%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT329+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.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 05:14:22 AM UTC 2025
% Result : Theorem 84.97s 85.16s
% Output : Proof 85.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LAT329+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:22:26 EDT 2025
% 0.12/0.33 % CPUTime :
% 84.97/85.16 % SZS status Theorem
% 84.97/85.16 % SZS output start Proof
% 84.97/85.16 tff(r2_hidden_type, type, (
% 84.97/85.16 r2_hidden: ( $i * $i ) > $o)).
% 84.97/85.16 tff(k2_filter_0_type, type, (
% 84.97/85.16 k2_filter_0: ( $i * $i ) > $i)).
% 84.97/85.16 tff(tptp_fun_B_1_type, type, (
% 84.97/85.16 tptp_fun_B_1: $i)).
% 84.97/85.16 tff(tptp_fun_A_0_type, type, (
% 84.97/85.16 tptp_fun_A_0: $i)).
% 84.97/85.16 tff(tptp_fun_D_2_type, type, (
% 84.97/85.16 tptp_fun_D_2: ( $i * $i * $i ) > $i)).
% 84.97/85.16 tff(u1_struct_0_type, type, (
% 84.97/85.16 u1_struct_0: $i > $i)).
% 84.97/85.16 tff(k22_filter_2_type, type, (
% 84.97/85.16 k22_filter_2: ( $i * $i * $i ) > $i)).
% 84.97/85.16 tff(k6_lattices_type, type, (
% 84.97/85.16 k6_lattices: $i > $i)).
% 84.97/85.16 tff(r3_lattices_type, type, (
% 84.97/85.16 r3_lattices: ( $i * $i * $i ) > $o)).
% 84.97/85.16 tff(m1_subset_1_type, type, (
% 84.97/85.16 m1_subset_1: ( $i * $i ) > $o)).
% 84.97/85.16 tff(r1_filter_2_type, type, (
% 84.97/85.16 r1_filter_2: ( $i * $i * $i ) > $o)).
% 84.97/85.16 tff(k1_zfmisc_1_type, type, (
% 84.97/85.16 k1_zfmisc_1: $i > $i)).
% 84.97/85.16 tff(v1_xboole_0_type, type, (
% 84.97/85.16 v1_xboole_0: $i > $o)).
% 84.97/85.16 tff(l1_struct_0_type, type, (
% 84.97/85.16 l1_struct_0: $i > $o)).
% 84.97/85.16 tff(l2_lattices_type, type, (
% 84.97/85.16 l2_lattices: $i > $o)).
% 84.97/85.16 tff(l1_lattices_type, type, (
% 84.97/85.16 l1_lattices: $i > $o)).
% 84.97/85.16 tff(l3_lattices_type, type, (
% 84.97/85.16 l3_lattices: $i > $o)).
% 84.97/85.16 tff(k2_filter_2_type, type, (
% 84.97/85.16 k2_filter_2: ( $i * $i ) > $i)).
% 84.97/85.16 tff(v14_lattices_type, type, (
% 84.97/85.16 v14_lattices: $i > $o)).
% 84.97/85.16 tff(v10_lattices_type, type, (
% 84.97/85.16 v10_lattices: $i > $o)).
% 84.97/85.16 tff(v3_struct_0_type, type, (
% 84.97/85.16 v3_struct_0: $i > $o)).
% 84.97/85.16 tff(m1_filter_0_type, type, (
% 84.97/85.16 m1_filter_0: ( $i * $i ) > $o)).
% 84.97/85.16 tff(m2_lattice4_type, type, (
% 84.97/85.16 m2_lattice4: ( $i * $i ) > $o)).
% 84.97/85.16 tff(1,assumption,(~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))), introduced(assumption)).
% 84.97/85.16 tff(2,plain,
% 84.97/85.16 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(3,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[2])).
% 84.97/85.16 tff(4,plain,
% 84.97/85.16 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(5,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[4])).
% 84.97/85.16 tff(6,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(7,plain,
% 84.97/85.16 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(8,plain,
% 84.97/85.16 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[7])).
% 84.97/85.16 tff(9,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 84.97/85.16 tff(10,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[9, 8])).
% 84.97/85.16 tff(11,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[10, 6])).
% 84.97/85.16 tff(12,plain,(
% 84.97/85.16 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 84.97/85.16 inference(skolemize,[status(sab)],[11])).
% 84.97/85.16 tff(13,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[12, 5])).
% 84.97/85.16 tff(14,plain,
% 84.97/85.16 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[13, 3])).
% 84.97/85.16 tff(15,plain,
% 84.97/85.16 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(16,plain,
% 84.97/85.16 ((~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(17,plain,
% 84.97/85.16 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 84.97/85.16 inference(monotonicity,[status(thm)],[16])).
% 84.97/85.16 tff(18,plain,
% 84.97/85.16 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))))),
% 84.97/85.16 inference(transitivity,[status(thm)],[17, 15])).
% 84.97/85.16 tff(19,plain,
% 84.97/85.16 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(20,plain,
% 84.97/85.16 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(21,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t66_filter_2')).
% 84.97/85.16 tff(22,plain,
% 84.97/85.16 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[21, 20])).
% 84.97/85.16 tff(23,plain,
% 84.97/85.16 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[22, 19])).
% 84.97/85.16 tff(24,plain,
% 84.97/85.16 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[23, 19])).
% 84.97/85.16 tff(25,plain,
% 84.97/85.16 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (r1_filter_2(u1_struct_0(A), k2_filter_2(A, B), k22_filter_2(A, B, k6_lattices(A))) | (~v14_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[24, 19])).
% 84.97/85.16 tff(26,plain,
% 84.97/85.16 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0)))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[25, 18])).
% 84.97/85.16 tff(27,plain,
% 84.97/85.16 (l3_lattices(A!0)),
% 84.97/85.16 inference(and_elim,[status(thm)],[26])).
% 84.97/85.16 tff(28,plain,
% 84.97/85.16 (((~![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)))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(29,plain,
% 84.97/85.16 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 84.97/85.16 inference(quant_inst,[status(thm)],[])).
% 84.97/85.16 tff(30,plain,
% 84.97/85.16 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[29, 28])).
% 84.97/85.16 tff(31,plain,
% 84.97/85.16 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 84.97/85.16 inference(unit_resolution,[status(thm)],[30, 27, 14])).
% 84.97/85.16 tff(32,plain,
% 84.97/85.16 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 84.97/85.16 inference(tautology,[status(thm)],[])).
% 84.97/85.16 tff(33,plain,
% 84.97/85.16 (l2_lattices(A!0)),
% 84.97/85.16 inference(unit_resolution,[status(thm)],[32, 31])).
% 84.97/85.16 tff(34,plain,
% 84.97/85.16 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(35,plain,
% 84.97/85.16 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[34])).
% 84.97/85.16 tff(36,plain,
% 84.97/85.16 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(37,plain,
% 84.97/85.16 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(38,plain,
% 84.97/85.16 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[37])).
% 84.97/85.16 tff(39,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 84.97/85.16 tff(40,plain,
% 84.97/85.16 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[39, 38])).
% 84.97/85.16 tff(41,plain,
% 84.97/85.16 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[40, 36])).
% 84.97/85.16 tff(42,plain,(
% 84.97/85.16 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(skolemize,[status(sab)],[41])).
% 84.97/85.16 tff(43,plain,
% 84.97/85.16 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[42, 35])).
% 84.97/85.16 tff(44,plain,
% 84.97/85.16 (((~![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)))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(45,plain,
% 84.97/85.16 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 84.97/85.16 inference(quant_inst,[status(thm)],[])).
% 84.97/85.16 tff(46,plain,
% 84.97/85.16 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[45, 44])).
% 84.97/85.16 tff(47,plain,
% 84.97/85.16 (l1_struct_0(A!0)),
% 84.97/85.16 inference(unit_resolution,[status(thm)],[46, 43, 33])).
% 84.97/85.16 tff(48,plain,
% 84.97/85.16 (^[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))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(49,plain,
% 84.97/85.16 (![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)))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[48])).
% 84.97/85.16 tff(50,plain,
% 84.97/85.16 (^[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)))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(51,plain,
% 84.97/85.16 (![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)))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[50])).
% 84.97/85.16 tff(52,plain,
% 84.97/85.16 (![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))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(53,plain,
% 84.97/85.16 (^[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)))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(54,plain,
% 84.97/85.16 (![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))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[53])).
% 84.97/85.16 tff(55,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 84.97/85.16 tff(56,plain,
% 84.97/85.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[55, 54])).
% 84.97/85.16 tff(57,plain,
% 84.97/85.16 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[56, 52])).
% 84.97/85.16 tff(58,plain,(
% 84.97/85.16 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 84.97/85.16 inference(skolemize,[status(sab)],[57])).
% 84.97/85.16 tff(59,plain,
% 84.97/85.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[58, 51])).
% 84.97/85.16 tff(60,plain,
% 84.97/85.16 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[59, 49])).
% 84.97/85.16 tff(61,plain,
% 84.97/85.16 (~v3_struct_0(A!0)),
% 84.97/85.16 inference(and_elim,[status(thm)],[26])).
% 84.97/85.16 tff(62,plain,
% 84.97/85.16 (((~![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))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(63,plain,
% 84.97/85.16 ((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))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(64,plain,
% 84.97/85.16 (((~![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)))))),
% 84.97/85.16 inference(monotonicity,[status(thm)],[63])).
% 84.97/85.16 tff(65,plain,
% 84.97/85.16 (((~![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))))),
% 84.97/85.16 inference(transitivity,[status(thm)],[64, 62])).
% 84.97/85.16 tff(66,plain,
% 84.97/85.16 ((~![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)))),
% 84.97/85.16 inference(quant_inst,[status(thm)],[])).
% 84.97/85.16 tff(67,plain,
% 84.97/85.16 ((~![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)))),
% 84.97/85.16 inference(modus_ponens,[status(thm)],[66, 65])).
% 84.97/85.16 tff(68,plain,
% 84.97/85.16 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 84.97/85.16 inference(unit_resolution,[status(thm)],[67, 61, 60])).
% 84.97/85.16 tff(69,plain,
% 84.97/85.16 (~v1_xboole_0(u1_struct_0(A!0))),
% 84.97/85.16 inference(unit_resolution,[status(thm)],[68, 47])).
% 84.97/85.16 tff(70,plain,
% 84.97/85.16 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(71,plain,
% 84.97/85.16 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[70])).
% 84.97/85.16 tff(72,plain,
% 84.97/85.16 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(73,plain,
% 84.97/85.16 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[72])).
% 84.97/85.16 tff(74,plain,
% 84.97/85.16 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.16 inference(transitivity,[status(thm)],[73, 71])).
% 84.97/85.16 tff(75,plain,
% 84.97/85.16 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(76,plain,
% 84.97/85.16 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C))))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.16 inference(quant_intro,[status(thm)],[75])).
% 84.97/85.16 tff(77,plain,
% 84.97/85.16 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 84.97/85.16 inference(rewrite,[status(thm)],[])).
% 84.97/85.16 tff(78,plain,
% 84.97/85.16 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))) <=> (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), rewrite((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))), ((m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))) <=> ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))), ((m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), (((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))))),
% 84.97/85.16 inference(bind,[status(th)],[])).
% 84.97/85.16 tff(79,plain,
% 84.97/85.16 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[78])).
% 84.97/85.17 tff(80,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(A)) => ![C: $i] : (m1_subset_1(C, k1_zfmisc_1(A)) => (r1_filter_2(A, B, C) <=> ![D: $i] : (m1_subset_1(D, A) => (r2_hidden(D, B) <=> r2_hidden(D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_filter_2')).
% 84.97/85.17 tff(81,plain,
% 84.97/85.17 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[80, 79])).
% 84.97/85.17 tff(82,plain,
% 84.97/85.17 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (r1_filter_2(A, B, C) <=> ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[81, 77])).
% 84.97/85.17 tff(83,plain,(
% 84.97/85.17 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C)))) & (r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))),
% 84.97/85.17 inference(skolemize,[status(sab)],[82])).
% 84.97/85.17 tff(84,plain,
% 84.97/85.17 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[83, 76])).
% 84.97/85.17 tff(85,plain,
% 84.97/85.17 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[84, 74])).
% 84.97/85.17 tff(86,plain,
% 84.97/85.17 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(87,plain,
% 84.97/85.17 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C)))))))))))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(88,plain,
% 84.97/85.17 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(A))) | (~((~((~r1_filter_2(A, B, C)) | ![D: $i] : ((~m1_subset_1(D, A)) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(A, B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, A), A)) | (r2_hidden(tptp_fun_D_2(C, B, A), B) <=> r2_hidden(tptp_fun_D_2(C, B, A), C)))))))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[87, 86])).
% 84.97/85.17 tff(89,plain,
% 84.97/85.17 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[88, 85, 69])).
% 84.97/85.17 tff(90,plain,
% 84.97/85.17 (^[A: $i, B: $i] : refl((m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(91,plain,
% 84.97/85.17 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[90])).
% 84.97/85.17 tff(92,plain,
% 84.97/85.17 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_0(k2_filter_0(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_0(k2_filter_0(A, B), A)) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(93,plain,
% 84.97/85.17 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[92])).
% 84.97/85.17 tff(94,plain,
% 84.97/85.17 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(95,plain,
% 84.97/85.17 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(96,plain,
% 84.97/85.17 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[95])).
% 84.97/85.17 tff(97,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_filter_0(k2_filter_0(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_filter_0')).
% 84.97/85.17 tff(98,plain,
% 84.97/85.17 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[97, 96])).
% 84.97/85.17 tff(99,plain,
% 84.97/85.17 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[98, 94])).
% 84.97/85.17 tff(100,plain,(
% 84.97/85.17 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_filter_0(k2_filter_0(A, B), A))),
% 84.97/85.17 inference(skolemize,[status(sab)],[99])).
% 84.97/85.17 tff(101,plain,
% 84.97/85.17 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[100, 93])).
% 84.97/85.17 tff(102,plain,
% 84.97/85.17 (![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[101, 91])).
% 84.97/85.17 tff(103,plain,
% 84.97/85.17 (~((~v14_lattices(A!0)) | r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 84.97/85.17 inference(and_elim,[status(thm)],[26])).
% 84.97/85.17 tff(104,plain,
% 84.97/85.17 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 84.97/85.17 inference(or_elim,[status(thm)],[103])).
% 84.97/85.17 tff(105,plain,
% 84.97/85.17 (v10_lattices(A!0)),
% 84.97/85.17 inference(and_elim,[status(thm)],[26])).
% 84.97/85.17 tff(106,plain,
% 84.97/85.17 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(107,plain,
% 84.97/85.17 ((m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(108,plain,
% 84.97/85.17 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0)))),
% 84.97/85.17 inference(monotonicity,[status(thm)],[107])).
% 84.97/85.17 tff(109,plain,
% 84.97/85.17 (((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0))),
% 84.97/85.17 inference(transitivity,[status(thm)],[108, 106])).
% 84.97/85.17 tff(110,plain,
% 84.97/85.17 ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_0(k2_filter_0(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(111,plain,
% 84.97/85.17 ((~![A: $i, B: $i] : (m1_filter_0(k2_filter_0(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(k2_filter_0(A!0, B!1), A!0)),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[110, 109])).
% 84.97/85.17 tff(112,plain,
% 84.97/85.17 (m1_filter_0(k2_filter_0(A!0, B!1), A!0)),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[111, 61, 105, 27, 104, 102])).
% 84.97/85.17 tff(113,plain,
% 84.97/85.17 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(114,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[113])).
% 84.97/85.17 tff(115,plain,
% 84.97/85.17 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(116,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[115])).
% 84.97/85.17 tff(117,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(transitivity,[status(thm)],[116, 114])).
% 84.97/85.17 tff(118,plain,
% 84.97/85.17 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(119,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[118])).
% 84.97/85.17 tff(120,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(121,plain,
% 84.97/85.17 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(122,plain,
% 84.97/85.17 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[121])).
% 84.97/85.17 tff(123,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 84.97/85.17 tff(124,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[123, 122])).
% 84.97/85.17 tff(125,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[124, 120])).
% 84.97/85.17 tff(126,plain,(
% 84.97/85.17 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.17 inference(skolemize,[status(sab)],[125])).
% 84.97/85.17 tff(127,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[126, 119])).
% 84.97/85.17 tff(128,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[127, 117])).
% 84.97/85.17 tff(129,plain,
% 84.97/85.17 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(130,plain,
% 84.97/85.17 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(131,plain,
% 84.97/85.17 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[130, 129])).
% 84.97/85.17 tff(132,plain,
% 84.97/85.17 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[131, 61, 105, 27, 128])).
% 84.97/85.17 tff(133,plain,
% 84.97/85.17 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(134,plain,
% 84.97/85.17 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(135,plain,
% 84.97/85.17 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(k2_filter_0(A!0, B!1), A!0)) | (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[134, 133])).
% 84.97/85.17 tff(136,plain,
% 84.97/85.17 (~(v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[135, 132, 112])).
% 84.97/85.17 tff(137,plain,
% 84.97/85.17 ((v1_xboole_0(k2_filter_0(A!0, B!1)) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 84.97/85.17 inference(tautology,[status(thm)],[])).
% 84.97/85.17 tff(138,plain,
% 84.97/85.17 (m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[137, 136])).
% 84.97/85.17 tff(139,plain,
% 84.97/85.17 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C))))))))))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(140,plain,
% 84.97/85.17 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | ((~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C))))))))))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(141,plain,
% 84.97/85.17 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), B, C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, B) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), B, C) | (~((~m1_subset_1(tptp_fun_D_2(C, B, u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), B) <=> r2_hidden(tptp_fun_D_2(C, B, u1_struct_0(A!0)), C))))))))))) | (~m1_subset_1(k2_filter_0(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[140, 139])).
% 84.97/85.17 tff(142,plain,
% 84.97/85.17 (![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[141, 138, 89])).
% 84.97/85.17 tff(143,plain,
% 84.97/85.17 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(144,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[143])).
% 84.97/85.17 tff(145,plain,
% 84.97/85.17 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(146,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[145])).
% 84.97/85.17 tff(147,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(148,plain,
% 84.97/85.17 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(149,plain,
% 84.97/85.17 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[148])).
% 84.97/85.17 tff(150,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_lattices')).
% 84.97/85.17 tff(151,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[150, 149])).
% 84.97/85.17 tff(152,plain,
% 84.97/85.17 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[151, 147])).
% 84.97/85.17 tff(153,plain,(
% 84.97/85.17 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 84.97/85.17 inference(skolemize,[status(sab)],[152])).
% 84.97/85.17 tff(154,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[153, 146])).
% 84.97/85.17 tff(155,plain,
% 84.97/85.17 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[154, 144])).
% 84.97/85.17 tff(156,plain,
% 84.97/85.17 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(157,plain,
% 84.97/85.17 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 84.97/85.17 inference(quant_inst,[status(thm)],[])).
% 84.97/85.17 tff(158,plain,
% 84.97/85.17 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[157, 156])).
% 84.97/85.17 tff(159,plain,
% 84.97/85.17 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[158, 61, 155])).
% 84.97/85.17 tff(160,plain,
% 84.97/85.17 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 84.97/85.17 inference(unit_resolution,[status(thm)],[159, 33])).
% 84.97/85.17 tff(161,plain,
% 84.97/85.17 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(162,plain,
% 84.97/85.17 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[161])).
% 84.97/85.17 tff(163,plain,
% 84.97/85.17 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite(((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)) <=> (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(164,plain,
% 84.97/85.17 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[163])).
% 84.97/85.17 tff(165,plain,
% 84.97/85.17 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 84.97/85.17 inference(rewrite,[status(thm)],[])).
% 84.97/85.17 tff(166,plain,
% 84.97/85.17 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 84.97/85.17 inference(bind,[status(th)],[])).
% 84.97/85.17 tff(167,plain,
% 84.97/85.17 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 84.97/85.17 inference(quant_intro,[status(thm)],[166])).
% 84.97/85.17 tff(168,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k22_filter_2')).
% 84.97/85.17 tff(169,plain,
% 84.97/85.17 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 84.97/85.17 inference(modus_ponens,[status(thm)],[168, 167])).
% 84.97/85.17 tff(170,plain,
% 84.97/85.18 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[169, 165])).
% 84.97/85.18 tff(171,plain,(
% 84.97/85.18 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | ((~v1_xboole_0(k22_filter_2(A, B, C))) & m2_lattice4(k22_filter_2(A, B, C), A)))),
% 84.97/85.18 inference(skolemize,[status(sab)],[170])).
% 84.97/85.18 tff(172,plain,
% 84.97/85.18 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[171, 164])).
% 84.97/85.18 tff(173,plain,
% 84.97/85.18 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[172, 162])).
% 84.97/85.18 tff(174,plain,
% 84.97/85.18 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | 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(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(175,plain,
% 84.97/85.18 ((v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(176,plain,
% 84.97/85.18 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (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(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))))),
% 84.97/85.18 inference(monotonicity,[status(thm)],[175])).
% 84.97/85.18 tff(177,plain,
% 84.97/85.18 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | 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(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 84.97/85.18 inference(transitivity,[status(thm)],[176, 174])).
% 84.97/85.18 tff(178,plain,
% 84.97/85.18 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | (v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))))),
% 84.97/85.18 inference(quant_inst,[status(thm)],[])).
% 84.97/85.18 tff(179,plain,
% 84.97/85.18 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~(v1_xboole_0(k22_filter_2(A, B, C)) | (~m2_lattice4(k22_filter_2(A, B, C), A)))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[178, 177])).
% 84.97/85.18 tff(180,plain,
% 84.97/85.18 ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))))),
% 84.97/85.18 inference(unit_resolution,[status(thm)],[179, 61, 105, 27, 104, 173])).
% 84.97/85.18 tff(181,plain,
% 84.97/85.18 (~(v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)))),
% 84.97/85.18 inference(unit_resolution,[status(thm)],[180, 160])).
% 84.97/85.18 tff(182,plain,
% 84.97/85.18 ((v1_xboole_0(k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0))) | m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)),
% 84.97/85.18 inference(tautology,[status(thm)],[])).
% 84.97/85.18 tff(183,plain,
% 84.97/85.18 (m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)),
% 84.97/85.18 inference(unit_resolution,[status(thm)],[182, 181])).
% 84.97/85.18 tff(184,plain,
% 84.97/85.18 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 84.97/85.18 inference(bind,[status(th)],[])).
% 84.97/85.18 tff(185,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(quant_intro,[status(thm)],[184])).
% 84.97/85.18 tff(186,plain,
% 84.97/85.18 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 84.97/85.18 inference(bind,[status(th)],[])).
% 84.97/85.18 tff(187,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(quant_intro,[status(thm)],[186])).
% 84.97/85.18 tff(188,plain,
% 84.97/85.18 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 84.97/85.18 inference(bind,[status(th)],[])).
% 84.97/85.18 tff(189,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(quant_intro,[status(thm)],[188])).
% 84.97/85.18 tff(190,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(transitivity,[status(thm)],[189, 187])).
% 84.97/85.18 tff(191,plain,
% 84.97/85.18 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 84.97/85.18 inference(bind,[status(th)],[])).
% 84.97/85.18 tff(192,plain,
% 84.97/85.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(quant_intro,[status(thm)],[191])).
% 84.97/85.18 tff(193,plain,
% 84.97/85.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(194,plain,
% 84.97/85.18 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 84.97/85.18 inference(bind,[status(th)],[])).
% 84.97/85.18 tff(195,plain,
% 84.97/85.18 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(quant_intro,[status(thm)],[194])).
% 84.97/85.18 tff(196,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 84.97/85.18 tff(197,plain,
% 84.97/85.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[196, 195])).
% 84.97/85.18 tff(198,plain,
% 84.97/85.18 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[197, 193])).
% 84.97/85.18 tff(199,plain,(
% 84.97/85.18 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(skolemize,[status(sab)],[198])).
% 84.97/85.18 tff(200,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[199, 192])).
% 84.97/85.18 tff(201,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[200, 190])).
% 84.97/85.18 tff(202,plain,
% 84.97/85.18 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[201, 185])).
% 84.97/85.18 tff(203,plain,
% 84.97/85.18 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(204,plain,
% 84.97/85.18 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 84.97/85.18 inference(quant_inst,[status(thm)],[])).
% 84.97/85.18 tff(205,plain,
% 84.97/85.18 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[204, 203])).
% 84.97/85.18 tff(206,plain,
% 84.97/85.18 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 84.97/85.18 inference(unit_resolution,[status(thm)],[205, 61, 105, 27, 202])).
% 84.97/85.18 tff(207,plain,
% 84.97/85.18 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(208,plain,
% 84.97/85.18 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 84.97/85.18 inference(quant_inst,[status(thm)],[])).
% 84.97/85.18 tff(209,plain,
% 84.97/85.18 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k22_filter_2(A!0, B!1, k6_lattices(A!0)), A!0)) | m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[208, 207])).
% 84.97/85.18 tff(210,plain,
% 84.97/85.18 (m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 84.97/85.18 inference(unit_resolution,[status(thm)],[209, 206, 183])).
% 84.97/85.18 tff(211,plain,
% 84.97/85.18 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(212,plain,
% 84.97/85.18 (((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))))) <=> ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))),
% 84.97/85.18 inference(rewrite,[status(thm)],[])).
% 84.97/85.18 tff(213,plain,
% 84.97/85.18 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))))),
% 84.97/85.18 inference(monotonicity,[status(thm)],[212])).
% 84.97/85.18 tff(214,plain,
% 84.97/85.18 (((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))),
% 84.97/85.18 inference(transitivity,[status(thm)],[213, 211])).
% 84.97/85.18 tff(215,plain,
% 84.97/85.18 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | ((~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))))))),
% 84.97/85.18 inference(quant_inst,[status(thm)],[])).
% 84.97/85.18 tff(216,plain,
% 84.97/85.18 ((~![C: $i] : ((~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C)) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, C))))) | (~(r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), C) | (~((~m1_subset_1(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(C, k2_filter_0(A!0, B!1), u1_struct_0(A!0)), C)))))))))) | (~m1_subset_1(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 84.97/85.18 inference(modus_ponens,[status(thm)],[215, 214])).
% 84.97/85.18 tff(217,plain,
% 84.97/85.18 (~((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[216, 210, 142])).
% 84.97/85.19 tff(218,plain,
% 84.97/85.19 (((~((~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (r2_hidden(D, k2_filter_0(A!0, B!1)) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 84.97/85.19 inference(tautology,[status(thm)],[])).
% 84.97/85.19 tff(219,plain,
% 84.97/85.19 ((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[218, 217])).
% 84.97/85.19 tff(220,plain,
% 84.97/85.19 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(221,plain,
% 84.97/85.19 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[220])).
% 84.97/85.19 tff(222,plain,
% 84.97/85.19 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(223,plain,
% 84.97/85.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[222])).
% 84.97/85.19 tff(224,plain,
% 84.97/85.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(225,plain,
% 84.97/85.19 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(226,plain,
% 84.97/85.19 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[225])).
% 84.97/85.19 tff(227,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 84.97/85.19 tff(228,plain,
% 84.97/85.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[227, 226])).
% 84.97/85.19 tff(229,plain,
% 84.97/85.19 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[228, 224])).
% 84.97/85.19 tff(230,plain,(
% 84.97/85.19 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 84.97/85.19 inference(skolemize,[status(sab)],[229])).
% 84.97/85.19 tff(231,plain,
% 84.97/85.19 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[230, 223])).
% 84.97/85.19 tff(232,plain,
% 84.97/85.19 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[231, 221])).
% 84.97/85.19 tff(233,plain,
% 84.97/85.19 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(234,plain,
% 84.97/85.19 ((v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(235,plain,
% 84.97/85.19 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1))))),
% 84.97/85.19 inference(monotonicity,[status(thm)],[234])).
% 84.97/85.19 tff(236,plain,
% 84.97/85.19 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)))),
% 84.97/85.19 inference(transitivity,[status(thm)],[235, 233])).
% 84.97/85.19 tff(237,plain,
% 84.97/85.19 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 84.97/85.19 inference(quant_inst,[status(thm)],[])).
% 84.97/85.19 tff(238,plain,
% 84.97/85.19 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[237, 236])).
% 84.97/85.19 tff(239,plain,
% 84.97/85.19 (k2_filter_2(A!0, B!1) = k2_filter_0(A!0, B!1)),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[238, 61, 105, 27, 104, 232])).
% 84.97/85.19 tff(240,plain,
% 84.97/85.19 (k2_filter_0(A!0, B!1) = k2_filter_2(A!0, B!1)),
% 84.97/85.19 inference(symmetry,[status(thm)],[239])).
% 84.97/85.19 tff(241,plain,
% 84.97/85.19 (r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(monotonicity,[status(thm)],[240])).
% 84.97/85.19 tff(242,plain,
% 84.97/85.19 (r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))) <=> r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(symmetry,[status(thm)],[241])).
% 84.97/85.19 tff(243,plain,
% 84.97/85.19 ((~r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) <=> (~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 84.97/85.19 inference(monotonicity,[status(thm)],[242])).
% 84.97/85.19 tff(244,plain,
% 84.97/85.19 (~r1_filter_2(u1_struct_0(A!0), k2_filter_2(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(or_elim,[status(thm)],[103])).
% 84.97/85.19 tff(245,plain,
% 84.97/85.19 (~r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[244, 243])).
% 84.97/85.19 tff(246,plain,
% 84.97/85.19 ((~((~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0))))) | (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) | r1_filter_2(u1_struct_0(A!0), k2_filter_0(A!0, B!1), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 84.97/85.19 inference(tautology,[status(thm)],[])).
% 84.97/85.19 tff(247,plain,
% 84.97/85.19 (~((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[246, 245, 219])).
% 84.97/85.19 tff(248,plain,
% 84.97/85.19 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))) | m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 84.97/85.19 inference(tautology,[status(thm)],[])).
% 84.97/85.19 tff(249,plain,
% 84.97/85.19 (m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[248, 247])).
% 84.97/85.19 tff(250,plain,
% 84.97/85.19 (^[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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(251,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[250])).
% 84.97/85.19 tff(252,plain,
% 84.97/85.19 (^[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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(253,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[252])).
% 84.97/85.19 tff(254,plain,
% 84.97/85.19 (^[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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(255,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[254])).
% 84.97/85.19 tff(256,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(transitivity,[status(thm)],[255, 253])).
% 84.97/85.19 tff(257,plain,
% 84.97/85.19 (^[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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, 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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, 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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(258,plain,
% 84.97/85.19 (![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, k2_filter_0(A, C)) <=> r3_lattices(A, 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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[257])).
% 84.97/85.19 tff(259,plain,
% 84.97/85.19 (![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, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(260,plain,
% 84.97/85.19 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), (((((~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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> (((~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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((~((~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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), (((((~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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B))))) <=> ((~((~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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))))),
% 84.97/85.19 inference(bind,[status(th)],[])).
% 84.97/85.19 tff(261,plain,
% 84.97/85.19 (![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, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(quant_intro,[status(thm)],[260])).
% 84.97/85.19 tff(262,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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t18_filter_0')).
% 84.97/85.19 tff(263,plain,
% 84.97/85.19 (![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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[262, 261])).
% 84.97/85.19 tff(264,plain,
% 84.97/85.19 (![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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[263, 259])).
% 84.97/85.19 tff(265,plain,(
% 84.97/85.19 ![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, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(skolemize,[status(sab)],[264])).
% 84.97/85.19 tff(266,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[265, 258])).
% 84.97/85.19 tff(267,plain,
% 84.97/85.19 (![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))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))) | (~v10_lattices(A)))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[266, 256])).
% 84.97/85.19 tff(268,plain,
% 84.97/85.19 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, B)))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[267, 251])).
% 84.97/85.19 tff(269,plain,
% 84.97/85.19 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(270,plain,
% 84.97/85.19 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B)))))),
% 84.97/85.19 inference(quant_inst,[status(thm)],[])).
% 84.97/85.19 tff(271,plain,
% 84.97/85.19 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (r2_hidden(B, k2_filter_0(A, C)) <=> r3_lattices(A, C, 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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[270, 269])).
% 84.97/85.19 tff(272,plain,
% 84.97/85.19 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[271, 61, 105, 27, 268])).
% 84.97/85.19 tff(273,plain,
% 84.97/85.19 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(274,plain,
% 84.97/85.19 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))))),
% 84.97/85.19 inference(quant_inst,[status(thm)],[])).
% 84.97/85.19 tff(275,plain,
% 84.97/85.19 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(B, k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, B))))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[274, 273])).
% 84.97/85.19 tff(276,plain,
% 84.97/85.19 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))),
% 84.97/85.19 inference(unit_resolution,[status(thm)],[275, 272, 249])).
% 84.97/85.19 tff(277,plain,
% 84.97/85.19 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))),
% 84.97/85.19 inference(rewrite,[status(thm)],[])).
% 84.97/85.19 tff(278,plain,
% 84.97/85.19 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))),
% 84.97/85.19 inference(quant_inst,[status(thm)],[])).
% 84.97/85.19 tff(279,plain,
% 84.97/85.19 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, C)) <=> r3_lattices(A!0, C, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))),
% 84.97/85.19 inference(modus_ponens,[status(thm)],[278, 277])).
% 85.05/85.20 tff(280,plain,
% 85.05/85.20 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[279, 104, 276])).
% 85.05/85.20 tff(281,plain,
% 85.05/85.20 ((~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))),
% 85.05/85.20 inference(tautology,[status(thm)],[])).
% 85.05/85.20 tff(282,plain,
% 85.05/85.20 ((~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[281, 280])).
% 85.05/85.20 tff(283,plain,
% 85.05/85.20 (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[282, 1])).
% 85.05/85.20 tff(284,plain,
% 85.05/85.20 (((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) | r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))),
% 85.05/85.20 inference(tautology,[status(thm)],[])).
% 85.05/85.20 tff(285,plain,
% 85.05/85.20 ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[284, 1])).
% 85.05/85.20 tff(286,plain,
% 85.05/85.20 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(287,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[286])).
% 85.05/85.20 tff(288,plain,
% 85.05/85.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(289,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[288])).
% 85.05/85.20 tff(290,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(transitivity,[status(thm)],[289, 287])).
% 85.05/85.20 tff(291,plain,
% 85.05/85.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(292,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[291])).
% 85.05/85.20 tff(293,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(294,plain,
% 85.05/85.20 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite((r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))) <=> ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~r3_lattices(A, B, C)) | (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))), ((m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))) <=> ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(295,plain,
% 85.05/85.20 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[294])).
% 85.05/85.20 tff(296,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => (r3_lattices(A, B, C) => (r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t63_filter_2')).
% 85.05/85.20 tff(297,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[296, 295])).
% 85.05/85.20 tff(298,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[297, 293])).
% 85.05/85.20 tff(299,plain,(
% 85.05/85.20 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(D, k22_filter_2(A, B, C)) <=> (r3_lattices(A, B, D) & r3_lattices(A, D, C))) | (~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A)))))))),
% 85.05/85.20 inference(skolemize,[status(sab)],[298])).
% 85.05/85.20 tff(300,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[299, 292])).
% 85.05/85.20 tff(301,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[300, 290])).
% 85.05/85.20 tff(302,plain,
% 85.05/85.20 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(303,plain,
% 85.05/85.20 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C))))))))),
% 85.05/85.20 inference(quant_inst,[status(thm)],[])).
% 85.05/85.20 tff(304,plain,
% 85.05/85.20 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~r3_lattices(A, B, C)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(((~r3_lattices(A, B, D)) | (~r3_lattices(A, D, C))) <=> r2_hidden(D, k22_filter_2(A, B, C))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[303, 302])).
% 85.05/85.20 tff(305,plain,
% 85.05/85.20 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[304, 61, 105, 27, 301])).
% 85.05/85.20 tff(306,plain,
% 85.05/85.20 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(307,plain,
% 85.05/85.20 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C)))))))),
% 85.05/85.20 inference(quant_inst,[status(thm)],[])).
% 85.05/85.20 tff(308,plain,
% 85.05/85.20 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B, C)))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[307, 306])).
% 85.05/85.20 tff(309,plain,
% 85.05/85.20 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[308, 104, 305])).
% 85.05/85.20 tff(310,plain,
% 85.05/85.20 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(311,plain,
% 85.05/85.20 (((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) <=> ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(312,plain,
% 85.05/85.20 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))))),
% 85.05/85.20 inference(monotonicity,[status(thm)],[311])).
% 85.05/85.20 tff(313,plain,
% 85.05/85.20 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 85.05/85.20 inference(transitivity,[status(thm)],[312, 310])).
% 85.05/85.20 tff(314,plain,
% 85.05/85.20 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | ((~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 85.05/85.20 inference(quant_inst,[status(thm)],[])).
% 85.05/85.20 tff(315,plain,
% 85.05/85.20 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~r3_lattices(A!0, B!1, C)) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, C))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, C))))))) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.20 inference(modus_ponens,[status(thm)],[314, 313])).
% 85.05/85.20 tff(316,plain,
% 85.05/85.20 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.20 inference(unit_resolution,[status(thm)],[315, 160, 309])).
% 85.05/85.20 tff(317,plain,
% 85.05/85.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(318,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[317])).
% 85.05/85.20 tff(319,plain,
% 85.05/85.20 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(320,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[319])).
% 85.05/85.20 tff(321,plain,
% 85.05/85.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(322,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[321])).
% 85.05/85.20 tff(323,plain,
% 85.05/85.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.20 inference(transitivity,[status(thm)],[322, 320])).
% 85.05/85.20 tff(324,plain,
% 85.05/85.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))))),
% 85.05/85.20 inference(bind,[status(th)],[])).
% 85.05/85.20 tff(325,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.20 inference(quant_intro,[status(thm)],[324])).
% 85.05/85.20 tff(326,plain,
% 85.05/85.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.20 inference(rewrite,[status(thm)],[])).
% 85.05/85.20 tff(327,plain,
% 85.05/85.20 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))))),
% 85.05/85.21 inference(bind,[status(th)],[])).
% 85.05/85.21 tff(328,plain,
% 85.05/85.21 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.21 inference(quant_intro,[status(thm)],[327])).
% 85.05/85.21 tff(329,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => r3_lattices(A, B, k6_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t45_lattices')).
% 85.05/85.21 tff(330,plain,
% 85.05/85.21 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[329, 328])).
% 85.05/85.21 tff(331,plain,
% 85.05/85.21 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[330, 326])).
% 85.05/85.21 tff(332,plain,(
% 85.05/85.21 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.21 inference(skolemize,[status(sab)],[331])).
% 85.05/85.21 tff(333,plain,
% 85.05/85.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[332, 325])).
% 85.05/85.21 tff(334,plain,
% 85.05/85.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[333, 323])).
% 85.05/85.21 tff(335,plain,
% 85.05/85.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[334, 318])).
% 85.05/85.21 tff(336,plain,
% 85.05/85.21 (v14_lattices(A!0)),
% 85.05/85.21 inference(or_elim,[status(thm)],[103])).
% 85.05/85.21 tff(337,plain,
% 85.05/85.21 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(338,plain,
% 85.05/85.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0))))),
% 85.05/85.21 inference(quant_inst,[status(thm)],[])).
% 85.05/85.21 tff(339,plain,
% 85.05/85.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | r3_lattices(A, B, k6_lattices(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[338, 337])).
% 85.05/85.21 tff(340,plain,
% 85.05/85.21 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[339, 61, 105, 27, 336, 335])).
% 85.05/85.21 tff(341,plain,
% 85.05/85.21 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(342,plain,
% 85.05/85.21 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.21 inference(quant_inst,[status(thm)],[])).
% 85.05/85.21 tff(343,plain,
% 85.05/85.21 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | r3_lattices(A!0, B!1, k6_lattices(A!0))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[342, 341])).
% 85.05/85.21 tff(344,plain,
% 85.05/85.21 (r3_lattices(A!0, B!1, k6_lattices(A!0))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[343, 104, 340])).
% 85.05/85.21 tff(345,plain,
% 85.05/85.21 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(346,plain,
% 85.05/85.21 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) <=> ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(347,plain,
% 85.05/85.21 ((~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))) <=> (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(348,plain,
% 85.05/85.21 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) <=> ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(monotonicity,[status(thm)],[347])).
% 85.05/85.21 tff(349,plain,
% 85.05/85.21 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))) <=> ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(transitivity,[status(thm)],[348, 346])).
% 85.05/85.21 tff(350,plain,
% 85.05/85.21 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | ((~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))))),
% 85.05/85.21 inference(monotonicity,[status(thm)],[349])).
% 85.05/85.21 tff(351,plain,
% 85.05/85.21 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(transitivity,[status(thm)],[350, 345])).
% 85.05/85.21 tff(352,plain,
% 85.05/85.21 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))))),
% 85.05/85.21 inference(quant_inst,[status(thm)],[])).
% 85.05/85.21 tff(353,plain,
% 85.05/85.21 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~(((~r3_lattices(A!0, B!1, D)) | (~r3_lattices(A!0, D, k6_lattices(A!0)))) <=> r2_hidden(D, k22_filter_2(A!0, B!1, k6_lattices(A!0))))))) | (~r3_lattices(A!0, B!1, k6_lattices(A!0))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))),
% 85.05/85.21 inference(modus_ponens,[status(thm)],[352, 351])).
% 85.05/85.21 tff(354,plain,
% 85.05/85.21 (~(((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[353, 344, 316, 249])).
% 85.05/85.21 tff(355,plain,
% 85.05/85.21 ((((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.21 inference(tautology,[status(thm)],[])).
% 85.05/85.21 tff(356,plain,
% 85.05/85.21 ((~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[355, 354])).
% 85.05/85.21 tff(357,plain,
% 85.05/85.21 (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[356, 285])).
% 85.05/85.21 tff(358,plain,
% 85.05/85.21 (((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))) | (~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))))),
% 85.05/85.21 inference(tautology,[status(thm)],[])).
% 85.05/85.21 tff(359,plain,
% 85.05/85.21 (~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[358, 247])).
% 85.05/85.21 tff(360,plain,
% 85.05/85.21 ((r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.21 inference(tautology,[status(thm)],[])).
% 85.05/85.21 tff(361,plain,
% 85.05/85.21 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[360, 359])).
% 85.05/85.21 tff(362,plain,
% 85.05/85.21 ($false),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[361, 357, 283])).
% 85.05/85.21 tff(363,plain,(r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))), inference(lemma,lemma(discharge,[]))).
% 85.05/85.21 tff(364,plain,
% 85.05/85.21 ((~(r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))),
% 85.05/85.21 inference(tautology,[status(thm)],[])).
% 85.05/85.21 tff(365,plain,
% 85.05/85.21 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[364, 280])).
% 85.05/85.21 tff(366,plain,
% 85.05/85.21 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))),
% 85.05/85.21 inference(unit_resolution,[status(thm)],[365, 363])).
% 85.05/85.21 tff(367,plain,
% 85.05/85.21 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 85.05/85.21 inference(rewrite,[status(thm)],[])).
% 85.05/85.21 tff(368,plain,
% 85.05/85.21 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | ((~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 85.05/85.21 inference(quant_inst,[status(thm)],[])).
% 85.05/85.21 tff(369,plain,
% 85.05/85.21 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | r3_lattices(A!0, B, k6_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), u1_struct_0(A!0))) | r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))),
% 85.05/85.22 inference(modus_ponens,[status(thm)],[368, 367])).
% 85.05/85.22 tff(370,plain,
% 85.05/85.22 (r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))),
% 85.05/85.22 inference(unit_resolution,[status(thm)],[369, 340, 249])).
% 85.05/85.22 tff(371,plain,
% 85.05/85.22 ((~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))),
% 85.05/85.22 inference(tautology,[status(thm)],[])).
% 85.05/85.22 tff(372,plain,
% 85.05/85.22 ((~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))))) | (~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0))))),
% 85.05/85.22 inference(unit_resolution,[status(thm)],[371, 370])).
% 85.05/85.22 tff(373,plain,
% 85.05/85.22 (~((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0))))),
% 85.05/85.22 inference(unit_resolution,[status(thm)],[372, 363])).
% 85.05/85.22 tff(374,plain,
% 85.05/85.22 ((((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | ((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.22 inference(tautology,[status(thm)],[])).
% 85.05/85.22 tff(375,plain,
% 85.05/85.22 (((~r3_lattices(A!0, B!1, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)))) | (~r3_lattices(A!0, tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k6_lattices(A!0)))) | r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.22 inference(unit_resolution,[status(thm)],[374, 354])).
% 85.05/85.22 tff(376,plain,
% 85.05/85.22 (r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))),
% 85.05/85.22 inference(unit_resolution,[status(thm)],[375, 373])).
% 85.05/85.22 tff(377,plain,
% 85.05/85.22 ((r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1)) <=> r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0)))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.22 inference(tautology,[status(thm)],[])).
% 85.05/85.22 tff(378,plain,
% 85.05/85.22 ((~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k2_filter_0(A!0, B!1))) | (~r2_hidden(tptp_fun_D_2(k22_filter_2(A!0, B!1, k6_lattices(A!0)), k2_filter_0(A!0, B!1), u1_struct_0(A!0)), k22_filter_2(A!0, B!1, k6_lattices(A!0))))),
% 85.05/85.26 inference(unit_resolution,[status(thm)],[377, 359])).
% 85.05/85.26 tff(379,plain,
% 85.05/85.26 ($false),
% 85.05/85.26 inference(unit_resolution,[status(thm)],[378, 376, 366])).
% 85.05/85.26 % SZS output end Proof
% 85.05/85.26 % E exiting
%------------------------------------------------------------------------------