%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT305+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:16 AM UTC 2025
% Result : Theorem 3.63s 3.84s
% Output : Proof 3.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT305+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 20:07:56 EDT 2025
% 0.12/0.34 % CPUTime :
% 3.63/3.84 % SZS status Theorem
% 3.63/3.84 % SZS output start Proof
% 3.63/3.84 tff(m1_subset_1_type, type, (
% 3.63/3.84 m1_subset_1: ( $i * $i ) > $o)).
% 3.63/3.84 tff(u1_struct_0_type, type, (
% 3.63/3.84 u1_struct_0: $i > $i)).
% 3.63/3.84 tff(tptp_fun_A_0_type, type, (
% 3.63/3.84 tptp_fun_A_0: $i)).
% 3.63/3.84 tff(k2_binop_1_type, type, (
% 3.63/3.84 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 3.63/3.84 tff(tptp_fun_B_1_type, type, (
% 3.63/3.84 tptp_fun_B_1: $i)).
% 3.63/3.84 tff(tptp_fun_C_2_type, type, (
% 3.63/3.84 tptp_fun_C_2: $i)).
% 3.63/3.84 tff(u1_lattices_type, type, (
% 3.63/3.84 u1_lattices: $i > $i)).
% 3.63/3.84 tff(m1_relset_1_type, type, (
% 3.63/3.84 m1_relset_1: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(k2_zfmisc_1_type, type, (
% 3.63/3.84 k2_zfmisc_1: ( $i * $i ) > $i)).
% 3.63/3.84 tff(m2_relset_1_type, type, (
% 3.63/3.84 m2_relset_1: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(v1_funct_2_type, type, (
% 3.63/3.84 v1_funct_2: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(v1_funct_1_type, type, (
% 3.63/3.84 v1_funct_1: $i > $o)).
% 3.63/3.84 tff(l1_lattices_type, type, (
% 3.63/3.84 l1_lattices: $i > $o)).
% 3.63/3.84 tff(l2_lattices_type, type, (
% 3.63/3.84 l2_lattices: $i > $o)).
% 3.63/3.84 tff(l3_lattices_type, type, (
% 3.63/3.84 l3_lattices: $i > $o)).
% 3.63/3.84 tff(r2_hidden_type, type, (
% 3.63/3.84 r2_hidden: ( $i * $i ) > $o)).
% 3.63/3.84 tff(k18_filter_2_type, type, (
% 3.63/3.84 k18_filter_2: ( $i * $i ) > $i)).
% 3.63/3.84 tff(k4_lattices_type, type, (
% 3.63/3.84 k4_lattices: ( $i * $i * $i ) > $i)).
% 3.63/3.84 tff(v10_lattices_type, type, (
% 3.63/3.84 v10_lattices: $i > $o)).
% 3.63/3.84 tff(v3_struct_0_type, type, (
% 3.63/3.84 v3_struct_0: $i > $o)).
% 3.63/3.84 tff(v1_xboole_0_type, type, (
% 3.63/3.84 v1_xboole_0: $i > $o)).
% 3.63/3.84 tff(l1_struct_0_type, type, (
% 3.63/3.84 l1_struct_0: $i > $o)).
% 3.63/3.84 tff(v2_binop_1_type, type, (
% 3.63/3.84 v2_binop_1: ( $i * $i ) > $o)).
% 3.63/3.84 tff(v1_partfun1_type, type, (
% 3.63/3.84 v1_partfun1: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(v1_relat_1_type, type, (
% 3.63/3.84 v1_relat_1: $i > $o)).
% 3.63/3.84 tff(v7_lattices_type, type, (
% 3.63/3.84 v7_lattices: $i > $o)).
% 3.63/3.84 tff(v9_lattices_type, type, (
% 3.63/3.84 v9_lattices: $i > $o)).
% 3.63/3.84 tff(v8_lattices_type, type, (
% 3.63/3.84 v8_lattices: $i > $o)).
% 3.63/3.84 tff(v6_lattices_type, type, (
% 3.63/3.84 v6_lattices: $i > $o)).
% 3.63/3.84 tff(v5_lattices_type, type, (
% 3.63/3.84 v5_lattices: $i > $o)).
% 3.63/3.84 tff(v4_lattices_type, type, (
% 3.63/3.84 v4_lattices: $i > $o)).
% 3.63/3.84 tff(r3_lattices_type, type, (
% 3.63/3.84 r3_lattices: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(a_2_0_filter_2_type, type, (
% 3.63/3.84 a_2_0_filter_2: ( $i * $i ) > $i)).
% 3.63/3.84 tff(k2_lattices_type, type, (
% 3.63/3.84 k2_lattices: ( $i * $i * $i ) > $i)).
% 3.63/3.84 tff(r1_lattices_type, type, (
% 3.63/3.84 r1_lattices: ( $i * $i * $i ) > $o)).
% 3.63/3.84 tff(1,plain,
% 3.63/3.84 (^[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)))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(2,plain,
% 3.63/3.84 (![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))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[1])).
% 3.63/3.84 tff(3,plain,
% 3.63/3.84 (![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))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(4,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')).
% 3.63/3.84 tff(5,plain,
% 3.63/3.84 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[4, 3])).
% 3.63/3.84 tff(6,plain,(
% 3.63/3.84 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.63/3.84 inference(skolemize,[status(sab)],[5])).
% 3.63/3.84 tff(7,plain,
% 3.63/3.84 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[6, 2])).
% 3.63/3.84 tff(8,plain,
% 3.63/3.84 ((~![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)))),
% 3.63/3.84 inference(quant_inst,[status(thm)],[])).
% 3.63/3.84 tff(9,plain,
% 3.63/3.84 (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))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[8, 7])).
% 3.63/3.84 tff(10,plain,
% 3.63/3.84 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(11,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[10])).
% 3.63/3.84 tff(12,plain,
% 3.63/3.84 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(13,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[12])).
% 3.63/3.84 tff(14,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(15,plain,
% 3.63/3.84 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(16,plain,
% 3.63/3.84 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[15])).
% 3.63/3.84 tff(17,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 3.63/3.84 tff(18,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[17, 16])).
% 3.63/3.84 tff(19,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[18, 14])).
% 3.63/3.84 tff(20,plain,(
% 3.63/3.84 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 3.63/3.84 inference(skolemize,[status(sab)],[19])).
% 3.63/3.84 tff(21,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[20, 13])).
% 3.63/3.84 tff(22,plain,
% 3.63/3.84 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[21, 11])).
% 3.63/3.84 tff(23,plain,
% 3.63/3.84 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(24,plain,
% 3.63/3.84 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B)))))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(25,plain,
% 3.63/3.84 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B))) & r2_hidden(k4_lattices(A, C, B), k18_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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B)))))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(26,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B))) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t31_filter_2')).
% 3.63/3.84 tff(27,plain,
% 3.63/3.84 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[26, 25])).
% 3.63/3.84 tff(28,plain,
% 3.63/3.84 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[27, 24])).
% 3.63/3.84 tff(29,plain,
% 3.63/3.84 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[28, 24])).
% 3.63/3.84 tff(30,plain,
% 3.63/3.84 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, B, C), k18_filter_2(A, B)) & r2_hidden(k4_lattices(A, C, B), k18_filter_2(A, B))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[29, 24])).
% 3.63/3.84 tff(31,plain,
% 3.63/3.84 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[30, 23])).
% 3.63/3.84 tff(32,plain,
% 3.63/3.84 (l3_lattices(A!0)),
% 3.63/3.84 inference(and_elim,[status(thm)],[31])).
% 3.63/3.84 tff(33,plain,
% 3.63/3.84 (((~![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)))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(34,plain,
% 3.63/3.84 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 3.63/3.84 inference(quant_inst,[status(thm)],[])).
% 3.63/3.84 tff(35,plain,
% 3.63/3.84 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[34, 33])).
% 3.63/3.84 tff(36,plain,
% 3.63/3.84 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[35, 32, 22])).
% 3.63/3.84 tff(37,plain,
% 3.63/3.84 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 3.63/3.84 inference(tautology,[status(thm)],[])).
% 3.63/3.84 tff(38,plain,
% 3.63/3.84 (l1_lattices(A!0)),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[37, 36])).
% 3.63/3.84 tff(39,plain,
% 3.63/3.84 (^[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)))))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(40,plain,
% 3.63/3.84 (![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))))))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[39])).
% 3.63/3.84 tff(41,plain,
% 3.63/3.84 (^[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)))))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(42,plain,
% 3.63/3.84 (![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))))))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[41])).
% 3.63/3.84 tff(43,plain,
% 3.63/3.84 (![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))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(44,plain,
% 3.63/3.84 (^[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))))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(45,plain,
% 3.63/3.84 (![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))))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[44])).
% 3.63/3.84 tff(46,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')).
% 3.63/3.84 tff(47,plain,
% 3.63/3.84 (![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))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[46, 45])).
% 3.63/3.84 tff(48,plain,
% 3.63/3.84 (![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))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[47, 43])).
% 3.63/3.84 tff(49,plain,(
% 3.63/3.84 ![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))))),
% 3.63/3.84 inference(skolemize,[status(sab)],[48])).
% 3.63/3.84 tff(50,plain,
% 3.63/3.84 (![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))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[49, 42])).
% 3.63/3.84 tff(51,plain,
% 3.63/3.84 (![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))))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[50, 40])).
% 3.63/3.84 tff(52,plain,
% 3.63/3.84 (((~![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))))))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.84 tff(53,plain,
% 3.63/3.84 ((~![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))))))),
% 3.63/3.84 inference(quant_inst,[status(thm)],[])).
% 3.63/3.84 tff(54,plain,
% 3.63/3.84 ((~![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)))))),
% 3.63/3.84 inference(modus_ponens,[status(thm)],[53, 52])).
% 3.63/3.84 tff(55,plain,
% 3.63/3.84 ((~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)))))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[54, 51])).
% 3.63/3.84 tff(56,plain,
% 3.63/3.84 (~((~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))))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[55, 38])).
% 3.63/3.84 tff(57,plain,
% 3.63/3.84 (((~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))),
% 3.63/3.84 inference(tautology,[status(thm)],[])).
% 3.63/3.84 tff(58,plain,
% 3.63/3.84 (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))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[57, 56])).
% 3.63/3.84 tff(59,plain,
% 3.63/3.84 ((~(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))),
% 3.63/3.84 inference(tautology,[status(thm)],[])).
% 3.63/3.84 tff(60,plain,
% 3.63/3.84 ((~(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))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[59, 58])).
% 3.63/3.84 tff(61,plain,
% 3.63/3.84 (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))),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[60, 9])).
% 3.63/3.84 tff(62,plain,
% 3.63/3.84 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 3.63/3.84 inference(tautology,[status(thm)],[])).
% 3.63/3.84 tff(63,plain,
% 3.63/3.84 (l2_lattices(A!0)),
% 3.63/3.84 inference(unit_resolution,[status(thm)],[62, 36])).
% 3.63/3.84 tff(64,plain,
% 3.63/3.84 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 3.63/3.84 inference(bind,[status(th)],[])).
% 3.63/3.84 tff(65,plain,
% 3.63/3.84 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.84 inference(quant_intro,[status(thm)],[64])).
% 3.63/3.84 tff(66,plain,
% 3.63/3.84 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.84 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(67,plain,
% 3.63/3.85 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(68,plain,
% 3.63/3.85 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[67])).
% 3.63/3.85 tff(69,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 3.63/3.85 tff(70,plain,
% 3.63/3.85 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[69, 68])).
% 3.63/3.85 tff(71,plain,
% 3.63/3.85 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[70, 66])).
% 3.63/3.85 tff(72,plain,(
% 3.63/3.85 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.85 inference(skolemize,[status(sab)],[71])).
% 3.63/3.85 tff(73,plain,
% 3.63/3.85 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[72, 65])).
% 3.63/3.85 tff(74,plain,
% 3.63/3.85 (((~![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)))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(75,plain,
% 3.63/3.85 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 3.63/3.85 inference(quant_inst,[status(thm)],[])).
% 3.63/3.85 tff(76,plain,
% 3.63/3.85 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[75, 74])).
% 3.63/3.85 tff(77,plain,
% 3.63/3.85 (l1_struct_0(A!0)),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[76, 73, 63])).
% 3.63/3.85 tff(78,plain,
% 3.63/3.85 (^[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))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(79,plain,
% 3.63/3.85 (![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)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[78])).
% 3.63/3.85 tff(80,plain,
% 3.63/3.85 (^[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)))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(81,plain,
% 3.63/3.85 (![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)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[80])).
% 3.63/3.85 tff(82,plain,
% 3.63/3.85 (![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))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(83,plain,
% 3.63/3.85 (^[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)))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(84,plain,
% 3.63/3.85 (![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))))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[83])).
% 3.63/3.85 tff(85,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')).
% 3.63/3.85 tff(86,plain,
% 3.63/3.85 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[85, 84])).
% 3.63/3.85 tff(87,plain,
% 3.63/3.85 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[86, 82])).
% 3.63/3.85 tff(88,plain,(
% 3.63/3.85 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 3.63/3.85 inference(skolemize,[status(sab)],[87])).
% 3.63/3.85 tff(89,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[88, 81])).
% 3.63/3.85 tff(90,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[89, 79])).
% 3.63/3.85 tff(91,plain,
% 3.63/3.85 (~v3_struct_0(A!0)),
% 3.63/3.85 inference(and_elim,[status(thm)],[31])).
% 3.63/3.85 tff(92,plain,
% 3.63/3.85 (((~![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))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(93,plain,
% 3.63/3.85 ((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))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(94,plain,
% 3.63/3.85 (((~![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)))))),
% 3.63/3.85 inference(monotonicity,[status(thm)],[93])).
% 3.63/3.85 tff(95,plain,
% 3.63/3.85 (((~![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))))),
% 3.63/3.85 inference(transitivity,[status(thm)],[94, 92])).
% 3.63/3.85 tff(96,plain,
% 3.63/3.85 ((~![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)))),
% 3.63/3.85 inference(quant_inst,[status(thm)],[])).
% 3.63/3.85 tff(97,plain,
% 3.63/3.85 ((~![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)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[96, 95])).
% 3.63/3.85 tff(98,plain,
% 3.63/3.85 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[97, 91, 90])).
% 3.63/3.85 tff(99,plain,
% 3.63/3.85 (~v1_xboole_0(u1_struct_0(A!0))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[98, 77])).
% 3.63/3.85 tff(100,plain,
% 3.63/3.85 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(101,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[100])).
% 3.63/3.85 tff(102,plain,
% 3.63/3.85 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))))), rewrite(((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(103,plain,
% 3.63/3.85 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[102])).
% 3.63/3.85 tff(104,plain,
% 3.63/3.85 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(105,plain,
% 3.63/3.85 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(106,plain,
% 3.63/3.85 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[105])).
% 3.63/3.85 tff(107,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 3.63/3.85 tff(108,plain,
% 3.63/3.85 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[107, 106])).
% 3.63/3.85 tff(109,plain,
% 3.63/3.85 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[108, 104])).
% 3.63/3.85 tff(110,plain,(
% 3.63/3.85 ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 3.63/3.85 inference(skolemize,[status(sab)],[109])).
% 3.63/3.85 tff(111,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[110, 103])).
% 3.63/3.85 tff(112,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[111, 101])).
% 3.63/3.85 tff(113,plain,
% 3.63/3.85 (v10_lattices(A!0)),
% 3.63/3.85 inference(and_elim,[status(thm)],[31])).
% 3.63/3.85 tff(114,plain,
% 3.63/3.85 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(115,plain,
% 3.63/3.85 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(116,plain,
% 3.63/3.85 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 3.63/3.85 inference(monotonicity,[status(thm)],[115])).
% 3.63/3.85 tff(117,plain,
% 3.63/3.85 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 3.63/3.85 inference(transitivity,[status(thm)],[116, 114])).
% 3.63/3.85 tff(118,plain,
% 3.63/3.85 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 3.63/3.85 inference(quant_inst,[status(thm)],[])).
% 3.63/3.85 tff(119,plain,
% 3.63/3.85 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[118, 117])).
% 3.63/3.85 tff(120,plain,
% 3.63/3.85 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[119, 91, 113, 32, 112])).
% 3.63/3.85 tff(121,plain,
% 3.63/3.85 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v7_lattices(A!0)),
% 3.63/3.85 inference(tautology,[status(thm)],[])).
% 3.63/3.85 tff(122,plain,
% 3.63/3.85 (v7_lattices(A!0)),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[121, 120])).
% 3.63/3.85 tff(123,plain,
% 3.63/3.85 (^[A: $i] : refl((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(124,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[123])).
% 3.63/3.85 tff(125,plain,
% 3.63/3.85 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), rewrite((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(126,plain,
% 3.63/3.85 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[125])).
% 3.63/3.85 tff(127,plain,
% 3.63/3.85 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(128,plain,
% 3.63/3.85 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u1_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))) <=> (v1_relat_1(u1_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)))), ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(129,plain,
% 3.63/3.85 (![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[128])).
% 3.63/3.85 tff(130,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(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','fc5_lattice2')).
% 3.63/3.85 tff(131,plain,
% 3.63/3.85 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[130, 129])).
% 3.63/3.85 tff(132,plain,
% 3.63/3.85 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[131, 127])).
% 3.63/3.85 tff(133,plain,(
% 3.63/3.85 ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 3.63/3.85 inference(skolemize,[status(sab)],[132])).
% 3.63/3.85 tff(134,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[133, 126])).
% 3.63/3.85 tff(135,plain,
% 3.63/3.85 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[134, 124])).
% 3.63/3.85 tff(136,plain,
% 3.63/3.85 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(137,plain,
% 3.63/3.85 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 3.63/3.85 inference(quant_inst,[status(thm)],[])).
% 3.63/3.85 tff(138,plain,
% 3.63/3.85 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[137, 136])).
% 3.63/3.85 tff(139,plain,
% 3.63/3.85 ((~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[138, 91, 135])).
% 3.63/3.85 tff(140,plain,
% 3.63/3.85 (~((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[139, 38, 122])).
% 3.63/3.85 tff(141,plain,
% 3.63/3.85 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(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))),
% 3.63/3.85 inference(tautology,[status(thm)],[])).
% 3.63/3.85 tff(142,plain,
% 3.63/3.85 (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))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[141, 140])).
% 3.63/3.85 tff(143,plain,
% 3.63/3.85 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 3.63/3.85 inference(tautology,[status(thm)],[])).
% 3.63/3.85 tff(144,plain,
% 3.63/3.85 (v1_funct_1(u1_lattices(A!0))),
% 3.63/3.85 inference(unit_resolution,[status(thm)],[143, 140])).
% 3.63/3.85 tff(145,plain,
% 3.63/3.85 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(146,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[145])).
% 3.63/3.85 tff(147,plain,
% 3.63/3.85 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) <=> (~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))))), rewrite((~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite(((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(148,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[147])).
% 3.63/3.85 tff(149,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 3.63/3.85 inference(rewrite,[status(thm)],[])).
% 3.63/3.85 tff(150,plain,
% 3.63/3.85 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))))),
% 3.63/3.85 inference(bind,[status(th)],[])).
% 3.63/3.85 tff(151,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 3.63/3.85 inference(quant_intro,[status(thm)],[150])).
% 3.63/3.85 tff(152,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_binop_1')).
% 3.63/3.85 tff(153,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[152, 151])).
% 3.63/3.85 tff(154,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[153, 149])).
% 3.63/3.85 tff(155,plain,(
% 3.63/3.85 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 3.63/3.85 inference(skolemize,[status(sab)],[154])).
% 3.63/3.85 tff(156,plain,
% 3.63/3.85 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.63/3.85 inference(modus_ponens,[status(thm)],[155, 148])).
% 3.70/3.86 tff(157,plain,
% 3.70/3.86 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 3.70/3.86 inference(modus_ponens,[status(thm)],[156, 146])).
% 3.70/3.86 tff(158,plain,
% 3.70/3.86 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 3.70/3.86 inference(and_elim,[status(thm)],[31])).
% 3.70/3.86 tff(159,plain,
% 3.70/3.86 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 3.70/3.86 inference(or_elim,[status(thm)],[158])).
% 3.70/3.86 tff(160,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(161,plain,
% 3.70/3.86 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> ((~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(162,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))),
% 3.70/3.86 inference(monotonicity,[status(thm)],[161])).
% 3.70/3.86 tff(163,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))),
% 3.70/3.86 inference(transitivity,[status(thm)],[162, 160])).
% 3.70/3.86 tff(164,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.70/3.86 inference(quant_inst,[status(thm)],[])).
% 3.70/3.86 tff(165,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))),
% 3.70/3.86 inference(modus_ponens,[status(thm)],[164, 163])).
% 3.70/3.86 tff(166,plain,
% 3.70/3.86 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))),
% 3.70/3.86 inference(unit_resolution,[status(thm)],[165, 159, 157, 144, 142, 99, 61])).
% 3.70/3.86 tff(167,plain,
% 3.70/3.86 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 3.70/3.86 inference(and_elim,[status(thm)],[31])).
% 3.70/3.86 tff(168,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(169,plain,
% 3.70/3.86 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(170,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))),
% 3.70/3.86 inference(monotonicity,[status(thm)],[169])).
% 3.70/3.86 tff(171,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))),
% 3.70/3.86 inference(transitivity,[status(thm)],[170, 168])).
% 3.70/3.86 tff(172,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 3.70/3.86 inference(quant_inst,[status(thm)],[])).
% 3.70/3.86 tff(173,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))),
% 3.70/3.86 inference(modus_ponens,[status(thm)],[172, 171])).
% 3.70/3.86 tff(174,plain,
% 3.70/3.86 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))),
% 3.70/3.86 inference(unit_resolution,[status(thm)],[173, 167, 159, 157, 144, 142, 99, 61])).
% 3.70/3.86 tff(175,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(176,plain,
% 3.70/3.86 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 3.70/3.86 inference(rewrite,[status(thm)],[])).
% 3.70/3.86 tff(177,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))),
% 3.70/3.86 inference(monotonicity,[status(thm)],[176])).
% 3.70/3.86 tff(178,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)))),
% 3.70/3.86 inference(transitivity,[status(thm)],[177, 175])).
% 3.70/3.86 tff(179,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))))),
% 3.70/3.86 inference(quant_inst,[status(thm)],[])).
% 3.70/3.86 tff(180,plain,
% 3.70/3.86 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))),
% 3.70/3.86 inference(modus_ponens,[status(thm)],[179, 178])).
% 3.70/3.86 tff(181,plain,
% 3.70/3.86 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))),
% 3.70/3.86 inference(unit_resolution,[status(thm)],[180, 157, 144, 142, 99, 61, 174, 166])).
% 3.70/3.86 tff(182,plain,
% 3.70/3.86 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 3.70/3.87 inference(rewrite,[status(thm)],[])).
% 3.70/3.87 tff(183,plain,
% 3.70/3.87 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 3.70/3.87 inference(rewrite,[status(thm)],[])).
% 3.70/3.87 tff(184,plain,
% 3.70/3.87 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))))),
% 3.70/3.87 inference(monotonicity,[status(thm)],[183])).
% 3.70/3.87 tff(185,plain,
% 3.70/3.87 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)))),
% 3.70/3.87 inference(transitivity,[status(thm)],[184, 182])).
% 3.70/3.87 tff(186,plain,
% 3.70/3.87 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))))),
% 3.70/3.87 inference(quant_inst,[status(thm)],[])).
% 3.70/3.87 tff(187,plain,
% 3.70/3.87 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~m1_subset_1(B!1, u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))),
% 3.70/3.87 inference(modus_ponens,[status(thm)],[186, 185])).
% 3.70/3.87 tff(188,plain,
% 3.70/3.87 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))),
% 3.70/3.87 inference(unit_resolution,[status(thm)],[187, 167, 157, 144, 142, 99, 61, 166])).
% 3.70/3.87 tff(189,plain,
% 3.70/3.87 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 3.70/3.87 inference(rewrite,[status(thm)],[])).
% 3.70/3.87 tff(190,plain,
% 3.70/3.87 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 3.70/3.87 inference(rewrite,[status(thm)],[])).
% 3.70/3.87 tff(191,plain,
% 3.70/3.87 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 3.70/3.87 inference(monotonicity,[status(thm)],[190])).
% 3.70/3.87 tff(192,plain,
% 3.70/3.87 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 3.72/3.87 inference(transitivity,[status(thm)],[191, 189])).
% 3.72/3.87 tff(193,plain,
% 3.72/3.87 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(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))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))))),
% 3.72/3.87 inference(quant_inst,[status(thm)],[])).
% 3.72/3.87 tff(194,plain,
% 3.72/3.87 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~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_xboole_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_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))),
% 3.72/3.87 inference(modus_ponens,[status(thm)],[193, 192])).
% 3.72/3.87 tff(195,plain,
% 3.72/3.87 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))),
% 3.72/3.87 inference(unit_resolution,[status(thm)],[194, 157, 144, 142, 99, 61, 188, 181])).
% 3.72/3.87 tff(196,plain,
% 3.72/3.87 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))))),
% 3.72/3.87 inference(bind,[status(th)],[])).
% 3.72/3.87 tff(197,plain,
% 3.72/3.87 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 3.72/3.87 inference(quant_intro,[status(thm)],[196])).
% 3.72/3.87 tff(198,plain,
% 3.72/3.87 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) <=> (~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))))), trans(trans(monotonicity(rewrite((r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (~((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), rewrite((~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))), ((r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))) <=> (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))))), rewrite(((v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B))) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))), (((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(199,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[198])).
% 3.72/3.88 tff(200,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(201,plain,
% 3.72/3.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))), (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))))), rewrite((r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))) <=> (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B))))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(202,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C)))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[201])).
% 3.72/3.88 tff(203,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) & m1_subset_1(C, u1_struct_0(B))) => (r2_hidden(A, a_2_0_filter_2(B, C)) <=> ?[D: $i] : ((m1_subset_1(D, u1_struct_0(B)) & (A = D)) & r3_lattices(B, D, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fraenkel_a_2_0_filter_2')).
% 3.72/3.88 tff(204,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[203, 202])).
% 3.72/3.88 tff(205,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[204, 200])).
% 3.72/3.88 tff(206,plain,(
% 3.72/3.88 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C, u1_struct_0(B)))) | (r2_hidden(A, a_2_0_filter_2(B, C)) <=> (r3_lattices(B, A, C) & m1_subset_1(A, u1_struct_0(B)))))),
% 3.72/3.88 inference(skolemize,[status(sab)],[205])).
% 3.72/3.88 tff(207,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[206, 199])).
% 3.72/3.88 tff(208,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[207, 197])).
% 3.72/3.88 tff(209,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(210,plain,
% 3.72/3.88 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(211,plain,
% 3.72/3.88 ((~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))) <=> (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(212,plain,
% 3.72/3.88 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(monotonicity,[status(thm)],[211])).
% 3.72/3.88 tff(213,plain,
% 3.72/3.88 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(transitivity,[status(thm)],[212, 210])).
% 3.72/3.88 tff(214,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))))),
% 3.72/3.88 inference(monotonicity,[status(thm)],[213])).
% 3.72/3.88 tff(215,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(transitivity,[status(thm)],[214, 209])).
% 3.72/3.88 tff(216,plain,
% 3.72/3.88 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(217,plain,
% 3.72/3.88 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[216, 215])).
% 3.72/3.88 tff(218,plain,
% 3.72/3.88 (~(((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[217, 91, 113, 32, 167, 208])).
% 3.72/3.88 tff(219,plain,
% 3.72/3.88 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(220,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[219])).
% 3.72/3.88 tff(221,plain,
% 3.72/3.88 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(222,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[221])).
% 3.72/3.88 tff(223,plain,
% 3.72/3.88 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(224,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[223])).
% 3.72/3.88 tff(225,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(transitivity,[status(thm)],[224, 222])).
% 3.72/3.88 tff(226,plain,
% 3.72/3.88 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(227,plain,
% 3.72/3.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[226])).
% 3.72/3.88 tff(228,plain,
% 3.72/3.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(229,plain,
% 3.72/3.88 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(230,plain,
% 3.72/3.88 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[229])).
% 3.72/3.88 tff(231,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d9_filter_2')).
% 3.72/3.88 tff(232,plain,
% 3.72/3.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[231, 230])).
% 3.72/3.88 tff(233,plain,
% 3.72/3.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[232, 228])).
% 3.72/3.88 tff(234,plain,(
% 3.72/3.88 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(skolemize,[status(sab)],[233])).
% 3.72/3.88 tff(235,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[234, 227])).
% 3.72/3.88 tff(236,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[235, 225])).
% 3.72/3.88 tff(237,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[236, 220])).
% 3.72/3.88 tff(238,plain,
% 3.72/3.88 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(239,plain,
% 3.72/3.88 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(240,plain,
% 3.72/3.88 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[239, 238])).
% 3.72/3.88 tff(241,plain,
% 3.72/3.88 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[240, 91, 113, 32, 237])).
% 3.72/3.88 tff(242,plain,
% 3.72/3.88 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(243,plain,
% 3.72/3.88 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(244,plain,
% 3.72/3.88 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[243, 242])).
% 3.72/3.88 tff(245,plain,
% 3.72/3.88 (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[244, 167, 241])).
% 3.72/3.88 tff(246,plain,
% 3.72/3.88 (a_2_0_filter_2(A!0, B!1) = k18_filter_2(A!0, B!1)),
% 3.72/3.88 inference(symmetry,[status(thm)],[245])).
% 3.72/3.88 tff(247,plain,
% 3.72/3.88 (r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(B!1, k18_filter_2(A!0, B!1))),
% 3.72/3.88 inference(monotonicity,[status(thm)],[246])).
% 3.72/3.88 tff(248,plain,
% 3.72/3.88 (r2_hidden(B!1, k18_filter_2(A!0, B!1)) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))),
% 3.72/3.88 inference(symmetry,[status(thm)],[247])).
% 3.72/3.88 tff(249,plain,
% 3.72/3.88 ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) <=> (~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.88 inference(monotonicity,[status(thm)],[248])).
% 3.72/3.88 tff(250,plain,
% 3.72/3.88 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 3.72/3.88 inference(tautology,[status(thm)],[])).
% 3.72/3.88 tff(251,plain,
% 3.72/3.88 (v6_lattices(A!0)),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[250, 120])).
% 3.72/3.88 tff(252,plain,
% 3.72/3.88 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(253,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[252])).
% 3.72/3.88 tff(254,plain,
% 3.72/3.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(255,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[254])).
% 3.72/3.88 tff(256,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(257,plain,
% 3.72/3.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(258,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[257])).
% 3.72/3.88 tff(259,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 3.72/3.88 tff(260,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[259, 258])).
% 3.72/3.88 tff(261,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[260, 256])).
% 3.72/3.88 tff(262,plain,(
% 3.72/3.88 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 3.72/3.88 inference(skolemize,[status(sab)],[261])).
% 3.72/3.88 tff(263,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[262, 255])).
% 3.72/3.88 tff(264,plain,
% 3.72/3.88 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[263, 253])).
% 3.72/3.88 tff(265,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(266,plain,
% 3.72/3.88 ((v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 3.72/3.88 inference(rewrite,[status(thm)],[])).
% 3.72/3.88 tff(267,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1))))),
% 3.72/3.88 inference(monotonicity,[status(thm)],[266])).
% 3.72/3.88 tff(268,plain,
% 3.72/3.88 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)))),
% 3.72/3.88 inference(transitivity,[status(thm)],[267, 265])).
% 3.72/3.88 tff(269,plain,
% 3.72/3.88 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.72/3.88 inference(quant_inst,[status(thm)],[])).
% 3.72/3.88 tff(270,plain,
% 3.72/3.88 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1))),
% 3.72/3.88 inference(modus_ponens,[status(thm)],[269, 268])).
% 3.72/3.88 tff(271,plain,
% 3.72/3.88 (k4_lattices(A!0, C!2, B!1) = k2_lattices(A!0, C!2, B!1)),
% 3.72/3.88 inference(unit_resolution,[status(thm)],[270, 91, 167, 159, 264, 251, 38])).
% 3.72/3.88 tff(272,plain,
% 3.72/3.88 (k2_lattices(A!0, C!2, B!1) = k4_lattices(A!0, C!2, B!1)),
% 3.72/3.88 inference(symmetry,[status(thm)],[271])).
% 3.72/3.88 tff(273,plain,
% 3.72/3.88 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(274,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[273])).
% 3.72/3.88 tff(275,plain,
% 3.72/3.88 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(276,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[275])).
% 3.72/3.88 tff(277,plain,
% 3.72/3.88 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 3.72/3.88 inference(bind,[status(th)],[])).
% 3.72/3.88 tff(278,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.88 inference(quant_intro,[status(thm)],[277])).
% 3.72/3.88 tff(279,plain,
% 3.72/3.88 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.88 inference(transitivity,[status(thm)],[278, 276])).
% 3.72/3.88 tff(280,plain,
% 3.72/3.88 (^[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))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))))),
% 3.72/3.89 inference(bind,[status(th)],[])).
% 3.72/3.89 tff(281,plain,
% 3.72/3.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.89 inference(quant_intro,[status(thm)],[280])).
% 3.72/3.89 tff(282,plain,
% 3.72/3.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(283,plain,
% 3.72/3.89 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))))),
% 3.72/3.89 inference(bind,[status(th)],[])).
% 3.72/3.89 tff(284,plain,
% 3.72/3.89 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(quant_intro,[status(thm)],[283])).
% 3.72/3.89 tff(285,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattices')).
% 3.72/3.89 tff(286,plain,
% 3.72/3.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[285, 284])).
% 3.72/3.89 tff(287,plain,
% 3.72/3.89 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[286, 282])).
% 3.72/3.89 tff(288,plain,(
% 3.72/3.89 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(skolemize,[status(sab)],[287])).
% 3.72/3.89 tff(289,plain,
% 3.72/3.89 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[288, 281])).
% 3.72/3.89 tff(290,plain,
% 3.72/3.89 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[289, 279])).
% 3.72/3.89 tff(291,plain,
% 3.72/3.89 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[290, 274])).
% 3.72/3.89 tff(292,plain,
% 3.72/3.89 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(293,plain,
% 3.72/3.89 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 3.72/3.89 inference(quant_inst,[status(thm)],[])).
% 3.72/3.89 tff(294,plain,
% 3.72/3.89 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[293, 292])).
% 3.72/3.89 tff(295,plain,
% 3.72/3.89 ((~l1_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 3.72/3.89 inference(unit_resolution,[status(thm)],[294, 91, 291])).
% 3.72/3.89 tff(296,plain,
% 3.72/3.89 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 3.72/3.89 inference(unit_resolution,[status(thm)],[295, 38])).
% 3.72/3.89 tff(297,plain,
% 3.72/3.89 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(298,plain,
% 3.72/3.89 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C))))),
% 3.72/3.89 inference(quant_inst,[status(thm)],[])).
% 3.72/3.89 tff(299,plain,
% 3.72/3.89 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[298, 297])).
% 3.72/3.89 tff(300,plain,
% 3.72/3.89 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))),
% 3.72/3.89 inference(unit_resolution,[status(thm)],[299, 159, 296])).
% 3.72/3.89 tff(301,plain,
% 3.72/3.89 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(302,plain,
% 3.72/3.89 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)))),
% 3.72/3.89 inference(quant_inst,[status(thm)],[])).
% 3.72/3.89 tff(303,plain,
% 3.72/3.89 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[302, 301])).
% 3.72/3.89 tff(304,plain,
% 3.72/3.89 (k2_lattices(A!0, C!2, B!1) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1)),
% 3.72/3.89 inference(unit_resolution,[status(thm)],[303, 167, 300])).
% 3.72/3.89 tff(305,plain,
% 3.72/3.89 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k2_lattices(A!0, C!2, B!1)),
% 3.72/3.89 inference(symmetry,[status(thm)],[304])).
% 3.72/3.89 tff(306,plain,
% 3.72/3.89 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k4_lattices(A!0, C!2, B!1)),
% 3.72/3.89 inference(transitivity,[status(thm)],[305, 272])).
% 3.72/3.89 tff(307,plain,
% 3.72/3.89 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))),
% 3.72/3.89 inference(monotonicity,[status(thm)],[306, 246])).
% 3.72/3.89 tff(308,plain,
% 3.72/3.89 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(309,plain,
% 3.72/3.89 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(310,plain,
% 3.72/3.89 ((~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(311,plain,
% 3.72/3.89 ((((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) <=> (((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.89 inference(rewrite,[status(thm)],[])).
% 3.72/3.89 tff(312,plain,
% 3.72/3.89 ((~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.89 inference(monotonicity,[status(thm)],[311])).
% 3.72/3.89 tff(313,plain,
% 3.72/3.89 ((~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))) <=> (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.89 inference(transitivity,[status(thm)],[312, 310])).
% 3.72/3.89 tff(314,plain,
% 3.72/3.89 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(monotonicity,[status(thm)],[313])).
% 3.72/3.89 tff(315,plain,
% 3.72/3.89 ((v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(transitivity,[status(thm)],[314, 309])).
% 3.72/3.89 tff(316,plain,
% 3.72/3.89 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))))),
% 3.72/3.89 inference(monotonicity,[status(thm)],[315])).
% 3.72/3.89 tff(317,plain,
% 3.72/3.89 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(transitivity,[status(thm)],[316, 308])).
% 3.72/3.89 tff(318,plain,
% 3.72/3.89 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(((~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0)))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))))),
% 3.72/3.89 inference(quant_inst,[status(thm)],[])).
% 3.72/3.89 tff(319,plain,
% 3.72/3.89 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(B) | (~m1_subset_1(C, u1_struct_0(B))) | (~v10_lattices(B)) | (~l3_lattices(B)) | (~(((~r3_lattices(B, A, C)) | (~m1_subset_1(A, u1_struct_0(B)))) <=> r2_hidden(A, a_2_0_filter_2(B, C)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))))),
% 3.72/3.89 inference(modus_ponens,[status(thm)],[318, 317])).
% 3.72/3.89 tff(320,plain,
% 3.72/3.89 (~(((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)))),
% 3.72/3.89 inference(unit_resolution,[status(thm)],[319, 91, 113, 32, 167, 208])).
% 3.72/3.89 tff(321,plain,
% 3.72/3.89 (^[A: $i, B: $i, C: $i] : refl(((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 3.72/3.89 inference(bind,[status(th)],[])).
% 3.72/3.89 tff(322,plain,
% 3.72/3.89 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.89 inference(quant_intro,[status(thm)],[321])).
% 3.72/3.89 tff(323,plain,
% 3.72/3.89 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 3.72/3.89 inference(bind,[status(th)],[])).
% 3.72/3.89 tff(324,plain,
% 3.72/3.89 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[323])).
% 3.72/3.90 tff(325,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(326,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(327,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[326])).
% 3.72/3.90 tff(328,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 3.72/3.90 tff(329,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[328, 327])).
% 3.72/3.90 tff(330,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[329, 325])).
% 3.72/3.90 tff(331,plain,(
% 3.72/3.90 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 3.72/3.90 inference(skolemize,[status(sab)],[330])).
% 3.72/3.90 tff(332,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[331, 324])).
% 3.72/3.90 tff(333,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[332, 322])).
% 3.72/3.90 tff(334,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(335,plain,
% 3.72/3.90 (((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(336,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2))))),
% 3.72/3.90 inference(monotonicity,[status(thm)],[335])).
% 3.72/3.90 tff(337,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)))),
% 3.72/3.90 inference(transitivity,[status(thm)],[336, 334])).
% 3.72/3.90 tff(338,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))))),
% 3.72/3.90 inference(quant_inst,[status(thm)],[])).
% 3.72/3.90 tff(339,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[338, 337])).
% 3.72/3.90 tff(340,plain,
% 3.72/3.90 (k4_lattices(A!0, C!2, B!1) = k4_lattices(A!0, B!1, C!2)),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[339, 91, 167, 159, 333, 251, 38])).
% 3.72/3.90 tff(341,plain,
% 3.72/3.90 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1) = k4_lattices(A!0, B!1, C!2)),
% 3.72/3.90 inference(transitivity,[status(thm)],[305, 272, 340])).
% 3.72/3.90 tff(342,plain,
% 3.72/3.90 (r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1) <=> r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.90 inference(monotonicity,[status(thm)],[341])).
% 3.72/3.90 tff(343,plain,
% 3.72/3.90 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)),
% 3.72/3.90 inference(symmetry,[status(thm)],[342])).
% 3.72/3.90 tff(344,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(345,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[344])).
% 3.72/3.90 tff(346,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(347,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[346])).
% 3.72/3.90 tff(348,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(349,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(350,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[349])).
% 3.72/3.90 tff(351,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattices')).
% 3.72/3.90 tff(352,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[351, 350])).
% 3.72/3.90 tff(353,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[352, 348])).
% 3.72/3.90 tff(354,plain,(
% 3.72/3.90 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 3.72/3.90 inference(skolemize,[status(sab)],[353])).
% 3.72/3.90 tff(355,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[354, 347])).
% 3.72/3.90 tff(356,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[355, 345])).
% 3.72/3.90 tff(357,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(358,plain,
% 3.72/3.90 ((v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(359,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 3.72/3.90 inference(monotonicity,[status(thm)],[358])).
% 3.72/3.90 tff(360,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 3.72/3.90 inference(transitivity,[status(thm)],[359, 357])).
% 3.72/3.90 tff(361,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 3.72/3.90 inference(quant_inst,[status(thm)],[])).
% 3.72/3.90 tff(362,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[361, 360])).
% 3.72/3.90 tff(363,plain,
% 3.72/3.90 (m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[362, 91, 167, 159, 356, 251, 38])).
% 3.72/3.90 tff(364,plain,
% 3.72/3.90 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v9_lattices(A!0)),
% 3.72/3.90 inference(tautology,[status(thm)],[])).
% 3.72/3.90 tff(365,plain,
% 3.72/3.90 (v9_lattices(A!0)),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[364, 120])).
% 3.72/3.90 tff(366,plain,
% 3.72/3.90 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v8_lattices(A!0)),
% 3.72/3.90 inference(tautology,[status(thm)],[])).
% 3.72/3.90 tff(367,plain,
% 3.72/3.90 (v8_lattices(A!0)),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[366, 120])).
% 3.72/3.90 tff(368,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(369,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[368])).
% 3.72/3.90 tff(370,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(371,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[370])).
% 3.72/3.90 tff(372,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(373,plain,
% 3.72/3.90 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(374,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[373])).
% 3.72/3.90 tff(375,axiom,(![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 3.72/3.90 tff(376,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[375, 374])).
% 3.72/3.90 tff(377,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[376, 372])).
% 3.72/3.90 tff(378,plain,(
% 3.72/3.90 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 3.72/3.90 inference(skolemize,[status(sab)],[377])).
% 3.72/3.90 tff(379,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[378, 371])).
% 3.72/3.90 tff(380,plain,
% 3.72/3.90 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[379, 369])).
% 3.72/3.90 tff(381,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(382,plain,
% 3.72/3.90 ((v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 3.72/3.90 inference(rewrite,[status(thm)],[])).
% 3.72/3.90 tff(383,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))))),
% 3.72/3.90 inference(monotonicity,[status(thm)],[382])).
% 3.72/3.90 tff(384,plain,
% 3.72/3.90 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))))),
% 3.72/3.90 inference(transitivity,[status(thm)],[383, 381])).
% 3.72/3.90 tff(385,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))),
% 3.72/3.90 inference(quant_inst,[status(thm)],[])).
% 3.72/3.90 tff(386,plain,
% 3.72/3.90 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 3.72/3.90 inference(modus_ponens,[status(thm)],[385, 384])).
% 3.72/3.90 tff(387,plain,
% 3.72/3.90 ((r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)) | (~m1_subset_1(k4_lattices(A!0, B!1, C!2), u1_struct_0(A!0)))),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[386, 91, 32, 167, 380, 251, 367, 365])).
% 3.72/3.90 tff(388,plain,
% 3.72/3.90 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.90 inference(unit_resolution,[status(thm)],[387, 363])).
% 3.72/3.90 tff(389,plain,
% 3.72/3.90 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(390,plain,
% 3.72/3.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[389])).
% 3.72/3.90 tff(391,plain,
% 3.72/3.90 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(392,plain,
% 3.72/3.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.90 inference(quant_intro,[status(thm)],[391])).
% 3.72/3.90 tff(393,plain,
% 3.72/3.90 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))))),
% 3.72/3.90 inference(bind,[status(th)],[])).
% 3.72/3.90 tff(394,plain,
% 3.72/3.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[393])).
% 3.72/3.91 tff(395,plain,
% 3.72/3.91 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.91 inference(transitivity,[status(thm)],[394, 392])).
% 3.72/3.91 tff(396,plain,
% 3.72/3.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))))),
% 3.72/3.91 inference(bind,[status(th)],[])).
% 3.72/3.91 tff(397,plain,
% 3.72/3.91 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[396])).
% 3.72/3.91 tff(398,plain,
% 3.72/3.91 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(399,plain,
% 3.72/3.91 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)) <=> ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))))),
% 3.72/3.91 inference(bind,[status(th)],[])).
% 3.72/3.91 tff(400,plain,
% 3.72/3.91 (![A: $i] : (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[399])).
% 3.72/3.91 tff(401,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => r1_lattices(A, k4_lattices(A, B, C), B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t23_lattices')).
% 3.72/3.91 tff(402,plain,
% 3.72/3.91 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[401, 400])).
% 3.72/3.91 tff(403,plain,
% 3.72/3.91 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[402, 398])).
% 3.72/3.91 tff(404,plain,(
% 3.72/3.91 ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(skolemize,[status(sab)],[403])).
% 3.72/3.91 tff(405,plain,
% 3.72/3.91 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[404, 397])).
% 3.72/3.91 tff(406,plain,
% 3.72/3.91 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))) | (~v6_lattices(A)) | (~v8_lattices(A)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[405, 395])).
% 3.72/3.91 tff(407,plain,
% 3.72/3.91 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[406, 390])).
% 3.72/3.91 tff(408,plain,
% 3.72/3.91 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(409,plain,
% 3.72/3.91 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B))))),
% 3.72/3.91 inference(quant_inst,[status(thm)],[])).
% 3.72/3.91 tff(410,plain,
% 3.72/3.91 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v6_lattices(A)) | (~v8_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | r1_lattices(A, k4_lattices(A, B, C), B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[409, 408])).
% 3.72/3.91 tff(411,plain,
% 3.72/3.91 ((~v6_lattices(A!0)) | (~v8_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[410, 91, 32, 407])).
% 3.72/3.91 tff(412,plain,
% 3.72/3.91 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[411, 367, 251])).
% 3.72/3.91 tff(413,plain,
% 3.72/3.91 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1)))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(414,plain,
% 3.72/3.91 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1)))),
% 3.72/3.91 inference(quant_inst,[status(thm)],[])).
% 3.72/3.91 tff(415,plain,
% 3.72/3.91 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B, C), B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[414, 413])).
% 3.72/3.91 tff(416,plain,
% 3.72/3.91 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[415, 167, 412])).
% 3.72/3.91 tff(417,plain,
% 3.72/3.91 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(418,plain,
% 3.72/3.91 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 3.72/3.91 inference(quant_inst,[status(thm)],[])).
% 3.72/3.91 tff(419,plain,
% 3.72/3.91 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C), B!1))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[418, 417])).
% 3.72/3.91 tff(420,plain,
% 3.72/3.91 (r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[419, 159, 416])).
% 3.72/3.91 tff(421,plain,
% 3.72/3.91 ((~(r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) | r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) | (~r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))),
% 3.72/3.91 inference(tautology,[status(thm)],[])).
% 3.72/3.91 tff(422,plain,
% 3.72/3.91 ((~(r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1) <=> r1_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1))) | r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[421, 420])).
% 3.72/3.91 tff(423,plain,
% 3.72/3.91 (r3_lattices(A!0, k4_lattices(A!0, B!1, C!2), B!1)),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[422, 388])).
% 3.72/3.91 tff(424,plain,
% 3.72/3.91 (r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[423, 343])).
% 3.72/3.91 tff(425,plain,
% 3.72/3.91 ((~((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))),
% 3.72/3.91 inference(tautology,[status(thm)],[])).
% 3.72/3.91 tff(426,plain,
% 3.72/3.91 ((~((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[425, 174])).
% 3.72/3.91 tff(427,plain,
% 3.72/3.91 (~((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1)))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[426, 424])).
% 3.72/3.91 tff(428,plain,
% 3.72/3.91 ((((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) <=> r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))) | ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), u1_struct_0(A!0))) | (~r3_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), B!1))) | r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 3.72/3.91 inference(tautology,[status(thm)],[])).
% 3.72/3.91 tff(429,plain,
% 3.72/3.91 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[428, 427, 320])).
% 3.72/3.91 tff(430,plain,
% 3.72/3.91 (r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[429, 307])).
% 3.72/3.91 tff(431,plain,
% 3.72/3.91 (k4_lattices(A!0, B!1, C!2) = k4_lattices(A!0, C!2, B!1)),
% 3.72/3.91 inference(symmetry,[status(thm)],[340])).
% 3.72/3.91 tff(432,plain,
% 3.72/3.91 (r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(monotonicity,[status(thm)],[431])).
% 3.72/3.91 tff(433,plain,
% 3.72/3.91 (r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(symmetry,[status(thm)],[432])).
% 3.72/3.91 tff(434,plain,
% 3.72/3.91 (r2_hidden(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1), a_2_0_filter_2(A!0, B!1)) <=> r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(transitivity,[status(thm)],[307, 433])).
% 3.72/3.91 tff(435,plain,
% 3.72/3.91 (r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[429, 434])).
% 3.72/3.91 tff(436,plain,
% 3.72/3.91 ((~(~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))) <=> ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(437,plain,
% 3.72/3.91 ((r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))) <=> (~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(438,plain,
% 3.72/3.91 ((~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))) <=> (~(~((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))))),
% 3.72/3.91 inference(monotonicity,[status(thm)],[437])).
% 3.72/3.91 tff(439,plain,
% 3.72/3.91 ((~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))) <=> ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1))))),
% 3.72/3.91 inference(transitivity,[status(thm)],[438, 436])).
% 3.72/3.91 tff(440,plain,
% 3.72/3.91 (~(r2_hidden(B!1, k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1)) & r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))),
% 3.72/3.91 inference(or_elim,[status(thm)],[158])).
% 3.72/3.91 tff(441,plain,
% 3.72/3.91 ((~r2_hidden(B!1, k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, B!1, C!2), k18_filter_2(A!0, B!1))) | (~r2_hidden(k4_lattices(A!0, C!2, B!1), k18_filter_2(A!0, B!1)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[440, 439])).
% 3.72/3.91 tff(442,plain,
% 3.72/3.91 (~r2_hidden(B!1, k18_filter_2(A!0, B!1))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[441, 435, 430])).
% 3.72/3.91 tff(443,plain,
% 3.72/3.91 (~r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[442, 249])).
% 3.72/3.91 tff(444,plain,
% 3.72/3.91 ((((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))) | ((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) | r2_hidden(B!1, a_2_0_filter_2(A!0, B!1))),
% 3.72/3.91 inference(tautology,[status(thm)],[])).
% 3.72/3.91 tff(445,plain,
% 3.72/3.91 ((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[444, 443, 218])).
% 3.72/3.91 tff(446,plain,
% 3.72/3.91 ((~((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) | (~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))),
% 3.72/3.91 inference(tautology,[status(thm)],[])).
% 3.72/3.91 tff(447,plain,
% 3.72/3.91 ((~((~r3_lattices(A!0, B!1, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) | (~r3_lattices(A!0, B!1, B!1))),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[446, 167])).
% 3.72/3.91 tff(448,plain,
% 3.72/3.91 (~r3_lattices(A!0, B!1, B!1)),
% 3.72/3.91 inference(unit_resolution,[status(thm)],[447, 445])).
% 3.72/3.91 tff(449,plain,
% 3.72/3.91 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))),
% 3.72/3.91 inference(bind,[status(th)],[])).
% 3.72/3.91 tff(450,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[449])).
% 3.72/3.91 tff(451,plain,
% 3.72/3.91 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | r3_lattices(A, B, B)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | r3_lattices(A, B, B)) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))))),
% 3.72/3.91 inference(bind,[status(th)],[])).
% 3.72/3.91 tff(452,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[451])).
% 3.72/3.91 tff(453,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(454,plain,
% 3.72/3.91 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))))),
% 3.72/3.91 inference(bind,[status(th)],[])).
% 3.72/3.91 tff(455,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B)) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 3.72/3.91 inference(quant_intro,[status(thm)],[454])).
% 3.72/3.91 tff(456,axiom,(![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => r3_lattices(A, B, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','reflexivity_r3_lattices')).
% 3.72/3.91 tff(457,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[456, 455])).
% 3.72/3.91 tff(458,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[457, 453])).
% 3.72/3.91 tff(459,plain,(
% 3.72/3.91 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | r3_lattices(A, B, B))),
% 3.72/3.91 inference(skolemize,[status(sab)],[458])).
% 3.72/3.91 tff(460,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[459, 452])).
% 3.72/3.91 tff(461,plain,
% 3.72/3.91 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 3.72/3.91 inference(modus_ponens,[status(thm)],[460, 450])).
% 3.72/3.91 tff(462,plain,
% 3.72/3.91 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 3.72/3.91 inference(rewrite,[status(thm)],[])).
% 3.72/3.91 tff(463,plain,
% 3.72/3.91 ((v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 3.72/3.92 inference(rewrite,[status(thm)],[])).
% 3.72/3.92 tff(464,plain,
% 3.72/3.92 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))))),
% 3.72/3.92 inference(monotonicity,[status(thm)],[463])).
% 3.72/3.92 tff(465,plain,
% 3.72/3.92 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))))),
% 3.72/3.92 inference(transitivity,[status(thm)],[464, 462])).
% 3.72/3.92 tff(466,plain,
% 3.72/3.92 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))),
% 3.72/3.92 inference(quant_inst,[status(thm)],[])).
% 3.72/3.92 tff(467,plain,
% 3.72/3.92 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | r3_lattices(A, B, B) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v8_lattices(A!0)) | (~v6_lattices(A!0)) | (~l3_lattices(A!0)) | (~v9_lattices(A!0)) | r3_lattices(A!0, B!1, B!1) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B!1, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2)), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, C!2), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), C!2, B!1))), u1_struct_0(A!0)))),
% 3.72/3.92 inference(modus_ponens,[status(thm)],[466, 465])).
% 3.72/3.92 tff(468,plain,
% 3.72/3.92 ($false),
% 3.72/3.92 inference(unit_resolution,[status(thm)],[467, 91, 32, 167, 461, 251, 367, 365, 448, 195])).
% 3.72/3.92 % SZS output end Proof
% 3.79/3.94 % E exiting
%------------------------------------------------------------------------------