47/0.66 tff(645,plain,
% 0.47/0.66 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(646,plain,
% 0.47/0.66 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[645])).
% 0.47/0.66 tff(647,plain,
% 0.47/0.66 (^[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)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~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)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(648,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[647])).
% 0.47/0.66 tff(649,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(650,plain,
% 0.47/0.66 (^[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))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 0.47/0.66 inference(bind,[status(th)],[])).
% 0.47/0.66 tff(651,plain,
% 0.47/0.66 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.47/0.66 inference(quant_intro,[status(thm)],[650])).
% 0.47/0.66 tff(652,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 0.47/0.66 tff(653,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[652, 651])).
% 0.47/0.66 tff(654,plain,
% 0.47/0.66 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[653, 649])).
% 0.47/0.66 tff(655,plain,(
% 0.47/0.66 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.47/0.66 inference(skolemize,[status(sab)],[654])).
% 0.47/0.66 tff(656,plain,
% 0.47/0.66 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[655, 648])).
% 0.47/0.66 tff(657,plain,
% 0.47/0.66 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.47/0.66 inference(modus_ponens,[status(thm)],[656, 646])).
% 0.47/0.66 tff(658,plain,
% 0.47/0.66 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.66 inference(rewrite,[status(thm)],[])).
% 0.47/0.66 tff(659,plain,
% 0.47/0.66 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(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)))) | (~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)))) | v3_struct_0(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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.67 inference(rewrite,[status(thm)],[])).
% 0.47/0.67 tff(660,plain,
% 0.47/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(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)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))))),
% 0.47/0.67 inference(monotonicity,[status(thm)],[659])).
% 0.47/0.67 tff(661,plain,
% 0.47/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(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)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.47/0.67 inference(transitivity,[status(thm)],[660, 658])).
% 0.47/0.67 tff(662,plain,
% 0.47/0.67 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(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)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.47/0.67 inference(quant_inst,[status(thm)],[])).
% 0.47/0.67 tff(663,plain,
% 0.47/0.67 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.67 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.47/0.67 tff(664,plain,
% 0.47/0.67 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[663, 657, 143, 174, 271])).
% 0.47/0.67 tff(665,plain,
% 0.47/0.67 ($false),
% 0.47/0.67 inference(unit_resolution,[status(thm)],[664, 644, 193])).
% 0.47/0.67 % SZS output end Proof
% 0.52/0.68 % E exiting
%------------------------------------------------------------------------------