%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT334+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:14:24 AM UTC 2025
% Result : Theorem 11.12s 11.28s
% Output : Proof 11.27s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT334+1 : TPTP v9.0.0. Released v3.4.0.
% 0.10/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n008.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 20:24:18 EDT 2025
% 0.12/0.33 % CPUTime :
% 11.12/11.28 % SZS status Theorem
% 11.12/11.28 % SZS output start Proof
% 11.12/11.28 tff(k2_lattices_type, type, (
% 11.12/11.28 k2_lattices: ( $i * $i * $i ) > $i)).
% 11.12/11.28 tff(tptp_fun_D_4_type, type, (
% 11.12/11.28 tptp_fun_D_4: $i > $i)).
% 11.12/11.28 tff(k23_filter_2_type, type, (
% 11.12/11.28 k23_filter_2: ( $i * $i ) > $i)).
% 11.12/11.28 tff(tptp_fun_B_1_type, type, (
% 11.12/11.28 tptp_fun_B_1: $i)).
% 11.12/11.28 tff(tptp_fun_A_0_type, type, (
% 11.12/11.28 tptp_fun_A_0: $i)).
% 11.12/11.28 tff(k1_lattices_type, type, (
% 11.12/11.28 k1_lattices: ( $i * $i * $i ) > $i)).
% 11.12/11.28 tff(tptp_fun_C_3_type, type, (
% 11.12/11.28 tptp_fun_C_3: $i > $i)).
% 11.12/11.28 tff(tptp_fun_B_2_type, type, (
% 11.12/11.28 tptp_fun_B_2: $i > $i)).
% 11.12/11.28 tff(g3_lattices_type, type, (
% 11.12/11.28 g3_lattices: ( $i * $i * $i ) > $i)).
% 11.12/11.28 tff(u1_lattices_type, type, (
% 11.12/11.28 u1_lattices: $i > $i)).
% 11.12/11.28 tff(u2_lattices_type, type, (
% 11.12/11.28 u2_lattices: $i > $i)).
% 11.12/11.28 tff(u1_struct_0_type, type, (
% 11.12/11.28 u1_struct_0: $i > $i)).
% 11.12/11.28 tff(l3_lattices_type, type, (
% 11.12/11.28 l3_lattices: $i > $o)).
% 11.12/11.28 tff(v10_lattices_type, type, (
% 11.12/11.28 v10_lattices: $i > $o)).
% 11.12/11.28 tff(v3_struct_0_type, type, (
% 11.12/11.28 v3_struct_0: $i > $o)).
% 11.12/11.28 tff(m2_nat_lat_type, type, (
% 11.12/11.28 m2_nat_lat: ( $i * $i ) > $o)).
% 11.12/11.28 tff(m2_lattice4_type, type, (
% 11.12/11.28 m2_lattice4: ( $i * $i ) > $o)).
% 11.12/11.28 tff(v1_xboole_0_type, type, (
% 11.12/11.28 v1_xboole_0: $i > $o)).
% 11.12/11.28 tff(v12_lattices_type, type, (
% 11.12/11.28 v12_lattices: $i > $o)).
% 11.12/11.28 tff(v3_lattices_type, type, (
% 11.12/11.28 v3_lattices: $i > $o)).
% 11.12/11.28 tff(v9_lattices_type, type, (
% 11.12/11.28 v9_lattices: $i > $o)).
% 11.12/11.28 tff(v8_lattices_type, type, (
% 11.12/11.28 v8_lattices: $i > $o)).
% 11.12/11.28 tff(v7_lattices_type, type, (
% 11.12/11.28 v7_lattices: $i > $o)).
% 11.12/11.28 tff(v6_lattices_type, type, (
% 11.12/11.28 v6_lattices: $i > $o)).
% 11.12/11.28 tff(v5_lattices_type, type, (
% 11.12/11.28 v5_lattices: $i > $o)).
% 11.12/11.28 tff(v4_lattices_type, type, (
% 11.12/11.28 v4_lattices: $i > $o)).
% 11.12/11.28 tff(k4_lattices_type, type, (
% 11.12/11.28 k4_lattices: ( $i * $i * $i ) > $i)).
% 11.12/11.28 tff(l1_lattices_type, type, (
% 11.12/11.28 l1_lattices: $i > $o)).
% 11.12/11.28 tff(l2_lattices_type, type, (
% 11.12/11.28 l2_lattices: $i > $o)).
% 11.12/11.28 tff(m1_subset_1_type, type, (
% 11.12/11.28 m1_subset_1: ( $i * $i ) > $o)).
% 11.12/11.28 tff(r1_lattices_type, type, (
% 11.12/11.28 r1_lattices: ( $i * $i * $i ) > $o)).
% 11.12/11.28 tff(k3_lattices_type, type, (
% 11.12/11.28 k3_lattices: ( $i * $i * $i ) > $i)).
% 11.12/11.28 tff(r3_lattices_type, type, (
% 11.12/11.28 r3_lattices: ( $i * $i * $i ) > $o)).
% 11.12/11.28 tff(1,plain,
% 11.12/11.28 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 11.12/11.28 inference(bind,[status(th)],[])).
% 11.12/11.28 tff(2,plain,
% 11.12/11.28 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.28 inference(quant_intro,[status(thm)],[1])).
% 11.12/11.28 tff(3,plain,
% 11.12/11.28 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_nat_lat(k23_filter_2(A, B), A)))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 11.12/11.28 inference(bind,[status(th)],[])).
% 11.12/11.28 tff(4,plain,
% 11.12/11.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.28 inference(quant_intro,[status(thm)],[3])).
% 11.12/11.28 tff(5,plain,
% 11.12/11.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(6,plain,
% 11.12/11.28 (^[A: $i, B: $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)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))))),
% 11.12/11.28 inference(bind,[status(th)],[])).
% 11.12/11.28 tff(7,plain,
% 11.12/11.28 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 11.12/11.28 inference(quant_intro,[status(thm)],[6])).
% 11.12/11.28 tff(8,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k23_filter_2')).
% 11.12/11.28 tff(9,plain,
% 11.12/11.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[8, 7])).
% 11.12/11.28 tff(10,plain,
% 11.12/11.28 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[9, 5])).
% 11.12/11.28 tff(11,plain,(
% 11.12/11.28 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 11.12/11.28 inference(skolemize,[status(sab)],[10])).
% 11.12/11.28 tff(12,plain,
% 11.12/11.28 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[11, 4])).
% 11.12/11.28 tff(13,plain,
% 11.12/11.28 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[12, 2])).
% 11.12/11.28 tff(14,plain,
% 11.12/11.28 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(15,plain,
% 11.12/11.28 ((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~v12_lattices(A!0)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))) <=> (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(16,plain,
% 11.12/11.28 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(v12_lattices(k23_filter_2(A!0, B!1)) | (~v12_lattices(A!0)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 11.12/11.28 inference(monotonicity,[status(thm)],[15])).
% 11.12/11.28 tff(17,plain,
% 11.12/11.28 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~(v12_lattices(k23_filter_2(A!0, B!1)) | (~v12_lattices(A!0)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 11.12/11.28 inference(transitivity,[status(thm)],[16, 14])).
% 11.12/11.28 tff(18,plain,
% 11.12/11.28 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(19,plain,
% 11.12/11.28 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v12_lattices(A) => v12_lattices(k23_filter_2(A, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => (v12_lattices(A) => v12_lattices(k23_filter_2(A, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t77_filter_2')).
% 11.12/11.28 tff(21,plain,
% 11.12/11.28 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[20, 19])).
% 11.12/11.28 tff(22,plain,
% 11.12/11.28 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[21, 18])).
% 11.12/11.28 tff(23,plain,
% 11.12/11.28 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[22, 18])).
% 11.12/11.28 tff(24,plain,
% 11.12/11.28 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v12_lattices(k23_filter_2(A, B)) | (~v12_lattices(A)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[23, 18])).
% 11.12/11.28 tff(25,plain,
% 11.12/11.28 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))),
% 11.12/11.28 inference(modus_ponens,[status(thm)],[24, 17])).
% 11.12/11.28 tff(26,plain,
% 11.12/11.28 (~((~v12_lattices(A!0)) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))),
% 11.12/11.28 inference(and_elim,[status(thm)],[25])).
% 11.12/11.28 tff(27,plain,
% 11.12/11.28 ((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)),
% 11.12/11.28 inference(or_elim,[status(thm)],[26])).
% 11.12/11.28 tff(28,plain,
% 11.12/11.28 (m2_lattice4(B!1, A!0)),
% 11.12/11.28 inference(and_elim,[status(thm)],[27])).
% 11.12/11.28 tff(29,plain,
% 11.12/11.28 (~v1_xboole_0(B!1)),
% 11.12/11.28 inference(and_elim,[status(thm)],[27])).
% 11.12/11.28 tff(30,plain,
% 11.12/11.28 (l3_lattices(A!0)),
% 11.12/11.28 inference(and_elim,[status(thm)],[25])).
% 11.12/11.28 tff(31,plain,
% 11.12/11.28 (v10_lattices(A!0)),
% 11.12/11.28 inference(and_elim,[status(thm)],[25])).
% 11.12/11.28 tff(32,plain,
% 11.12/11.28 (~v3_struct_0(A!0)),
% 11.12/11.28 inference(and_elim,[status(thm)],[25])).
% 11.12/11.28 tff(33,plain,
% 11.12/11.28 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0)))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(34,plain,
% 11.12/11.28 ((v1_xboole_0(B!1) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0)))),
% 11.12/11.28 inference(rewrite,[status(thm)],[])).
% 11.12/11.28 tff(35,plain,
% 11.12/11.28 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0))))),
% 11.12/11.28 inference(monotonicity,[status(thm)],[34])).
% 11.12/11.28 tff(36,plain,
% 11.12/11.28 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0)))),
% 11.12/11.29 inference(transitivity,[status(thm)],[35, 33])).
% 11.12/11.29 tff(37,plain,
% 11.12/11.29 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 11.12/11.29 inference(quant_inst,[status(thm)],[])).
% 11.12/11.29 tff(38,plain,
% 11.12/11.29 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_nat_lat(k23_filter_2(A!0, B!1), A!0) | (~m2_lattice4(B!1, A!0))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[37, 36])).
% 11.12/11.29 tff(39,plain,
% 11.12/11.29 (m2_nat_lat(k23_filter_2(A!0, B!1), A!0)),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[38, 32, 31, 30, 29, 28, 13])).
% 11.12/11.29 tff(40,plain,
% 11.12/11.29 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(41,plain,
% 11.12/11.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[40])).
% 11.12/11.29 tff(42,plain,
% 11.12/11.29 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(43,plain,
% 11.12/11.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[42])).
% 11.12/11.29 tff(44,plain,
% 11.12/11.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(transitivity,[status(thm)],[43, 41])).
% 11.12/11.29 tff(45,plain,
% 11.12/11.29 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) <=> ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))), (![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) <=> ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(46,plain,
% 11.12/11.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[45])).
% 11.12/11.29 tff(47,plain,
% 11.12/11.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(48,plain,
% 11.12/11.29 (^[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(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))), ((m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B))) <=> (m2_nat_lat(B, A) => ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))), rewrite((m2_nat_lat(B, A) => ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))) <=> ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))), ((m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B))) <=> ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))), (![B: $i] : (m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B))) <=> ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(49,plain,
% 11.12/11.29 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[48])).
% 11.12/11.29 tff(50,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => (((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_nat_lat')).
% 11.12/11.29 tff(51,plain,
% 11.12/11.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[50, 49])).
% 11.12/11.29 tff(52,plain,
% 11.12/11.29 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[51, 47])).
% 11.12/11.29 tff(53,plain,(
% 11.12/11.29 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))),
% 11.12/11.29 inference(skolemize,[status(sab)],[52])).
% 11.12/11.29 tff(54,plain,
% 11.12/11.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[53, 46])).
% 11.12/11.29 tff(55,plain,
% 11.12/11.29 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[54, 44])).
% 11.12/11.29 tff(56,plain,
% 11.12/11.29 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(57,plain,
% 11.12/11.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))),
% 11.12/11.29 inference(quant_inst,[status(thm)],[])).
% 11.12/11.29 tff(58,plain,
% 11.12/11.29 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[57, 56])).
% 11.12/11.29 tff(59,plain,
% 11.12/11.29 (![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[58, 32, 31, 30, 55])).
% 11.12/11.29 tff(60,plain,
% 11.12/11.29 (((~![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) | ((~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) | (~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(61,plain,
% 11.12/11.29 ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) | ((~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(quant_inst,[status(thm)],[])).
% 11.12/11.29 tff(62,plain,
% 11.12/11.29 ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)))))) | (~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[61, 60])).
% 11.12/11.29 tff(63,plain,
% 11.12/11.29 (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[62, 59, 39])).
% 11.12/11.29 tff(64,plain,
% 11.12/11.29 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | l3_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.29 inference(tautology,[status(thm)],[])).
% 11.12/11.29 tff(65,plain,
% 11.12/11.29 (l3_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[64, 63])).
% 11.12/11.29 tff(66,plain,
% 11.12/11.29 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(67,plain,
% 11.12/11.29 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[66])).
% 11.12/11.29 tff(68,plain,
% 11.12/11.29 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), rewrite(((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))) <=> (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B)))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(69,plain,
% 11.12/11.29 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[68])).
% 11.12/11.29 tff(70,plain,
% 11.12/11.29 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(71,plain,
% 11.12/11.29 (^[A: $i, B: $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)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)))), (((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)))), (((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B))))), ((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)))), ((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B))))), (((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)))), (((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B))))), ((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)))), ((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B))))), (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)))), (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B))))), ((((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B))) <=> (((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B))))), rewrite((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))), ((((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B))) <=> ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(72,plain,
% 11.12/11.29 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[71])).
% 11.12/11.29 tff(73,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => (((((((((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B))) & v4_lattices(k23_filter_2(A, B))) & v5_lattices(k23_filter_2(A, B))) & v6_lattices(k23_filter_2(A, B))) & v7_lattices(k23_filter_2(A, B))) & v8_lattices(k23_filter_2(A, B))) & v9_lattices(k23_filter_2(A, B))) & v10_lattices(k23_filter_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc5_filter_2')).
% 11.12/11.29 tff(74,plain,
% 11.12/11.29 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[73, 72])).
% 11.12/11.29 tff(75,plain,
% 11.12/11.29 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[74, 70])).
% 11.12/11.29 tff(76,plain,(
% 11.12/11.29 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | ((~v3_struct_0(k23_filter_2(A, B))) & v3_lattices(k23_filter_2(A, B)) & v4_lattices(k23_filter_2(A, B)) & v5_lattices(k23_filter_2(A, B)) & v6_lattices(k23_filter_2(A, B)) & v7_lattices(k23_filter_2(A, B)) & v8_lattices(k23_filter_2(A, B)) & v9_lattices(k23_filter_2(A, B)) & v10_lattices(k23_filter_2(A, B))))),
% 11.12/11.29 inference(skolemize,[status(sab)],[75])).
% 11.12/11.29 tff(77,plain,
% 11.12/11.29 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[76, 69])).
% 11.12/11.29 tff(78,plain,
% 11.12/11.29 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[77, 67])).
% 11.12/11.29 tff(79,plain,
% 11.12/11.29 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(80,plain,
% 11.12/11.29 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))) <=> (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(81,plain,
% 11.12/11.29 ((~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))) <=> (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(82,plain,
% 11.12/11.29 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))) <=> (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(monotonicity,[status(thm)],[81])).
% 11.12/11.29 tff(83,plain,
% 11.12/11.29 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))) <=> (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(transitivity,[status(thm)],[82, 80])).
% 11.12/11.29 tff(84,plain,
% 11.12/11.29 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | (v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.29 inference(monotonicity,[status(thm)],[83])).
% 11.12/11.29 tff(85,plain,
% 11.12/11.29 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(transitivity,[status(thm)],[84, 79])).
% 11.12/11.29 tff(86,plain,
% 11.12/11.29 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~m2_lattice4(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.29 inference(quant_inst,[status(thm)],[])).
% 11.12/11.29 tff(87,plain,
% 11.12/11.29 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~(v3_struct_0(k23_filter_2(A, B)) | (~v3_lattices(k23_filter_2(A, B))) | (~v4_lattices(k23_filter_2(A, B))) | (~v5_lattices(k23_filter_2(A, B))) | (~v6_lattices(k23_filter_2(A, B))) | (~v7_lattices(k23_filter_2(A, B))) | (~v8_lattices(k23_filter_2(A, B))) | (~v9_lattices(k23_filter_2(A, B))) | (~v10_lattices(k23_filter_2(A, B))))))) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_lattice4(B!1, A!0)) | (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.29 inference(modus_ponens,[status(thm)],[86, 85])).
% 11.12/11.29 tff(88,plain,
% 11.12/11.29 (~(v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[87, 32, 31, 30, 29, 28, 78])).
% 11.12/11.29 tff(89,plain,
% 11.12/11.29 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | v3_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.29 inference(tautology,[status(thm)],[])).
% 11.12/11.29 tff(90,plain,
% 11.12/11.29 (v3_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.29 inference(unit_resolution,[status(thm)],[89, 88])).
% 11.12/11.29 tff(91,plain,
% 11.12/11.29 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(92,plain,
% 11.12/11.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[91])).
% 11.12/11.29 tff(93,plain,
% 11.12/11.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.29 inference(rewrite,[status(thm)],[])).
% 11.12/11.29 tff(94,plain,
% 11.12/11.29 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 11.12/11.29 inference(bind,[status(th)],[])).
% 11.12/11.29 tff(95,plain,
% 11.12/11.29 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.29 inference(quant_intro,[status(thm)],[94])).
% 11.12/11.29 tff(96,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 11.12/11.29 tff(97,plain,
% 11.12/11.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[96, 95])).
% 11.12/11.30 tff(98,plain,
% 11.12/11.30 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[97, 93])).
% 11.12/11.30 tff(99,plain,(
% 11.12/11.30 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.30 inference(skolemize,[status(sab)],[98])).
% 11.12/11.30 tff(100,plain,
% 11.12/11.30 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[99, 92])).
% 11.12/11.30 tff(101,plain,
% 11.12/11.30 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.30 inference(rewrite,[status(thm)],[])).
% 11.12/11.30 tff(102,plain,
% 11.12/11.30 (((k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~l3_lattices(k23_filter_2(A!0, B!1)))) <=> ((~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.30 inference(rewrite,[status(thm)],[])).
% 11.12/11.30 tff(103,plain,
% 11.12/11.30 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~l3_lattices(k23_filter_2(A!0, B!1))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[102])).
% 11.12/11.30 tff(104,plain,
% 11.12/11.30 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~l3_lattices(k23_filter_2(A!0, B!1))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.30 inference(transitivity,[status(thm)],[103, 101])).
% 11.12/11.30 tff(105,plain,
% 11.12/11.30 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~l3_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(quant_inst,[status(thm)],[])).
% 11.12/11.30 tff(106,plain,
% 11.12/11.30 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[105, 104])).
% 11.12/11.30 tff(107,plain,
% 11.12/11.30 ((~l3_lattices(k23_filter_2(A!0, B!1))) | (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[106, 100, 90])).
% 11.12/11.30 tff(108,plain,
% 11.12/11.30 (k23_filter_2(A!0, B!1) = g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[107, 65])).
% 11.12/11.30 tff(109,plain,
% 11.12/11.30 (k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[108])).
% 11.12/11.30 tff(110,plain,
% 11.12/11.30 (k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.12/11.30 inference(symmetry,[status(thm)],[109])).
% 11.12/11.30 tff(111,plain,
% 11.12/11.30 (g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))) = k23_filter_2(A!0, B!1)),
% 11.12/11.30 inference(symmetry,[status(thm)],[108])).
% 11.12/11.30 tff(112,plain,
% 11.12/11.30 (v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> v6_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.30 tff(113,plain,
% 11.12/11.30 (v6_lattices(k23_filter_2(A!0, B!1)) <=> v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(symmetry,[status(thm)],[112])).
% 11.12/11.30 tff(114,plain,
% 11.12/11.30 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | v6_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(tautology,[status(thm)],[])).
% 11.12/11.30 tff(115,plain,
% 11.12/11.30 (v6_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[114, 88])).
% 11.12/11.30 tff(116,plain,
% 11.12/11.30 (v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[115, 113])).
% 11.12/11.30 tff(117,plain,
% 11.12/11.30 (l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> l3_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.30 tff(118,plain,
% 11.12/11.30 (l3_lattices(k23_filter_2(A!0, B!1)) <=> l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(symmetry,[status(thm)],[117])).
% 11.12/11.30 tff(119,plain,
% 11.12/11.30 (l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[65, 118])).
% 11.12/11.30 tff(120,plain,
% 11.12/11.30 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(121,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[120])).
% 11.12/11.30 tff(122,plain,
% 11.12/11.30 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(123,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[122])).
% 11.12/11.30 tff(124,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.12/11.30 inference(rewrite,[status(thm)],[])).
% 11.12/11.30 tff(125,plain,
% 11.12/11.30 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(126,plain,
% 11.12/11.30 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[125])).
% 11.12/11.30 tff(127,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 11.12/11.30 tff(128,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[127, 126])).
% 11.12/11.30 tff(129,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[128, 124])).
% 11.12/11.30 tff(130,plain,(
% 11.12/11.30 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.12/11.30 inference(skolemize,[status(sab)],[129])).
% 11.12/11.30 tff(131,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[130, 123])).
% 11.12/11.30 tff(132,plain,
% 11.12/11.30 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[131, 121])).
% 11.12/11.30 tff(133,plain,
% 11.12/11.30 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.30 inference(rewrite,[status(thm)],[])).
% 11.12/11.30 tff(134,plain,
% 11.12/11.30 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.30 inference(quant_inst,[status(thm)],[])).
% 11.12/11.30 tff(135,plain,
% 11.12/11.30 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[134, 133])).
% 11.12/11.30 tff(136,plain,
% 11.12/11.30 ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[135, 132])).
% 11.12/11.30 tff(137,plain,
% 11.12/11.30 (~((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[136, 119])).
% 11.12/11.30 tff(138,plain,
% 11.12/11.30 (((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(tautology,[status(thm)],[])).
% 11.12/11.30 tff(139,plain,
% 11.12/11.30 (l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[138, 137])).
% 11.12/11.30 tff(140,plain,
% 11.12/11.30 (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> v3_struct_0(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.30 tff(141,plain,
% 11.12/11.30 (v3_struct_0(k23_filter_2(A!0, B!1)) <=> v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(symmetry,[status(thm)],[140])).
% 11.12/11.30 tff(142,plain,
% 11.12/11.30 ((~v3_struct_0(k23_filter_2(A!0, B!1))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[141])).
% 11.12/11.30 tff(143,plain,
% 11.12/11.30 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | (~v3_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.30 inference(tautology,[status(thm)],[])).
% 11.12/11.30 tff(144,plain,
% 11.12/11.30 (~v3_struct_0(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(unit_resolution,[status(thm)],[143, 88])).
% 11.12/11.30 tff(145,plain,
% 11.12/11.30 (~v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[144, 142])).
% 11.12/11.30 tff(146,plain,
% 11.12/11.30 (u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) = u1_struct_0(k23_filter_2(A!0, B!1))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.30 tff(147,plain,
% 11.12/11.30 (m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.30 inference(monotonicity,[status(thm)],[146])).
% 11.12/11.30 tff(148,plain,
% 11.12/11.30 (m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))) <=> m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.30 inference(symmetry,[status(thm)],[147])).
% 11.12/11.30 tff(149,plain,
% 11.12/11.30 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(150,plain,
% 11.12/11.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[149])).
% 11.12/11.30 tff(151,plain,
% 11.12/11.30 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(152,plain,
% 11.12/11.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[151])).
% 11.12/11.30 tff(153,plain,
% 11.12/11.30 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(154,plain,
% 11.12/11.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[153])).
% 11.12/11.30 tff(155,plain,
% 11.12/11.30 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(transitivity,[status(thm)],[154, 152])).
% 11.12/11.30 tff(156,plain,
% 11.12/11.30 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A))))), trans(monotonicity(rewrite(((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) <=> ((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))), rewrite((v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) <=> (v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))), ((((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))) <=> (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))), rewrite((((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) <=> (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))), ((((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))) <=> (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A))) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A))) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(157,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[156])).
% 11.12/11.30 tff(158,plain,
% 11.12/11.30 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & (m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(159,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & (m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[158])).
% 11.12/11.30 tff(160,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 11.12/11.30 inference(rewrite,[status(thm)],[])).
% 11.12/11.30 tff(161,plain,
% 11.12/11.30 (^[A: $i] : trans(monotonicity(rewrite((v12_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)) => (r1_lattices(A, B, D) => (k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D))))))) <=> (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v12_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)) => (r1_lattices(A, B, D) => (k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)))))))) <=> (((~v3_struct_0(A)) & l3_lattices(A)) => (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))), rewrite((((~v3_struct_0(A)) & l3_lattices(A)) => (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v12_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)) => (r1_lattices(A, B, D) => (k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)))))))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))))),
% 11.12/11.30 inference(bind,[status(th)],[])).
% 11.12/11.30 tff(162,plain,
% 11.12/11.30 (![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v12_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)) => (r1_lattices(A, B, D) => (k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 11.12/11.30 inference(quant_intro,[status(thm)],[161])).
% 11.12/11.30 tff(163,axiom,(![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v12_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)) => (r1_lattices(A, B, D) => (k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d12_lattices')).
% 11.12/11.30 tff(164,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[163, 162])).
% 11.12/11.30 tff(165,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v12_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))))),
% 11.12/11.30 inference(modus_ponens,[status(thm)],[164, 160])).
% 11.12/11.30 tff(166,plain,(
% 11.12/11.30 ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & (m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.30 inference(skolemize,[status(sab)],[165])).
% 11.12/11.30 tff(167,plain,
% 11.12/11.30 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A))))))) & (v12_lattices(A) | (m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A)) & m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A)) & (~((k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A)))))))))),
% 11.12/11.31 inference(modus_ponens,[status(thm)],[166, 159])).
% 11.12/11.31 tff(168,plain,
% 11.12/11.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.31 inference(modus_ponens,[status(thm)],[167, 157])).
% 11.12/11.31 tff(169,plain,
% 11.12/11.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))) | (~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))))))),
% 11.12/11.31 inference(modus_ponens,[status(thm)],[168, 155])).
% 11.12/11.31 tff(170,plain,
% 11.12/11.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))),
% 11.12/11.31 inference(modus_ponens,[status(thm)],[169, 150])).
% 11.12/11.31 tff(171,plain,
% 11.12/11.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))),
% 11.12/11.31 inference(rewrite,[status(thm)],[])).
% 11.12/11.31 tff(172,plain,
% 11.12/11.31 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))))))))))) <=> (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))),
% 11.12/11.31 inference(rewrite,[status(thm)],[])).
% 11.12/11.31 tff(173,plain,
% 11.12/11.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))))))))))))),
% 11.12/11.31 inference(monotonicity,[status(thm)],[172])).
% 11.12/11.31 tff(174,plain,
% 11.12/11.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))),
% 11.12/11.31 inference(transitivity,[status(thm)],[173, 171])).
% 11.12/11.31 tff(175,plain,
% 11.12/11.31 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))))),
% 11.12/11.31 inference(quant_inst,[status(thm)],[])).
% 11.12/11.31 tff(176,plain,
% 11.12/11.31 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))))))))))),
% 11.12/11.31 inference(modus_ponens,[status(thm)],[175, 174])).
% 11.12/11.31 tff(177,plain,
% 11.12/11.31 (v3_struct_0(k23_filter_2(A!0, B!1)) | (~l3_lattices(k23_filter_2(A!0, B!1))) | (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))))))))))),
% 11.12/11.31 inference(unit_resolution,[status(thm)],[176, 170])).
% 11.12/11.31 tff(178,plain,
% 11.12/11.31 (~((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1))))))))))),
% 11.12/11.31 inference(unit_resolution,[status(thm)],[177, 65, 144])).
% 11.12/11.31 tff(179,plain,
% 11.12/11.31 (((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~v12_lattices(k23_filter_2(A!0, B!1))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | ![D: $i] : ((k1_lattices(k23_filter_2(A!0, B!1), B, k2_lattices(k23_filter_2(A!0, B!1), C, D)) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), B, C), D)) | (~r1_lattices(k23_filter_2(A!0, B!1), B, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))))))))) | (v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.31 inference(tautology,[status(thm)],[])).
% 11.12/11.31 tff(180,plain,
% 11.12/11.31 (v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[179, 178])).
% 11.12/11.32 tff(181,plain,
% 11.12/11.32 (~v12_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.32 inference(or_elim,[status(thm)],[26])).
% 11.12/11.32 tff(182,plain,
% 11.12/11.32 ((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(tautology,[status(thm)],[])).
% 11.12/11.32 tff(183,plain,
% 11.12/11.32 ((~(v12_lattices(k23_filter_2(A!0, B!1)) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))))) | (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[182, 181])).
% 11.12/11.32 tff(184,plain,
% 11.12/11.32 (~((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[183, 180])).
% 11.12/11.32 tff(185,plain,
% 11.12/11.32 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))) | m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(tautology,[status(thm)],[])).
% 11.12/11.32 tff(186,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[185, 184])).
% 11.12/11.32 tff(187,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[186, 148])).
% 11.12/11.32 tff(188,plain,
% 11.12/11.32 (k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.32 tff(189,plain,
% 11.12/11.32 (m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(monotonicity,[status(thm)],[188])).
% 11.12/11.32 tff(190,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(monotonicity,[status(thm)],[146])).
% 11.12/11.32 tff(191,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))) <=> m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(symmetry,[status(thm)],[190])).
% 11.12/11.32 tff(192,plain,
% 11.12/11.32 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))) | m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(tautology,[status(thm)],[])).
% 11.12/11.32 tff(193,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[192, 184])).
% 11.12/11.32 tff(194,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[193, 191])).
% 11.12/11.32 tff(195,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(monotonicity,[status(thm)],[146])).
% 11.12/11.32 tff(196,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))) <=> m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(symmetry,[status(thm)],[195])).
% 11.12/11.32 tff(197,plain,
% 11.12/11.32 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))) | m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(tautology,[status(thm)],[])).
% 11.12/11.32 tff(198,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[197, 184])).
% 11.12/11.32 tff(199,plain,
% 11.12/11.32 (m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[198, 196])).
% 11.12/11.32 tff(200,plain,
% 11.12/11.32 (((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.32 inference(tautology,[status(thm)],[])).
% 11.12/11.32 tff(201,plain,
% 11.12/11.32 (l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[200, 137])).
% 11.12/11.32 tff(202,plain,
% 11.12/11.32 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 11.12/11.32 inference(bind,[status(th)],[])).
% 11.12/11.32 tff(203,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.32 inference(quant_intro,[status(thm)],[202])).
% 11.12/11.32 tff(204,plain,
% 11.12/11.32 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_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))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l2_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))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l2_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))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 11.12/11.32 inference(bind,[status(th)],[])).
% 11.12/11.32 tff(205,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.32 inference(quant_intro,[status(thm)],[204])).
% 11.12/11.32 tff(206,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))),
% 11.12/11.32 inference(rewrite,[status(thm)],[])).
% 11.12/11.32 tff(207,plain,
% 11.12/11.32 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))), ((((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))))),
% 11.12/11.32 inference(bind,[status(th)],[])).
% 11.12/11.32 tff(208,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))),
% 11.12/11.32 inference(quant_intro,[status(thm)],[207])).
% 11.12/11.32 tff(209,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k1_lattices')).
% 11.12/11.32 tff(210,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[209, 208])).
% 11.12/11.32 tff(211,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[210, 206])).
% 11.12/11.32 tff(212,plain,(
% 11.12/11.32 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)))),
% 11.12/11.32 inference(skolemize,[status(sab)],[211])).
% 11.12/11.32 tff(213,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[212, 205])).
% 11.12/11.32 tff(214,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[213, 203])).
% 11.12/11.32 tff(215,plain,
% 11.12/11.32 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(rewrite,[status(thm)],[])).
% 11.12/11.32 tff(216,plain,
% 11.12/11.32 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(rewrite,[status(thm)],[])).
% 11.12/11.32 tff(217,plain,
% 11.12/11.32 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.32 inference(monotonicity,[status(thm)],[216])).
% 11.12/11.32 tff(218,plain,
% 11.12/11.32 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.32 inference(transitivity,[status(thm)],[217, 215])).
% 11.12/11.32 tff(219,plain,
% 11.12/11.32 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.32 inference(quant_inst,[status(thm)],[])).
% 11.12/11.32 tff(220,plain,
% 11.12/11.32 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k1_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[219, 218])).
% 11.12/11.32 tff(221,plain,
% 11.12/11.32 ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[220, 214])).
% 11.12/11.32 tff(222,plain,
% 11.12/11.32 (m1_subset_1(k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(unit_resolution,[status(thm)],[221, 201, 199, 194, 145])).
% 11.12/11.32 tff(223,plain,
% 11.12/11.32 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.32 inference(modus_ponens,[status(thm)],[222, 189])).
% 11.12/11.32 tff(224,plain,
% 11.12/11.32 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 11.12/11.32 inference(bind,[status(th)],[])).
% 11.12/11.32 tff(225,plain,
% 11.12/11.32 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.32 inference(quant_intro,[status(thm)],[224])).
% 11.12/11.32 tff(226,plain,
% 11.12/11.32 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 11.12/11.33 inference(bind,[status(th)],[])).
% 11.12/11.33 tff(227,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(quant_intro,[status(thm)],[226])).
% 11.12/11.33 tff(228,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 11.12/11.33 inference(rewrite,[status(thm)],[])).
% 11.12/11.33 tff(229,plain,
% 11.12/11.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 11.12/11.33 inference(bind,[status(th)],[])).
% 11.12/11.33 tff(230,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 11.12/11.33 inference(quant_intro,[status(thm)],[229])).
% 11.12/11.33 tff(231,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 11.12/11.33 tff(232,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[231, 230])).
% 11.12/11.33 tff(233,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[232, 228])).
% 11.12/11.33 tff(234,plain,(
% 11.12/11.33 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 11.12/11.33 inference(skolemize,[status(sab)],[233])).
% 11.12/11.33 tff(235,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[234, 227])).
% 11.12/11.33 tff(236,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[235, 225])).
% 11.12/11.33 tff(237,plain,
% 11.12/11.33 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.33 inference(rewrite,[status(thm)],[])).
% 11.12/11.33 tff(238,plain,
% 11.12/11.33 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.33 inference(rewrite,[status(thm)],[])).
% 11.12/11.33 tff(239,plain,
% 11.12/11.33 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.33 inference(monotonicity,[status(thm)],[238])).
% 11.12/11.33 tff(240,plain,
% 11.12/11.33 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.33 inference(transitivity,[status(thm)],[239, 237])).
% 11.12/11.33 tff(241,plain,
% 11.12/11.33 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.33 inference(quant_inst,[status(thm)],[])).
% 11.12/11.33 tff(242,plain,
% 11.12/11.33 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[241, 240])).
% 11.12/11.33 tff(243,plain,
% 11.12/11.33 ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.12/11.33 inference(unit_resolution,[status(thm)],[242, 236])).
% 11.12/11.33 tff(244,plain,
% 11.12/11.33 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.12/11.33 inference(unit_resolution,[status(thm)],[243, 223, 187, 145, 139, 116])).
% 11.12/11.33 tff(245,plain,
% 11.12/11.33 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 11.12/11.33 inference(bind,[status(th)],[])).
% 11.12/11.33 tff(246,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(quant_intro,[status(thm)],[245])).
% 11.12/11.33 tff(247,plain,
% 11.12/11.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 11.12/11.33 inference(bind,[status(th)],[])).
% 11.12/11.33 tff(248,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(quant_intro,[status(thm)],[247])).
% 11.12/11.33 tff(249,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 11.12/11.33 inference(rewrite,[status(thm)],[])).
% 11.12/11.33 tff(250,plain,
% 11.12/11.33 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))))),
% 11.12/11.33 inference(bind,[status(th)],[])).
% 11.12/11.33 tff(251,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 11.12/11.33 inference(quant_intro,[status(thm)],[250])).
% 11.12/11.33 tff(252,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 11.12/11.33 tff(253,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[252, 251])).
% 11.12/11.33 tff(254,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[253, 249])).
% 11.12/11.33 tff(255,plain,(
% 11.12/11.33 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 11.12/11.33 inference(skolemize,[status(sab)],[254])).
% 11.12/11.33 tff(256,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[255, 248])).
% 11.12/11.33 tff(257,plain,
% 11.12/11.33 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.12/11.33 inference(modus_ponens,[status(thm)],[256, 246])).
% 11.12/11.33 tff(258,plain,
% 11.12/11.33 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(259,plain,
% 11.12/11.34 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(260,plain,
% 11.12/11.34 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.34 inference(monotonicity,[status(thm)],[259])).
% 11.12/11.34 tff(261,plain,
% 11.12/11.34 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.12/11.34 inference(transitivity,[status(thm)],[260, 258])).
% 11.12/11.34 tff(262,plain,
% 11.12/11.34 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.12/11.34 inference(quant_inst,[status(thm)],[])).
% 11.12/11.34 tff(263,plain,
% 11.12/11.34 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[262, 261])).
% 11.12/11.34 tff(264,plain,
% 11.12/11.34 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.12/11.34 inference(unit_resolution,[status(thm)],[263, 257, 139, 145, 187, 223, 116])).
% 11.12/11.34 tff(265,plain,
% 11.12/11.34 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.12/11.34 inference(symmetry,[status(thm)],[264])).
% 11.12/11.34 tff(266,plain,
% 11.12/11.34 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.12/11.34 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.34 tff(267,plain,
% 11.12/11.34 (k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.12/11.34 inference(symmetry,[status(thm)],[266])).
% 11.12/11.34 tff(268,plain,
% 11.12/11.34 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(269,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[268])).
% 11.12/11.34 tff(270,plain,
% 11.12/11.34 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(271,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[270])).
% 11.12/11.34 tff(272,plain,
% 11.12/11.34 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(273,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[272])).
% 11.12/11.34 tff(274,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(transitivity,[status(thm)],[273, 271])).
% 11.12/11.34 tff(275,plain,
% 11.12/11.34 (^[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_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(276,plain,
% 11.12/11.34 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[275])).
% 11.12/11.34 tff(277,plain,
% 11.12/11.34 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(278,plain,
% 11.12/11.34 (^[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(B)) => m1_subset_1(C, u1_struct_0(A))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))), ((m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A)))) <=> (m2_nat_lat(B, A) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))), rewrite((m2_nat_lat(B, A) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) <=> ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))), ((m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A)))) <=> ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))))), (![B: $i] : (m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A)))) <=> ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(279,plain,
% 11.12/11.34 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[278])).
% 11.12/11.34 tff(280,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_nat_lat(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(B)) => m1_subset_1(C, u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t69_filter_2')).
% 11.12/11.34 tff(281,plain,
% 11.12/11.34 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[280, 279])).
% 11.12/11.34 tff(282,plain,
% 11.12/11.34 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[281, 277])).
% 11.12/11.34 tff(283,plain,(
% 11.12/11.34 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(skolemize,[status(sab)],[282])).
% 11.12/11.34 tff(284,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[283, 276])).
% 11.12/11.34 tff(285,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))) | (~v10_lattices(A)))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[284, 274])).
% 11.12/11.34 tff(286,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[285, 269])).
% 11.12/11.34 tff(287,plain,
% 11.12/11.34 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0)))))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(288,plain,
% 11.12/11.34 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0)))))),
% 11.12/11.34 inference(quant_inst,[status(thm)],[])).
% 11.12/11.34 tff(289,plain,
% 11.12/11.34 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_nat_lat(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[288, 287])).
% 11.12/11.34 tff(290,plain,
% 11.12/11.34 (![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 11.12/11.34 inference(unit_resolution,[status(thm)],[289, 32, 31, 30, 286])).
% 11.12/11.34 tff(291,plain,
% 11.12/11.34 (((~![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))) | ((~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))) | (~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(292,plain,
% 11.12/11.34 ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))) | ((~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0))))),
% 11.12/11.34 inference(quant_inst,[status(thm)],[])).
% 11.12/11.34 tff(293,plain,
% 11.12/11.34 ((~![B: $i] : ((~m2_nat_lat(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | m1_subset_1(C, u1_struct_0(A!0))))) | (~m2_nat_lat(k23_filter_2(A!0, B!1), A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[292, 291])).
% 11.12/11.34 tff(294,plain,
% 11.12/11.34 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))),
% 11.12/11.34 inference(unit_resolution,[status(thm)],[293, 290, 39])).
% 11.12/11.34 tff(295,plain,
% 11.12/11.34 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(296,plain,
% 11.12/11.34 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.12/11.34 inference(quant_inst,[status(thm)],[])).
% 11.12/11.34 tff(297,plain,
% 11.12/11.34 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[296, 295])).
% 11.12/11.34 tff(298,plain,
% 11.12/11.34 (m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.12/11.34 inference(unit_resolution,[status(thm)],[297, 198, 294])).
% 11.12/11.34 tff(299,plain,
% 11.12/11.34 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.12/11.34 inference(rewrite,[status(thm)],[])).
% 11.12/11.34 tff(300,plain,
% 11.12/11.34 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.12/11.34 inference(quant_inst,[status(thm)],[])).
% 11.12/11.34 tff(301,plain,
% 11.12/11.34 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.12/11.34 inference(modus_ponens,[status(thm)],[300, 299])).
% 11.12/11.34 tff(302,plain,
% 11.12/11.34 (m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.12/11.34 inference(unit_resolution,[status(thm)],[301, 193, 294])).
% 11.12/11.34 tff(303,plain,
% 11.12/11.34 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(304,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.34 inference(quant_intro,[status(thm)],[303])).
% 11.12/11.34 tff(305,plain,
% 11.12/11.34 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))))),
% 11.12/11.34 inference(bind,[status(th)],[])).
% 11.12/11.34 tff(306,plain,
% 11.12/11.34 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(quant_intro,[status(thm)],[305])).
% 11.12/11.35 tff(307,plain,
% 11.12/11.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(transitivity,[status(thm)],[306, 304])).
% 11.12/11.35 tff(308,plain,
% 11.12/11.35 (^[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] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), rewrite((~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))), (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))) <=> ((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))), rewrite(((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))))),
% 11.12/11.35 inference(bind,[status(th)],[])).
% 11.12/11.35 tff(309,plain,
% 11.12/11.35 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(quant_intro,[status(thm)],[308])).
% 11.12/11.35 tff(310,plain,
% 11.12/11.35 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.12/11.35 inference(rewrite,[status(thm)],[])).
% 11.12/11.35 tff(311,plain,
% 11.12/11.35 (^[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(trans(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(rewrite((((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))) <=> ((~((C = E) & (D = F))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))), ((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))) <=> (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => ((~((C = E) & (D = F))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))), rewrite((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => ((~((C = E) & (D = F))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))) <=> (((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B)))))), ((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))) <=> (((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B)))))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))) <=> ![F: $i] : (((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))))), trans(der(![F: $i] : (((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))) <=> ![F: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)))), elim_unused(![F: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)))), (![F: $i] : (((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E))))), ((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))) <=> (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)))))), rewrite((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))))), ((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))) <=> ![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))))))), trans(der(![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))))) <=> ![E: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))), elim_unused(![E: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))), (![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, D))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))))) <=> (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))), rewrite((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(bind,[status(th)],[])).
% 11.12/11.35 tff(312,plain,
% 11.12/11.35 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F)))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.12/11.35 inference(quant_intro,[status(thm)],[311])).
% 11.12/11.35 tff(313,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), E, F)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), E, F))))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t74_filter_2')).
% 11.12/11.35 tff(314,plain,
% 11.12/11.35 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[313, 312])).
% 11.12/11.35 tff(315,plain,
% 11.12/11.35 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[314, 310])).
% 11.12/11.35 tff(316,plain,(
% 11.12/11.35 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | ((k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D)) & (k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.12/11.35 inference(skolemize,[status(sab)],[315])).
% 11.12/11.35 tff(317,plain,
% 11.12/11.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[316, 309])).
% 11.12/11.35 tff(318,plain,
% 11.12/11.35 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[317, 307])).
% 11.12/11.35 tff(319,plain,
% 11.12/11.35 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D)))))))))),
% 11.12/11.35 inference(rewrite,[status(thm)],[])).
% 11.12/11.35 tff(320,plain,
% 11.12/11.35 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D)))))))))),
% 11.12/11.35 inference(quant_inst,[status(thm)],[])).
% 11.12/11.35 tff(321,plain,
% 11.12/11.35 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~((~(k3_lattices(A, C, D) = k3_lattices(k23_filter_2(A, B), C, D))) | (~(k4_lattices(A, C, D) = k4_lattices(k23_filter_2(A, B), C, D)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[320, 319])).
% 11.12/11.35 tff(322,plain,
% 11.12/11.35 (![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))),
% 11.12/11.35 inference(unit_resolution,[status(thm)],[321, 32, 31, 30, 318])).
% 11.12/11.35 tff(323,plain,
% 11.12/11.35 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))),
% 11.12/11.35 inference(rewrite,[status(thm)],[])).
% 11.12/11.35 tff(324,plain,
% 11.12/11.35 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) <=> (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))),
% 11.12/11.35 inference(rewrite,[status(thm)],[])).
% 11.12/11.35 tff(325,plain,
% 11.12/11.35 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))))),
% 11.12/11.35 inference(monotonicity,[status(thm)],[324])).
% 11.12/11.35 tff(326,plain,
% 11.12/11.35 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))),
% 11.12/11.35 inference(transitivity,[status(thm)],[325, 323])).
% 11.12/11.35 tff(327,plain,
% 11.12/11.35 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D))))))))),
% 11.12/11.35 inference(quant_inst,[status(thm)],[])).
% 11.12/11.35 tff(328,plain,
% 11.12/11.35 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B), C, D))))))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))),
% 11.12/11.35 inference(modus_ponens,[status(thm)],[327, 326])).
% 11.12/11.35 tff(329,plain,
% 11.12/11.35 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))),
% 11.12/11.35 inference(unit_resolution,[status(thm)],[328, 29, 28, 322])).
% 11.12/11.35 tff(330,plain,
% 11.12/11.35 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))))),
% 11.12/11.36 inference(rewrite,[status(thm)],[])).
% 11.12/11.36 tff(331,plain,
% 11.12/11.36 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))))),
% 11.12/11.36 inference(quant_inst,[status(thm)],[])).
% 11.12/11.36 tff(332,plain,
% 11.12/11.36 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[331, 330])).
% 11.12/11.36 tff(333,plain,
% 11.12/11.36 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))),
% 11.12/11.36 inference(unit_resolution,[status(thm)],[332, 329, 302])).
% 11.12/11.36 tff(334,plain,
% 11.12/11.36 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.36 inference(rewrite,[status(thm)],[])).
% 11.12/11.36 tff(335,plain,
% 11.12/11.36 (((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))) <=> ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.36 inference(rewrite,[status(thm)],[])).
% 11.12/11.36 tff(336,plain,
% 11.12/11.36 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))),
% 11.12/11.36 inference(monotonicity,[status(thm)],[335])).
% 11.12/11.36 tff(337,plain,
% 11.12/11.36 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.36 inference(transitivity,[status(thm)],[336, 334])).
% 11.12/11.36 tff(338,plain,
% 11.12/11.36 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))),
% 11.12/11.36 inference(quant_inst,[status(thm)],[])).
% 11.12/11.36 tff(339,plain,
% 11.12/11.36 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[338, 337])).
% 11.12/11.36 tff(340,plain,
% 11.12/11.36 (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.12/11.36 inference(unit_resolution,[status(thm)],[339, 198, 193, 333, 298])).
% 11.12/11.36 tff(341,plain,
% 11.12/11.36 (((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.12/11.36 inference(tautology,[status(thm)],[])).
% 11.12/11.36 tff(342,plain,
% 11.12/11.36 (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.12/11.36 inference(unit_resolution,[status(thm)],[341, 340])).
% 11.12/11.36 tff(343,plain,
% 11.12/11.36 (k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.12/11.36 inference(symmetry,[status(thm)],[342])).
% 11.12/11.36 tff(344,plain,
% 11.12/11.36 (k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.12/11.36 inference(monotonicity,[status(thm)],[108])).
% 11.12/11.36 tff(345,plain,
% 11.12/11.36 (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.12/11.36 inference(symmetry,[status(thm)],[344])).
% 11.12/11.36 tff(346,plain,
% 11.12/11.36 (v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> v4_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.36 inference(monotonicity,[status(thm)],[111])).
% 11.12/11.36 tff(347,plain,
% 11.12/11.36 (v4_lattices(k23_filter_2(A!0, B!1)) <=> v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.36 inference(symmetry,[status(thm)],[346])).
% 11.12/11.36 tff(348,plain,
% 11.12/11.36 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | v4_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.36 inference(tautology,[status(thm)],[])).
% 11.12/11.36 tff(349,plain,
% 11.12/11.36 (v4_lattices(k23_filter_2(A!0, B!1))),
% 11.12/11.36 inference(unit_resolution,[status(thm)],[348, 88])).
% 11.12/11.36 tff(350,plain,
% 11.12/11.36 (v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[349, 347])).
% 11.12/11.36 tff(351,plain,
% 11.12/11.36 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 11.12/11.36 inference(bind,[status(th)],[])).
% 11.12/11.36 tff(352,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.36 inference(quant_intro,[status(thm)],[351])).
% 11.12/11.36 tff(353,plain,
% 11.12/11.36 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 11.12/11.36 inference(bind,[status(th)],[])).
% 11.12/11.36 tff(354,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.36 inference(quant_intro,[status(thm)],[353])).
% 11.12/11.36 tff(355,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 11.12/11.36 inference(rewrite,[status(thm)],[])).
% 11.12/11.36 tff(356,plain,
% 11.12/11.36 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))))),
% 11.12/11.36 inference(bind,[status(th)],[])).
% 11.12/11.36 tff(357,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 11.12/11.36 inference(quant_intro,[status(thm)],[356])).
% 11.12/11.36 tff(358,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k3_lattices')).
% 11.12/11.36 tff(359,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[358, 357])).
% 11.12/11.36 tff(360,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[359, 355])).
% 11.12/11.36 tff(361,plain,(
% 11.12/11.36 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 11.12/11.36 inference(skolemize,[status(sab)],[360])).
% 11.12/11.36 tff(362,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[361, 354])).
% 11.12/11.36 tff(363,plain,
% 11.12/11.36 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.12/11.36 inference(modus_ponens,[status(thm)],[362, 352])).
% 11.12/11.36 tff(364,plain,
% 11.12/11.36 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.12/11.36 inference(rewrite,[status(thm)],[])).
% 11.12/11.36 tff(365,plain,
% 11.12/11.36 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.21/11.36 inference(rewrite,[status(thm)],[])).
% 11.21/11.36 tff(366,plain,
% 11.21/11.36 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.21/11.37 inference(monotonicity,[status(thm)],[365])).
% 11.21/11.37 tff(367,plain,
% 11.21/11.37 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.21/11.37 inference(transitivity,[status(thm)],[366, 364])).
% 11.21/11.37 tff(368,plain,
% 11.21/11.37 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.21/11.37 inference(quant_inst,[status(thm)],[])).
% 11.21/11.37 tff(369,plain,
% 11.21/11.37 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[368, 367])).
% 11.21/11.37 tff(370,plain,
% 11.21/11.37 ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[369, 363])).
% 11.21/11.37 tff(371,plain,
% 11.21/11.37 (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[370, 201, 199, 194, 350, 145])).
% 11.21/11.37 tff(372,plain,
% 11.21/11.37 (k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.21/11.37 inference(symmetry,[status(thm)],[371])).
% 11.21/11.37 tff(373,plain,
% 11.21/11.37 (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.21/11.37 inference(symmetry,[status(thm)],[188])).
% 11.21/11.37 tff(374,plain,
% 11.21/11.37 (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.21/11.37 inference(transitivity,[status(thm)],[373, 372, 345, 343])).
% 11.21/11.37 tff(375,plain,
% 11.21/11.37 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) <=> m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.21/11.37 inference(monotonicity,[status(thm)],[374])).
% 11.21/11.37 tff(376,plain,
% 11.21/11.37 (m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) <=> m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.21/11.37 inference(symmetry,[status(thm)],[375])).
% 11.21/11.37 tff(377,plain,
% 11.21/11.37 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(378,plain,
% 11.21/11.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[377])).
% 11.21/11.37 tff(379,plain,
% 11.21/11.37 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(380,plain,
% 11.21/11.37 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[379])).
% 11.21/11.37 tff(381,plain,
% 11.21/11.37 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(382,plain,
% 11.21/11.37 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(383,plain,
% 11.21/11.37 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[382])).
% 11.21/11.37 tff(384,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 11.21/11.37 tff(385,plain,
% 11.21/11.37 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[384, 383])).
% 11.21/11.37 tff(386,plain,
% 11.21/11.37 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[385, 381])).
% 11.21/11.37 tff(387,plain,(
% 11.21/11.37 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 11.21/11.37 inference(skolemize,[status(sab)],[386])).
% 11.21/11.37 tff(388,plain,
% 11.21/11.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[387, 380])).
% 11.21/11.37 tff(389,plain,
% 11.21/11.37 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[388, 378])).
% 11.21/11.37 tff(390,plain,
% 11.21/11.37 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(391,plain,
% 11.21/11.37 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(392,plain,
% 11.21/11.37 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 11.21/11.37 inference(monotonicity,[status(thm)],[391])).
% 11.21/11.37 tff(393,plain,
% 11.21/11.37 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 11.21/11.37 inference(transitivity,[status(thm)],[392, 390])).
% 11.21/11.37 tff(394,plain,
% 11.21/11.37 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 11.21/11.37 inference(quant_inst,[status(thm)],[])).
% 11.21/11.37 tff(395,plain,
% 11.21/11.37 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[394, 393])).
% 11.21/11.37 tff(396,plain,
% 11.21/11.37 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[395, 32, 31, 30, 389])).
% 11.21/11.37 tff(397,plain,
% 11.21/11.37 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v4_lattices(A!0)),
% 11.21/11.37 inference(tautology,[status(thm)],[])).
% 11.21/11.37 tff(398,plain,
% 11.21/11.37 (v4_lattices(A!0)),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[397, 396])).
% 11.21/11.37 tff(399,plain,
% 11.21/11.37 (((~![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)))))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(400,plain,
% 11.21/11.37 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 11.21/11.37 inference(quant_inst,[status(thm)],[])).
% 11.21/11.37 tff(401,plain,
% 11.21/11.37 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[400, 399])).
% 11.21/11.37 tff(402,plain,
% 11.21/11.37 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[401, 30, 132])).
% 11.21/11.37 tff(403,plain,
% 11.21/11.37 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 11.21/11.37 inference(tautology,[status(thm)],[])).
% 11.21/11.37 tff(404,plain,
% 11.21/11.37 (l2_lattices(A!0)),
% 11.21/11.37 inference(unit_resolution,[status(thm)],[403, 402])).
% 11.21/11.37 tff(405,plain,
% 11.21/11.37 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(406,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[405])).
% 11.21/11.37 tff(407,plain,
% 11.21/11.37 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_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))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(408,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[407])).
% 11.21/11.37 tff(409,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(410,plain,
% 11.21/11.37 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))))),
% 11.21/11.37 inference(bind,[status(th)],[])).
% 11.21/11.37 tff(411,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 11.21/11.37 inference(quant_intro,[status(thm)],[410])).
% 11.21/11.37 tff(412,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k3_lattices')).
% 11.21/11.37 tff(413,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[412, 411])).
% 11.21/11.37 tff(414,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[413, 409])).
% 11.21/11.37 tff(415,plain,(
% 11.21/11.37 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 11.21/11.37 inference(skolemize,[status(sab)],[414])).
% 11.21/11.37 tff(416,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[415, 408])).
% 11.21/11.37 tff(417,plain,
% 11.21/11.37 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 11.21/11.37 inference(modus_ponens,[status(thm)],[416, 406])).
% 11.21/11.37 tff(418,plain,
% 11.21/11.37 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(419,plain,
% 11.21/11.37 ((v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.21/11.37 inference(rewrite,[status(thm)],[])).
% 11.21/11.37 tff(420,plain,
% 11.21/11.37 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))))),
% 11.21/11.37 inference(monotonicity,[status(thm)],[419])).
% 11.21/11.37 tff(421,plain,
% 11.21/11.37 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.21/11.37 inference(transitivity,[status(thm)],[420, 418])).
% 11.21/11.37 tff(422,plain,
% 11.21/11.37 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))),
% 11.21/11.37 inference(quant_inst,[status(thm)],[])).
% 11.21/11.37 tff(423,plain,
% 11.21/11.37 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[422, 421])).
% 11.21/11.38 tff(424,plain,
% 11.21/11.38 (m1_subset_1(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[423, 32, 417, 404, 398, 302, 298])).
% 11.21/11.38 tff(425,plain,
% 11.21/11.38 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[424, 376])).
% 11.21/11.38 tff(426,plain,
% 11.21/11.38 (u1_struct_0(k23_filter_2(A!0, B!1)) = u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.21/11.38 inference(symmetry,[status(thm)],[146])).
% 11.21/11.38 tff(427,plain,
% 11.21/11.38 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1))) <=> m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.21/11.38 inference(monotonicity,[status(thm)],[426])).
% 11.21/11.38 tff(428,plain,
% 11.21/11.38 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.21/11.38 inference(symmetry,[status(thm)],[427])).
% 11.21/11.38 tff(429,plain,
% 11.21/11.38 (m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[223, 428])).
% 11.21/11.38 tff(430,plain,
% 11.21/11.38 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.21/11.38 inference(rewrite,[status(thm)],[])).
% 11.21/11.38 tff(431,plain,
% 11.21/11.38 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))),
% 11.21/11.38 inference(quant_inst,[status(thm)],[])).
% 11.21/11.38 tff(432,plain,
% 11.21/11.38 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(C, u1_struct_0(A!0)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[431, 430])).
% 11.21/11.38 tff(433,plain,
% 11.21/11.38 (m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[432, 186, 294])).
% 11.21/11.38 tff(434,plain,
% 11.21/11.38 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D)))))))),
% 11.21/11.38 inference(rewrite,[status(thm)],[])).
% 11.21/11.38 tff(435,plain,
% 11.21/11.38 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D)))))))),
% 11.21/11.38 inference(quant_inst,[status(thm)],[])).
% 11.21/11.38 tff(436,plain,
% 11.21/11.38 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[435, 434])).
% 11.21/11.38 tff(437,plain,
% 11.21/11.38 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[436, 329, 433])).
% 11.21/11.38 tff(438,plain,
% 11.21/11.38 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))),
% 11.21/11.38 inference(rewrite,[status(thm)],[])).
% 11.21/11.38 tff(439,plain,
% 11.21/11.38 (((~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))) <=> ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))),
% 11.21/11.38 inference(rewrite,[status(thm)],[])).
% 11.21/11.38 tff(440,plain,
% 11.21/11.38 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))))),
% 11.21/11.38 inference(monotonicity,[status(thm)],[439])).
% 11.21/11.38 tff(441,plain,
% 11.21/11.38 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))),
% 11.21/11.38 inference(transitivity,[status(thm)],[440, 438])).
% 11.21/11.38 tff(442,plain,
% 11.21/11.38 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))))),
% 11.21/11.38 inference(quant_inst,[status(thm)],[])).
% 11.21/11.38 tff(443,plain,
% 11.21/11.38 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))))),
% 11.21/11.38 inference(modus_ponens,[status(thm)],[442, 441])).
% 11.21/11.38 tff(444,plain,
% 11.21/11.38 (~((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))))),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[443, 186, 437, 429, 425])).
% 11.21/11.38 tff(445,plain,
% 11.21/11.38 (((~(k3_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.21/11.38 inference(tautology,[status(thm)],[])).
% 11.21/11.38 tff(446,plain,
% 11.21/11.38 (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[445, 444])).
% 11.21/11.38 tff(447,plain,
% 11.21/11.38 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 11.21/11.38 inference(tautology,[status(thm)],[])).
% 11.21/11.38 tff(448,plain,
% 11.21/11.38 (v6_lattices(A!0)),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[447, 396])).
% 11.21/11.38 tff(449,plain,
% 11.21/11.38 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 11.21/11.38 inference(tautology,[status(thm)],[])).
% 11.21/11.38 tff(450,plain,
% 11.21/11.38 (l1_lattices(A!0)),
% 11.21/11.38 inference(unit_resolution,[status(thm)],[449, 402])).
% 11.21/11.38 tff(451,plain,
% 11.21/11.38 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.21/11.38 inference(rewrite,[status(thm)],[])).
% 11.21/11.38 tff(452,plain,
% 11.21/11.38 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.21/11.39 inference(rewrite,[status(thm)],[])).
% 11.21/11.39 tff(453,plain,
% 11.21/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.21/11.39 inference(monotonicity,[status(thm)],[452])).
% 11.21/11.39 tff(454,plain,
% 11.21/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.21/11.39 inference(transitivity,[status(thm)],[453, 451])).
% 11.21/11.39 tff(455,plain,
% 11.21/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 11.21/11.39 inference(quant_inst,[status(thm)],[])).
% 11.21/11.39 tff(456,plain,
% 11.21/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.21/11.39 inference(modus_ponens,[status(thm)],[455, 454])).
% 11.21/11.39 tff(457,plain,
% 11.21/11.39 (k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.21/11.39 inference(unit_resolution,[status(thm)],[456, 32, 257, 450, 448, 433, 425])).
% 11.21/11.39 tff(458,plain,
% 11.21/11.39 (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(A!0, tptp_fun_D_4(k23_filter_2(A!0, B!1)), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.21/11.39 inference(symmetry,[status(thm)],[457])).
% 11.21/11.39 tff(459,plain,
% 11.21/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(rewrite,[status(thm)],[])).
% 11.23/11.39 tff(460,plain,
% 11.23/11.39 ((v3_struct_0(A!0) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(rewrite,[status(thm)],[])).
% 11.23/11.39 tff(461,plain,
% 11.23/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.23/11.39 inference(monotonicity,[status(thm)],[460])).
% 11.23/11.39 tff(462,plain,
% 11.23/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(transitivity,[status(thm)],[461, 459])).
% 11.23/11.39 tff(463,plain,
% 11.23/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 11.23/11.39 inference(quant_inst,[status(thm)],[])).
% 11.23/11.39 tff(464,plain,
% 11.23/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.23/11.39 inference(modus_ponens,[status(thm)],[463, 462])).
% 11.23/11.39 tff(465,plain,
% 11.23/11.39 (k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(unit_resolution,[status(thm)],[464, 32, 236, 450, 448, 433, 425])).
% 11.23/11.39 tff(466,plain,
% 11.23/11.39 (k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(symmetry,[status(thm)],[465])).
% 11.23/11.39 tff(467,plain,
% 11.23/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(rewrite,[status(thm)],[])).
% 11.23/11.39 tff(468,plain,
% 11.23/11.39 ((v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(rewrite,[status(thm)],[])).
% 11.23/11.39 tff(469,plain,
% 11.23/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))))),
% 11.23/11.39 inference(monotonicity,[status(thm)],[468])).
% 11.23/11.39 tff(470,plain,
% 11.23/11.39 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))))),
% 11.23/11.39 inference(transitivity,[status(thm)],[469, 467])).
% 11.23/11.39 tff(471,plain,
% 11.23/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))),
% 11.23/11.39 inference(quant_inst,[status(thm)],[])).
% 11.23/11.39 tff(472,plain,
% 11.23/11.39 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))))),
% 11.23/11.39 inference(modus_ponens,[status(thm)],[471, 470])).
% 11.23/11.39 tff(473,plain,
% 11.23/11.39 (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(unit_resolution,[status(thm)],[472, 32, 363, 404, 398, 302, 298])).
% 11.23/11.39 tff(474,plain,
% 11.23/11.39 (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(transitivity,[status(thm)],[373, 372, 345, 343, 473])).
% 11.23/11.39 tff(475,plain,
% 11.23/11.39 (k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(monotonicity,[status(thm)],[474])).
% 11.23/11.39 tff(476,plain,
% 11.23/11.39 (k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.23/11.39 inference(symmetry,[status(thm)],[475])).
% 11.23/11.39 tff(477,plain,
% 11.23/11.39 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))))))),
% 11.23/11.39 inference(rewrite,[status(thm)],[])).
% 11.23/11.39 tff(478,plain,
% 11.23/11.39 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)) | (~m1_subset_1(D, u1_struct_0(A!0))))))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))))))),
% 11.23/11.40 inference(rewrite,[status(thm)],[])).
% 11.23/11.40 tff(479,plain,
% 11.23/11.40 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)) | (~m1_subset_1(D, u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))))))))),
% 11.23/11.40 inference(monotonicity,[status(thm)],[478])).
% 11.23/11.40 tff(480,plain,
% 11.23/11.40 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)) | (~m1_subset_1(D, u1_struct_0(A!0)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))))))),
% 11.23/11.40 inference(transitivity,[status(thm)],[479, 477])).
% 11.23/11.40 tff(481,plain,
% 11.23/11.40 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)) | (~m1_subset_1(D, u1_struct_0(A!0)))))))))))),
% 11.23/11.40 inference(quant_inst,[status(thm)],[])).
% 11.23/11.40 tff(482,plain,
% 11.23/11.40 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v12_lattices(A) | (~((~m1_subset_1(tptp_fun_B_2(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_3(A), u1_struct_0(A))) | (k1_lattices(A, tptp_fun_B_2(A), k2_lattices(A, tptp_fun_C_3(A), tptp_fun_D_4(A))) = k2_lattices(A, k1_lattices(A, tptp_fun_B_2(A), tptp_fun_C_3(A)), tptp_fun_D_4(A))) | (~r1_lattices(A, tptp_fun_B_2(A), tptp_fun_D_4(A))) | (~m1_subset_1(tptp_fun_D_4(A), u1_struct_0(A))))))) | (~((~v12_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((k1_lattices(A, B, k2_lattices(A, C, D)) = k2_lattices(A, k1_lattices(A, B, C), D)) | (~r1_lattices(A, B, D)) | (~m1_subset_1(D, u1_struct_0(A)))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))))))),
% 11.23/11.40 inference(modus_ponens,[status(thm)],[481, 480])).
% 11.23/11.40 tff(483,plain,
% 11.23/11.40 (~((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[482, 32, 30, 170])).
% 11.23/11.40 tff(484,plain,
% 11.23/11.40 (((~(v12_lattices(A!0) | (~((~m1_subset_1(tptp_fun_D_4(A!0), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_D_4(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(A!0), k2_lattices(A!0, tptp_fun_C_3(A!0), tptp_fun_D_4(A!0))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(A!0), tptp_fun_C_3(A!0)), tptp_fun_D_4(A!0))) | (~m1_subset_1(tptp_fun_C_3(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(A!0), u1_struct_0(A!0))))))) | (~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))))) | ((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))),
% 11.23/11.40 inference(tautology,[status(thm)],[])).
% 11.23/11.40 tff(485,plain,
% 11.23/11.40 ((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[484, 483])).
% 11.23/11.40 tff(486,plain,
% 11.23/11.40 (v12_lattices(A!0)),
% 11.23/11.40 inference(or_elim,[status(thm)],[26])).
% 11.23/11.40 tff(487,plain,
% 11.23/11.40 ((~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))) | (~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))),
% 11.23/11.40 inference(tautology,[status(thm)],[])).
% 11.23/11.40 tff(488,plain,
% 11.23/11.40 ((~((~v12_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] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D))))))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[487, 486])).
% 11.23/11.40 tff(489,plain,
% 11.23/11.40 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[488, 485])).
% 11.23/11.40 tff(490,plain,
% 11.23/11.40 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))),
% 11.23/11.40 inference(rewrite,[status(thm)],[])).
% 11.23/11.40 tff(491,plain,
% 11.23/11.40 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))))),
% 11.23/11.40 inference(quant_inst,[status(thm)],[])).
% 11.23/11.40 tff(492,plain,
% 11.23/11.40 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, B, k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, B, C), D)) | (~r1_lattices(A!0, B, D)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))),
% 11.23/11.40 inference(modus_ponens,[status(thm)],[491, 490])).
% 11.23/11.40 tff(493,plain,
% 11.23/11.40 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[492, 489, 302])).
% 11.23/11.40 tff(494,plain,
% 11.23/11.40 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D))))),
% 11.23/11.40 inference(rewrite,[status(thm)],[])).
% 11.23/11.40 tff(495,plain,
% 11.23/11.40 (((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) <=> ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D))))),
% 11.23/11.40 inference(rewrite,[status(thm)],[])).
% 11.23/11.40 tff(496,plain,
% 11.23/11.40 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))))),
% 11.23/11.40 inference(monotonicity,[status(thm)],[495])).
% 11.23/11.40 tff(497,plain,
% 11.23/11.40 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D))))),
% 11.23/11.40 inference(transitivity,[status(thm)],[496, 494])).
% 11.23/11.40 tff(498,plain,
% 11.23/11.40 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))),
% 11.23/11.40 inference(quant_inst,[status(thm)],[])).
% 11.23/11.40 tff(499,plain,
% 11.23/11.40 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, C, D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), C), D)) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))),
% 11.23/11.40 inference(modus_ponens,[status(thm)],[498, 497])).
% 11.23/11.40 tff(500,plain,
% 11.23/11.40 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[499, 298, 493])).
% 11.23/11.40 tff(501,plain,
% 11.23/11.40 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v9_lattices(A!0)),
% 11.23/11.40 inference(tautology,[status(thm)],[])).
% 11.23/11.40 tff(502,plain,
% 11.23/11.40 (v9_lattices(A!0)),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[501, 396])).
% 11.23/11.40 tff(503,plain,
% 11.23/11.40 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v8_lattices(A!0)),
% 11.23/11.40 inference(tautology,[status(thm)],[])).
% 11.23/11.40 tff(504,plain,
% 11.23/11.40 (v8_lattices(A!0)),
% 11.23/11.40 inference(unit_resolution,[status(thm)],[503, 396])).
% 11.23/11.40 tff(505,plain,
% 11.23/11.40 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))),
% 11.23/11.40 inference(bind,[status(th)],[])).
% 11.23/11.40 tff(506,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 11.23/11.40 inference(quant_intro,[status(thm)],[505])).
% 11.23/11.40 tff(507,plain,
% 11.23/11.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))))),
% 11.23/11.40 inference(bind,[status(th)],[])).
% 11.23/11.40 tff(508,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 11.23/11.40 inference(quant_intro,[status(thm)],[507])).
% 11.23/11.40 tff(509,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 11.23/11.40 inference(rewrite,[status(thm)],[])).
% 11.23/11.40 tff(510,plain,
% 11.23/11.40 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))), (((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))))),
% 11.23/11.40 inference(bind,[status(th)],[])).
% 11.23/11.40 tff(511,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 11.23/11.40 inference(quant_intro,[status(thm)],[510])).
% 11.23/11.40 tff(512,axiom,(![A: $i, B: $i, C: $i] : ((((((((~v3_struct_0(A)) & v6_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r3_lattices')).
% 11.23/11.40 tff(513,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 11.23/11.40 inference(modus_ponens,[status(thm)],[512, 511])).
% 11.23/11.40 tff(514,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 11.23/11.40 inference(modus_ponens,[status(thm)],[513, 509])).
% 11.23/11.40 tff(515,plain,(
% 11.23/11.40 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)))),
% 11.23/11.40 inference(skolemize,[status(sab)],[514])).
% 11.23/11.40 tff(516,plain,
% 11.23/11.40 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[515, 508])).
% 11.23/11.41 tff(517,plain,
% 11.23/11.41 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[516, 506])).
% 11.23/11.41 tff(518,plain,
% 11.23/11.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(519,plain,
% 11.23/11.41 ((v3_struct_0(A!0) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(520,plain,
% 11.23/11.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.23/11.41 inference(monotonicity,[status(thm)],[519])).
% 11.23/11.41 tff(521,plain,
% 11.23/11.41 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.41 inference(transitivity,[status(thm)],[520, 518])).
% 11.23/11.41 tff(522,plain,
% 11.23/11.41 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~l3_lattices(A!0)))),
% 11.23/11.41 inference(quant_inst,[status(thm)],[])).
% 11.23/11.41 tff(523,plain,
% 11.23/11.41 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v6_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[522, 521])).
% 11.23/11.41 tff(524,plain,
% 11.23/11.41 (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.23/11.41 inference(unit_resolution,[status(thm)],[523, 32, 30, 517, 448, 504, 502, 302, 433])).
% 11.23/11.41 tff(525,plain,
% 11.23/11.41 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.23/11.41 inference(bind,[status(th)],[])).
% 11.23/11.41 tff(526,plain,
% 11.23/11.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(quant_intro,[status(thm)],[525])).
% 11.23/11.41 tff(527,plain,
% 11.23/11.41 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))),
% 11.23/11.41 inference(bind,[status(th)],[])).
% 11.23/11.41 tff(528,plain,
% 11.23/11.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(quant_intro,[status(thm)],[527])).
% 11.23/11.41 tff(529,plain,
% 11.23/11.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(transitivity,[status(thm)],[528, 526])).
% 11.23/11.41 tff(530,plain,
% 11.23/11.41 (^[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] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), rewrite((~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))) <=> ((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), rewrite(((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))))),
% 11.23/11.41 inference(bind,[status(th)],[])).
% 11.23/11.41 tff(531,plain,
% 11.23/11.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(quant_intro,[status(thm)],[530])).
% 11.23/11.41 tff(532,plain,
% 11.23/11.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(533,plain,
% 11.23/11.41 (^[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(trans(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(rewrite((((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))) <=> ((~((C = E) & (D = F))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))), ((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))) <=> (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => ((~((C = E) & (D = F))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))), rewrite((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => ((~((C = E) & (D = F))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))) <=> ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B)))))), ((m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))) <=> ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B)))))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))) <=> ![F: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))))), trans(trans(der(![F: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))) <=> ![F: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)) | (~(C = E)))), elim_unused(![F: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)) | (~(C = E))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)) | (~(C = E)))), (![F: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)) | (~(C = E))))), rewrite(((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)) | (~(C = E))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)))), (![F: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)) | (~((C = E) & (D = F))) | (~m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))))), ((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))) <=> (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)))))), rewrite((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)))), ((m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))) <=> ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D)))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))) <=> ![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))))), trans(trans(der(![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))) <=> ![E: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))))), elim_unused(![E: $i] : ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B))))) <=> ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))))), (![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))) <=> ((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B))))))), rewrite(((r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B))))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))), (![E: $i] : ((~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, D))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))) <=> ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))) <=> ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))))) <=> (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), rewrite((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))), (![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))))),
% 11.23/11.41 inference(bind,[status(th)],[])).
% 11.23/11.41 tff(534,plain,
% 11.23/11.41 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(quant_intro,[status(thm)],[533])).
% 11.23/11.41 tff(535,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(k23_filter_2(A, B))) => ![F: $i] : (m1_subset_1(F, u1_struct_0(k23_filter_2(A, B))) => (((C = E) & (D = F)) => (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), E, F)))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t75_filter_2')).
% 11.23/11.41 tff(536,plain,
% 11.23/11.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[535, 534])).
% 11.23/11.41 tff(537,plain,
% 11.23/11.41 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[536, 532])).
% 11.23/11.41 tff(538,plain,(
% 11.23/11.41 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(skolemize,[status(sab)],[537])).
% 11.23/11.41 tff(539,plain,
% 11.23/11.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[538, 531])).
% 11.23/11.41 tff(540,plain,
% 11.23/11.41 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[539, 529])).
% 11.23/11.41 tff(541,plain,
% 11.23/11.41 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D))))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(542,plain,
% 11.23/11.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D))))))),
% 11.23/11.41 inference(quant_inst,[status(thm)],[])).
% 11.23/11.41 tff(543,plain,
% 11.23/11.41 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A, B)))) | (r3_lattices(A, C, D) <=> r3_lattices(k23_filter_2(A, B), C, D))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))),
% 11.23/11.41 inference(modus_ponens,[status(thm)],[542, 541])).
% 11.23/11.41 tff(544,plain,
% 11.23/11.41 (![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))),
% 11.23/11.41 inference(unit_resolution,[status(thm)],[543, 32, 31, 30, 540])).
% 11.23/11.41 tff(545,plain,
% 11.23/11.41 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(546,plain,
% 11.23/11.41 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))) <=> (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))),
% 11.23/11.41 inference(rewrite,[status(thm)],[])).
% 11.23/11.41 tff(547,plain,
% 11.23/11.41 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))))),
% 11.23/11.41 inference(monotonicity,[status(thm)],[546])).
% 11.23/11.41 tff(548,plain,
% 11.23/11.41 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))),
% 11.23/11.42 inference(transitivity,[status(thm)],[547, 545])).
% 11.23/11.42 tff(549,plain,
% 11.23/11.42 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | (v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D)))))),
% 11.23/11.42 inference(quant_inst,[status(thm)],[])).
% 11.23/11.42 tff(550,plain,
% 11.23/11.42 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B)))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B), C, D)))))) | v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))),
% 11.23/11.42 inference(modus_ponens,[status(thm)],[549, 548])).
% 11.23/11.42 tff(551,plain,
% 11.23/11.42 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))),
% 11.23/11.42 inference(unit_resolution,[status(thm)],[550, 29, 28, 544])).
% 11.23/11.42 tff(552,plain,
% 11.23/11.42 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))),
% 11.23/11.42 inference(rewrite,[status(thm)],[])).
% 11.23/11.42 tff(553,plain,
% 11.23/11.42 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))),
% 11.23/11.42 inference(quant_inst,[status(thm)],[])).
% 11.23/11.42 tff(554,plain,
% 11.23/11.42 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, C, D) <=> r3_lattices(k23_filter_2(A!0, B!1), C, D))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))),
% 11.23/11.42 inference(modus_ponens,[status(thm)],[553, 552])).
% 11.23/11.42 tff(555,plain,
% 11.23/11.42 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))),
% 11.23/11.42 inference(unit_resolution,[status(thm)],[554, 551, 302])).
% 11.23/11.42 tff(556,plain,
% 11.23/11.42 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.23/11.42 inference(rewrite,[status(thm)],[])).
% 11.23/11.42 tff(557,plain,
% 11.23/11.42 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) <=> ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(558,plain,
% 11.26/11.42 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.26/11.42 inference(monotonicity,[status(thm)],[557])).
% 11.26/11.42 tff(559,plain,
% 11.26/11.42 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.26/11.42 inference(transitivity,[status(thm)],[558, 556])).
% 11.26/11.42 tff(560,plain,
% 11.26/11.42 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.26/11.42 inference(quant_inst,[status(thm)],[])).
% 11.26/11.42 tff(561,plain,
% 11.26/11.42 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[560, 559])).
% 11.26/11.42 tff(562,plain,
% 11.26/11.42 (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[561, 186, 193, 555, 433])).
% 11.26/11.42 tff(563,plain,
% 11.26/11.42 (r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.26/11.42 inference(monotonicity,[status(thm)],[108])).
% 11.26/11.42 tff(564,plain,
% 11.26/11.42 (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.26/11.42 inference(symmetry,[status(thm)],[563])).
% 11.26/11.42 tff(565,plain,
% 11.26/11.42 (v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> v9_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(monotonicity,[status(thm)],[111])).
% 11.26/11.42 tff(566,plain,
% 11.26/11.42 (v9_lattices(k23_filter_2(A!0, B!1)) <=> v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.26/11.42 inference(symmetry,[status(thm)],[565])).
% 11.26/11.42 tff(567,plain,
% 11.26/11.42 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | v9_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(568,plain,
% 11.26/11.42 (v9_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[567, 88])).
% 11.26/11.42 tff(569,plain,
% 11.26/11.42 (v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[568, 566])).
% 11.26/11.42 tff(570,plain,
% 11.26/11.42 (v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) <=> v8_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(monotonicity,[status(thm)],[111])).
% 11.26/11.42 tff(571,plain,
% 11.26/11.42 (v8_lattices(k23_filter_2(A!0, B!1)) <=> v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.26/11.42 inference(symmetry,[status(thm)],[570])).
% 11.26/11.42 tff(572,plain,
% 11.26/11.42 ((v3_struct_0(k23_filter_2(A!0, B!1)) | (~v3_lattices(k23_filter_2(A!0, B!1))) | (~v4_lattices(k23_filter_2(A!0, B!1))) | (~v5_lattices(k23_filter_2(A!0, B!1))) | (~v6_lattices(k23_filter_2(A!0, B!1))) | (~v7_lattices(k23_filter_2(A!0, B!1))) | (~v8_lattices(k23_filter_2(A!0, B!1))) | (~v9_lattices(k23_filter_2(A!0, B!1))) | (~v10_lattices(k23_filter_2(A!0, B!1)))) | v8_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(tautology,[status(thm)],[])).
% 11.26/11.42 tff(573,plain,
% 11.26/11.42 (v8_lattices(k23_filter_2(A!0, B!1))),
% 11.26/11.42 inference(unit_resolution,[status(thm)],[572, 88])).
% 11.26/11.42 tff(574,plain,
% 11.26/11.42 (v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))),
% 11.26/11.42 inference(modus_ponens,[status(thm)],[573, 571])).
% 11.26/11.42 tff(575,plain,
% 11.26/11.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(576,plain,
% 11.26/11.42 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.26/11.42 inference(rewrite,[status(thm)],[])).
% 11.26/11.42 tff(577,plain,
% 11.26/11.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.26/11.42 inference(monotonicity,[status(thm)],[576])).
% 11.26/11.42 tff(578,plain,
% 11.26/11.42 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.26/11.43 inference(transitivity,[status(thm)],[577, 575])).
% 11.26/11.43 tff(579,plain,
% 11.26/11.43 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.43 inference(quant_inst,[status(thm)],[])).
% 11.27/11.43 tff(580,plain,
% 11.27/11.43 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (r3_lattices(A, B, C) <=> r1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(modus_ponens,[status(thm)],[579, 578])).
% 11.27/11.43 tff(581,plain,
% 11.27/11.43 ((~l3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~v8_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~v9_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[580, 517])).
% 11.27/11.43 tff(582,plain,
% 11.27/11.43 (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[581, 145, 187, 116, 194, 119, 574, 569])).
% 11.27/11.43 tff(583,plain,
% 11.27/11.43 (r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(monotonicity,[status(thm)],[111])).
% 11.27/11.43 tff(584,plain,
% 11.27/11.43 (r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(symmetry,[status(thm)],[583])).
% 11.27/11.43 tff(585,plain,
% 11.27/11.43 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))) | r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(tautology,[status(thm)],[])).
% 11.27/11.43 tff(586,plain,
% 11.27/11.43 (r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[585, 184])).
% 11.27/11.43 tff(587,plain,
% 11.27/11.43 (r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(modus_ponens,[status(thm)],[586, 584])).
% 11.27/11.43 tff(588,plain,
% 11.27/11.43 ((~(r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) | (~r1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.43 inference(tautology,[status(thm)],[])).
% 11.27/11.43 tff(589,plain,
% 11.27/11.43 (r3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[588, 587, 582])).
% 11.27/11.43 tff(590,plain,
% 11.27/11.43 (r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(modus_ponens,[status(thm)],[589, 564])).
% 11.27/11.43 tff(591,plain,
% 11.27/11.43 ((~(r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) | (~r3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.43 inference(tautology,[status(thm)],[])).
% 11.27/11.43 tff(592,plain,
% 11.27/11.43 (r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[591, 590, 562])).
% 11.27/11.43 tff(593,plain,
% 11.27/11.43 ((~(r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) <=> r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~r3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(tautology,[status(thm)],[])).
% 11.27/11.43 tff(594,plain,
% 11.27/11.43 (r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[593, 592, 524])).
% 11.27/11.43 tff(595,plain,
% 11.27/11.43 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(rewrite,[status(thm)],[])).
% 11.27/11.43 tff(596,plain,
% 11.27/11.43 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(quant_inst,[status(thm)],[])).
% 11.27/11.43 tff(597,plain,
% 11.27/11.43 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D)) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), D)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~r1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.43 inference(modus_ponens,[status(thm)],[596, 595])).
% 11.27/11.43 tff(598,plain,
% 11.27/11.43 (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(A!0, k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(unit_resolution,[status(thm)],[597, 433, 594, 500])).
% 11.27/11.43 tff(599,plain,
% 11.27/11.43 (k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.43 inference(monotonicity,[status(thm)],[111])).
% 11.27/11.43 tff(600,plain,
% 11.27/11.43 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(rewrite,[status(thm)],[])).
% 11.27/11.43 tff(601,plain,
% 11.27/11.43 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.43 inference(rewrite,[status(thm)],[])).
% 11.27/11.43 tff(602,plain,
% 11.27/11.43 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.43 inference(monotonicity,[status(thm)],[601])).
% 11.27/11.43 tff(603,plain,
% 11.27/11.43 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.44 inference(transitivity,[status(thm)],[602, 600])).
% 11.27/11.44 tff(604,plain,
% 11.27/11.44 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.44 inference(quant_inst,[status(thm)],[])).
% 11.27/11.44 tff(605,plain,
% 11.27/11.44 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.44 inference(modus_ponens,[status(thm)],[604, 603])).
% 11.27/11.44 tff(606,plain,
% 11.27/11.44 ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v6_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.44 inference(unit_resolution,[status(thm)],[605, 236])).
% 11.27/11.44 tff(607,plain,
% 11.27/11.44 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.44 inference(unit_resolution,[status(thm)],[606, 139, 187, 116, 199, 145])).
% 11.27/11.44 tff(608,plain,
% 11.27/11.44 (k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.44 inference(monotonicity,[status(thm)],[108])).
% 11.27/11.44 tff(609,plain,
% 11.27/11.44 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)))))))),
% 11.27/11.44 inference(rewrite,[status(thm)],[])).
% 11.27/11.44 tff(610,plain,
% 11.27/11.44 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | ((~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D)))))))),
% 11.27/11.44 inference(quant_inst,[status(thm)],[])).
% 11.27/11.44 tff(611,plain,
% 11.27/11.44 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(C, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, C, D) = k3_lattices(k23_filter_2(A!0, B!1), C, D))) | (~(k4_lattices(A!0, C, D) = k4_lattices(k23_filter_2(A!0, B!1), C, D)))))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))),
% 11.27/11.44 inference(modus_ponens,[status(thm)],[610, 609])).
% 11.27/11.44 tff(612,plain,
% 11.27/11.44 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))),
% 11.27/11.44 inference(unit_resolution,[status(thm)],[611, 329, 298])).
% 11.27/11.44 tff(613,plain,
% 11.27/11.44 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.44 inference(rewrite,[status(thm)],[])).
% 11.27/11.44 tff(614,plain,
% 11.27/11.44 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))) <=> ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.44 inference(rewrite,[status(thm)],[])).
% 11.27/11.44 tff(615,plain,
% 11.27/11.44 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))),
% 11.27/11.44 inference(monotonicity,[status(thm)],[614])).
% 11.27/11.44 tff(616,plain,
% 11.27/11.44 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.44 inference(transitivity,[status(thm)],[615, 613])).
% 11.27/11.44 tff(617,plain,
% 11.27/11.44 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.44 inference(quant_inst,[status(thm)],[])).
% 11.27/11.44 tff(618,plain,
% 11.27/11.44 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.44 inference(modus_ponens,[status(thm)],[617, 616])).
% 11.27/11.44 tff(619,plain,
% 11.27/11.44 (~((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.44 inference(unit_resolution,[status(thm)],[618, 186, 198, 612, 433])).
% 11.27/11.44 tff(620,plain,
% 11.27/11.44 (((~(k3_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.44 inference(tautology,[status(thm)],[])).
% 11.27/11.44 tff(621,plain,
% 11.27/11.44 (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.44 inference(unit_resolution,[status(thm)],[620, 619])).
% 11.27/11.44 tff(622,plain,
% 11.27/11.44 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.44 inference(rewrite,[status(thm)],[])).
% 11.27/11.44 tff(623,plain,
% 11.27/11.44 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.44 inference(rewrite,[status(thm)],[])).
% 11.27/11.44 tff(624,plain,
% 11.27/11.44 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.44 inference(monotonicity,[status(thm)],[623])).
% 11.27/11.44 tff(625,plain,
% 11.27/11.44 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.44 inference(transitivity,[status(thm)],[624, 622])).
% 11.27/11.44 tff(626,plain,
% 11.27/11.44 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 11.27/11.44 inference(quant_inst,[status(thm)],[])).
% 11.27/11.44 tff(627,plain,
% 11.27/11.44 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[626, 625])).
% 11.27/11.45 tff(628,plain,
% 11.27/11.45 (k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(unit_resolution,[status(thm)],[627, 32, 236, 450, 448, 298, 433])).
% 11.27/11.45 tff(629,plain,
% 11.27/11.45 (k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[628])).
% 11.27/11.45 tff(630,plain,
% 11.27/11.45 (k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(transitivity,[status(thm)],[629, 621, 608, 607, 599])).
% 11.27/11.45 tff(631,plain,
% 11.27/11.45 (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[630])).
% 11.27/11.45 tff(632,plain,
% 11.27/11.45 (k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.45 inference(symmetry,[status(thm)],[631])).
% 11.27/11.45 tff(633,plain,
% 11.27/11.45 (k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[621])).
% 11.27/11.45 tff(634,plain,
% 11.27/11.45 (k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[608])).
% 11.27/11.45 tff(635,plain,
% 11.27/11.45 (k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[607])).
% 11.27/11.45 tff(636,plain,
% 11.27/11.45 (k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[599])).
% 11.27/11.45 tff(637,plain,
% 11.27/11.45 (k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))) = k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(transitivity,[status(thm)],[636, 635, 634, 633])).
% 11.27/11.45 tff(638,plain,
% 11.27/11.45 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) <=> m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[637])).
% 11.27/11.45 tff(639,plain,
% 11.27/11.45 (m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) <=> m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.27/11.45 inference(symmetry,[status(thm)],[638])).
% 11.27/11.45 tff(640,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(641,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[640])).
% 11.27/11.45 tff(642,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(643,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[642])).
% 11.27/11.45 tff(644,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(645,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(646,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[645])).
% 11.27/11.45 tff(647,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattices')).
% 11.27/11.45 tff(648,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[647, 646])).
% 11.27/11.45 tff(649,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[648, 644])).
% 11.27/11.45 tff(650,plain,(
% 11.27/11.45 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(skolemize,[status(sab)],[649])).
% 11.27/11.45 tff(651,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[650, 643])).
% 11.27/11.45 tff(652,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[651, 641])).
% 11.27/11.45 tff(653,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(654,plain,
% 11.27/11.45 ((v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(655,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[654])).
% 11.27/11.45 tff(656,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)))),
% 11.27/11.45 inference(transitivity,[status(thm)],[655, 653])).
% 11.27/11.45 tff(657,plain,
% 11.27/11.45 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 11.27/11.45 inference(quant_inst,[status(thm)],[])).
% 11.27/11.45 tff(658,plain,
% 11.27/11.45 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[657, 656])).
% 11.27/11.45 tff(659,plain,
% 11.27/11.45 (m1_subset_1(k4_lattices(A!0, tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.27/11.45 inference(unit_resolution,[status(thm)],[658, 32, 652, 450, 448, 298, 433])).
% 11.27/11.45 tff(660,plain,
% 11.27/11.45 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[659, 639])).
% 11.27/11.45 tff(661,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(662,plain,
% 11.27/11.45 ((v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(663,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[662])).
% 11.27/11.45 tff(664,plain,
% 11.27/11.45 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))),
% 11.27/11.45 inference(transitivity,[status(thm)],[663, 661])).
% 11.27/11.45 tff(665,plain,
% 11.27/11.45 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))))),
% 11.27/11.45 inference(quant_inst,[status(thm)],[])).
% 11.27/11.45 tff(666,plain,
% 11.27/11.45 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[665, 664])).
% 11.27/11.45 tff(667,plain,
% 11.27/11.45 (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.45 inference(unit_resolution,[status(thm)],[666, 32, 363, 404, 398, 302, 660])).
% 11.27/11.45 tff(668,plain,
% 11.27/11.45 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1))) <=> m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[426])).
% 11.27/11.45 tff(669,plain,
% 11.27/11.45 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.27/11.45 inference(symmetry,[status(thm)],[668])).
% 11.27/11.45 tff(670,plain,
% 11.27/11.45 (m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) <=> m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.45 inference(monotonicity,[status(thm)],[599])).
% 11.27/11.45 tff(671,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(672,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[671])).
% 11.27/11.45 tff(673,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(674,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[673])).
% 11.27/11.45 tff(675,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(rewrite,[status(thm)],[])).
% 11.27/11.45 tff(676,plain,
% 11.27/11.45 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))), ((((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))))),
% 11.27/11.45 inference(bind,[status(th)],[])).
% 11.27/11.45 tff(677,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(quant_intro,[status(thm)],[676])).
% 11.27/11.45 tff(678,axiom,(![A: $i, B: $i, C: $i] : (((((~v3_struct_0(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k2_lattices')).
% 11.27/11.45 tff(679,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[678, 677])).
% 11.27/11.45 tff(680,plain,
% 11.27/11.45 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.45 inference(modus_ponens,[status(thm)],[679, 675])).
% 11.27/11.46 tff(681,plain,(
% 11.27/11.46 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)))),
% 11.27/11.46 inference(skolemize,[status(sab)],[680])).
% 11.27/11.46 tff(682,plain,
% 11.27/11.46 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))),
% 11.27/11.46 inference(modus_ponens,[status(thm)],[681, 674])).
% 11.27/11.46 tff(683,plain,
% 11.27/11.46 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))),
% 11.27/11.46 inference(modus_ponens,[status(thm)],[682, 672])).
% 11.27/11.46 tff(684,plain,
% 11.27/11.46 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.46 inference(rewrite,[status(thm)],[])).
% 11.27/11.46 tff(685,plain,
% 11.27/11.46 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) <=> ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.46 inference(rewrite,[status(thm)],[])).
% 11.27/11.46 tff(686,plain,
% 11.27/11.46 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.46 inference(monotonicity,[status(thm)],[685])).
% 11.27/11.46 tff(687,plain,
% 11.27/11.46 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.46 inference(transitivity,[status(thm)],[686, 684])).
% 11.27/11.46 tff(688,plain,
% 11.27/11.46 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.46 inference(quant_inst,[status(thm)],[])).
% 11.27/11.46 tff(689,plain,
% 11.27/11.46 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k2_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~l1_lattices(A)))) | (~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.46 inference(modus_ponens,[status(thm)],[688, 687])).
% 11.27/11.46 tff(690,plain,
% 11.27/11.46 ((~l1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.46 inference(unit_resolution,[status(thm)],[689, 683])).
% 11.27/11.46 tff(691,plain,
% 11.27/11.46 (m1_subset_1(k2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.46 inference(unit_resolution,[status(thm)],[690, 139, 187, 145, 199])).
% 11.27/11.46 tff(692,plain,
% 11.27/11.46 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.46 inference(modus_ponens,[status(thm)],[691, 670])).
% 11.27/11.46 tff(693,plain,
% 11.27/11.46 (m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))),
% 11.27/11.46 inference(modus_ponens,[status(thm)],[692, 669])).
% 11.27/11.46 tff(694,plain,
% 11.27/11.46 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))),
% 11.27/11.46 inference(rewrite,[status(thm)],[])).
% 11.27/11.46 tff(695,plain,
% 11.27/11.46 (((~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))) <=> ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))),
% 11.27/11.46 inference(rewrite,[status(thm)],[])).
% 11.27/11.46 tff(696,plain,
% 11.27/11.46 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))))),
% 11.27/11.46 inference(monotonicity,[status(thm)],[695])).
% 11.27/11.46 tff(697,plain,
% 11.27/11.46 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))),
% 11.27/11.46 inference(transitivity,[status(thm)],[696, 694])).
% 11.27/11.46 tff(698,plain,
% 11.27/11.46 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | ((~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))))),
% 11.27/11.47 inference(quant_inst,[status(thm)],[])).
% 11.27/11.47 tff(699,plain,
% 11.27/11.47 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), D) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), D))))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(A!0))) | (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))))),
% 11.27/11.47 inference(modus_ponens,[status(thm)],[698, 697])).
% 11.27/11.47 tff(700,plain,
% 11.27/11.47 (~((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.47 inference(unit_resolution,[status(thm)],[699, 193, 333, 693, 660])).
% 11.27/11.47 tff(701,plain,
% 11.27/11.47 (((~(k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))) | (~(k4_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k4_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))))) | (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.47 inference(tautology,[status(thm)],[])).
% 11.27/11.47 tff(702,plain,
% 11.27/11.47 (k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.47 inference(unit_resolution,[status(thm)],[701, 700])).
% 11.27/11.47 tff(703,plain,
% 11.27/11.47 (k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(A!0, tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.47 inference(symmetry,[status(thm)],[702])).
% 11.27/11.47 tff(704,plain,
% 11.27/11.47 (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.47 inference(monotonicity,[status(thm)],[111])).
% 11.27/11.47 tff(705,plain,
% 11.27/11.47 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.47 inference(rewrite,[status(thm)],[])).
% 11.27/11.47 tff(706,plain,
% 11.27/11.47 ((v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))) <=> ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.47 inference(rewrite,[status(thm)],[])).
% 11.27/11.47 tff(707,plain,
% 11.27/11.47 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.47 inference(monotonicity,[status(thm)],[706])).
% 11.27/11.47 tff(708,plain,
% 11.27/11.47 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))))),
% 11.27/11.47 inference(transitivity,[status(thm)],[707, 705])).
% 11.27/11.47 tff(709,plain,
% 11.27/11.47 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))))),
% 11.27/11.47 inference(quant_inst,[status(thm)],[])).
% 11.27/11.47 tff(710,plain,
% 11.27/11.47 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.47 inference(modus_ponens,[status(thm)],[709, 708])).
% 11.27/11.47 tff(711,plain,
% 11.27/11.47 ((~l2_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))))) | v3_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))) | (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))) | (~v4_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1)))))),
% 11.27/11.47 inference(unit_resolution,[status(thm)],[710, 363])).
% 11.27/11.47 tff(712,plain,
% 11.27/11.47 (k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.47 inference(unit_resolution,[status(thm)],[711, 692, 145, 194, 201, 350])).
% 11.27/11.50 tff(713,plain,
% 11.27/11.50 (k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k3_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.50 inference(symmetry,[status(thm)],[712])).
% 11.27/11.50 tff(714,plain,
% 11.27/11.50 (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k1_lattices(g3_lattices(u1_struct_0(k23_filter_2(A!0, B!1)), u2_lattices(k23_filter_2(A!0, B!1)), u1_lattices(k23_filter_2(A!0, B!1))), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.50 inference(monotonicity,[status(thm)],[108])).
% 11.27/11.50 tff(715,plain,
% 11.27/11.50 (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))),
% 11.27/11.50 inference(transitivity,[status(thm)],[714, 713, 704, 703, 667, 632, 598, 476, 466, 458, 446, 267, 265, 244, 110])).
% 11.27/11.50 tff(716,plain,
% 11.27/11.50 (((~m1_subset_1(tptp_fun_D_4(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~r1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_C_3(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1)))) | (~m1_subset_1(tptp_fun_B_2(k23_filter_2(A!0, B!1)), u1_struct_0(k23_filter_2(A!0, B!1))))) | (~(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1)))))),
% 11.27/11.50 inference(tautology,[status(thm)],[])).
% 11.27/11.50 tff(717,plain,
% 11.27/11.50 (~(k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), k2_lattices(k23_filter_2(A!0, B!1), tptp_fun_C_3(k23_filter_2(A!0, B!1)), tptp_fun_D_4(k23_filter_2(A!0, B!1)))) = k2_lattices(k23_filter_2(A!0, B!1), k1_lattices(k23_filter_2(A!0, B!1), tptp_fun_B_2(k23_filter_2(A!0, B!1)), tptp_fun_C_3(k23_filter_2(A!0, B!1))), tptp_fun_D_4(k23_filter_2(A!0, B!1))))),
% 11.27/11.50 inference(unit_resolution,[status(thm)],[716, 184])).
% 11.27/11.50 tff(718,plain,
% 11.27/11.50 ($false),
% 11.27/11.50 inference(unit_resolution,[status(thm)],[717, 715])).
% 11.27/11.50 % SZS output end Proof
% 11.35/11.51 % E exiting
%------------------------------------------------------------------------------