%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT323+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:14:21 AM UTC 2025
% Result : Theorem 142.63s 142.98s
% Output : Proof 143.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT323+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 20:17:38 EDT 2025
% 0.12/0.33 % CPUTime :
% 142.63/142.98 % SZS status Theorem
% 142.63/142.98 % SZS output start Proof
% 142.63/142.98 tff(r2_hidden_type, type, (
% 142.63/142.98 r2_hidden: ( $i * $i ) > $o)).
% 142.63/142.98 tff(k7_filter_2_type, type, (
% 142.63/142.98 k7_filter_2: ( $i * $i ) > $i)).
% 142.63/142.98 tff(tptp_fun_B_1_type, type, (
% 142.63/142.98 tptp_fun_B_1: $i)).
% 142.63/142.98 tff(tptp_fun_A_0_type, type, (
% 142.63/142.98 tptp_fun_A_0: $i)).
% 142.63/142.98 tff(tptp_fun_C_2_type, type, (
% 142.63/142.98 tptp_fun_C_2: $i)).
% 142.63/142.98 tff(m1_subset_1_type, type, (
% 142.63/142.98 m1_subset_1: ( $i * $i ) > $o)).
% 142.63/142.98 tff(k1_zfmisc_1_type, type, (
% 142.63/142.98 k1_zfmisc_1: $i > $i)).
% 142.63/142.98 tff(u1_struct_0_type, type, (
% 142.63/142.98 u1_struct_0: $i > $i)).
% 142.63/142.98 tff(m2_lattice4_type, type, (
% 142.63/142.98 m2_lattice4: ( $i * $i ) > $o)).
% 142.63/142.98 tff(v1_xboole_0_type, type, (
% 142.63/142.98 v1_xboole_0: $i > $o)).
% 142.63/142.98 tff(m2_filter_2_type, type, (
% 142.63/142.98 m2_filter_2: ( $i * $i ) > $o)).
% 142.63/142.98 tff(v10_lattices_type, type, (
% 142.63/142.98 v10_lattices: $i > $o)).
% 142.63/142.98 tff(l3_lattices_type, type, (
% 142.63/142.98 l3_lattices: $i > $o)).
% 142.63/142.98 tff(v3_struct_0_type, type, (
% 142.63/142.98 v3_struct_0: $i > $o)).
% 142.63/142.98 tff(r2_filter_2_type, type, (
% 142.63/142.98 r2_filter_2: ( $i * $i ) > $o)).
% 142.63/142.98 tff(k7_lattices_type, type, (
% 142.63/142.98 k7_lattices: ( $i * $i ) > $i)).
% 142.63/142.98 tff(v17_lattices_type, type, (
% 142.63/142.98 v17_lattices: $i > $o)).
% 142.63/142.98 tff(g3_lattices_type, type, (
% 142.63/142.98 g3_lattices: ( $i * $i * $i ) > $i)).
% 142.63/142.98 tff(u2_lattices_type, type, (
% 142.63/142.98 u2_lattices: $i > $i)).
% 142.63/142.98 tff(u1_lattices_type, type, (
% 142.63/142.98 u1_lattices: $i > $i)).
% 142.63/142.98 tff(k5_filter_2_type, type, (
% 142.63/142.98 k5_filter_2: ( $i * $i ) > $i)).
% 142.63/142.98 tff(k1_lattice2_type, type, (
% 142.63/142.98 k1_lattice2: $i > $i)).
% 142.63/142.98 tff(v1_filter_0_type, type, (
% 142.63/142.98 v1_filter_0: ( $i * $i ) > $o)).
% 142.63/142.98 tff(k15_filter_2_type, type, (
% 142.63/142.98 k15_filter_2: ( $i * $i ) > $i)).
% 142.63/142.98 tff(m1_filter_0_type, type, (
% 142.63/142.98 m1_filter_0: ( $i * $i ) > $o)).
% 142.63/142.98 tff(m1_filter_2_type, type, (
% 142.63/142.98 m1_filter_2: ( $i * $i ) > $o)).
% 142.63/142.98 tff(v9_lattices_type, type, (
% 142.63/142.98 v9_lattices: $i > $o)).
% 142.63/142.98 tff(v8_lattices_type, type, (
% 142.63/142.98 v8_lattices: $i > $o)).
% 142.63/142.98 tff(v7_lattices_type, type, (
% 142.63/142.98 v7_lattices: $i > $o)).
% 142.63/142.98 tff(v6_lattices_type, type, (
% 142.63/142.98 v6_lattices: $i > $o)).
% 142.63/142.98 tff(v5_lattices_type, type, (
% 142.63/142.98 v5_lattices: $i > $o)).
% 142.63/142.98 tff(v4_lattices_type, type, (
% 142.63/142.98 v4_lattices: $i > $o)).
% 142.63/142.98 tff(v3_lattices_type, type, (
% 142.63/142.98 v3_lattices: $i > $o)).
% 142.63/142.98 tff(m1_relset_1_type, type, (
% 142.63/142.98 m1_relset_1: ( $i * $i * $i ) > $o)).
% 142.63/142.98 tff(k2_zfmisc_1_type, type, (
% 142.63/142.98 k2_zfmisc_1: ( $i * $i ) > $i)).
% 142.63/142.98 tff(m2_relset_1_type, type, (
% 142.63/142.98 m2_relset_1: ( $i * $i * $i ) > $o)).
% 142.63/142.98 tff(v1_funct_2_type, type, (
% 142.63/142.98 v1_funct_2: ( $i * $i * $i ) > $o)).
% 142.63/142.98 tff(v1_funct_1_type, type, (
% 142.63/142.98 v1_funct_1: $i > $o)).
% 142.63/142.98 tff(l1_lattices_type, type, (
% 142.63/142.98 l1_lattices: $i > $o)).
% 142.63/142.98 tff(l2_lattices_type, type, (
% 142.63/142.98 l2_lattices: $i > $o)).
% 142.63/142.98 tff(v16_lattices_type, type, (
% 142.63/142.98 v16_lattices: $i > $o)).
% 142.63/142.98 tff(v15_lattices_type, type, (
% 142.63/142.98 v15_lattices: $i > $o)).
% 142.63/142.98 tff(v14_lattices_type, type, (
% 142.63/142.98 v14_lattices: $i > $o)).
% 142.63/142.98 tff(v13_lattices_type, type, (
% 142.63/142.98 v13_lattices: $i > $o)).
% 142.63/142.98 tff(v12_lattices_type, type, (
% 142.63/142.98 v12_lattices: $i > $o)).
% 142.63/142.98 tff(v11_lattices_type, type, (
% 142.63/142.98 v11_lattices: $i > $o)).
% 142.63/142.98 tff(1,plain,
% 142.63/142.98 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 142.63/142.98 inference(bind,[status(th)],[])).
% 142.63/142.98 tff(2,plain,
% 142.63/142.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.98 inference(quant_intro,[status(thm)],[1])).
% 142.63/142.98 tff(3,plain,
% 142.63/142.98 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 142.63/142.98 inference(bind,[status(th)],[])).
% 142.63/142.98 tff(4,plain,
% 142.63/142.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.98 inference(quant_intro,[status(thm)],[3])).
% 142.63/142.98 tff(5,plain,
% 142.63/142.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.98 inference(transitivity,[status(thm)],[4, 2])).
% 142.63/142.98 tff(6,plain,
% 142.63/142.98 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 142.63/142.98 inference(bind,[status(th)],[])).
% 142.63/142.98 tff(7,plain,
% 142.63/142.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.98 inference(quant_intro,[status(thm)],[6])).
% 142.63/142.98 tff(8,plain,
% 142.63/142.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 142.63/142.98 inference(rewrite,[status(thm)],[])).
% 142.63/142.98 tff(9,plain,
% 142.63/142.98 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 142.63/142.99 inference(bind,[status(th)],[])).
% 142.63/142.99 tff(10,plain,
% 142.63/142.99 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 142.63/142.99 inference(quant_intro,[status(thm)],[9])).
% 142.63/142.99 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 142.63/142.99 tff(12,plain,
% 142.63/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[11, 10])).
% 142.63/142.99 tff(13,plain,
% 142.63/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[12, 8])).
% 142.63/142.99 tff(14,plain,(
% 142.63/142.99 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 142.63/142.99 inference(skolemize,[status(sab)],[13])).
% 142.63/142.99 tff(15,plain,
% 142.63/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[14, 7])).
% 142.63/142.99 tff(16,plain,
% 142.63/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[15, 5])).
% 142.63/142.99 tff(17,plain,
% 142.63/142.99 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))),
% 142.63/142.99 inference(rewrite,[status(thm)],[])).
% 142.63/142.99 tff(18,plain,
% 142.63/142.99 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1)))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))),
% 142.63/142.99 inference(rewrite,[status(thm)],[])).
% 142.63/142.99 tff(19,plain,
% 142.63/142.99 ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) <=> (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1)))))),
% 142.63/142.99 inference(monotonicity,[status(thm)],[18])).
% 142.63/142.99 tff(20,plain,
% 142.63/142.99 (((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0)) <=> ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))),
% 142.63/142.99 inference(monotonicity,[status(thm)],[19])).
% 142.63/142.99 tff(21,plain,
% 142.63/142.99 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0)))),
% 142.63/142.99 inference(monotonicity,[status(thm)],[20])).
% 142.63/142.99 tff(22,plain,
% 142.63/142.99 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0))),
% 142.63/142.99 inference(transitivity,[status(thm)],[21, 17])).
% 142.63/142.99 tff(23,plain,
% 142.63/142.99 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A)))))),
% 142.63/142.99 inference(rewrite,[status(thm)],[])).
% 142.63/142.99 tff(24,plain,
% 142.63/142.99 ((~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A)))))),
% 142.63/142.99 inference(rewrite,[status(thm)],[])).
% 142.63/142.99 tff(25,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t59_filter_2')).
% 142.63/142.99 tff(26,plain,
% 142.63/142.99 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[25, 24])).
% 142.63/142.99 tff(27,plain,
% 142.63/142.99 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[26, 23])).
% 142.63/142.99 tff(28,plain,
% 142.63/142.99 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[27, 23])).
% 142.63/142.99 tff(29,plain,
% 142.63/142.99 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~r2_filter_2(A, B)) | (~m2_filter_2(B, A))))),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[28, 23])).
% 142.63/142.99 tff(30,plain,
% 142.63/142.99 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))) & r2_filter_2(A!0, B!1) & m2_filter_2(B!1, A!0)),
% 142.63/142.99 inference(modus_ponens,[status(thm)],[29, 22])).
% 142.63/142.99 tff(31,plain,
% 142.63/142.99 (l3_lattices(A!0)),
% 142.63/142.99 inference(and_elim,[status(thm)],[30])).
% 142.63/142.99 tff(32,plain,
% 142.63/142.99 (v10_lattices(A!0)),
% 142.63/142.99 inference(and_elim,[status(thm)],[30])).
% 142.63/142.99 tff(33,plain,
% 142.63/142.99 (~v3_struct_0(A!0)),
% 142.70/142.99 inference(and_elim,[status(thm)],[30])).
% 142.70/142.99 tff(34,plain,
% 142.70/142.99 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(35,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(36,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[35, 34])).
% 142.70/142.99 tff(37,plain,
% 142.70/142.99 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[36, 33, 32, 31, 16])).
% 142.70/142.99 tff(38,plain,
% 142.70/142.99 (m2_filter_2(B!1, A!0)),
% 142.70/142.99 inference(and_elim,[status(thm)],[30])).
% 142.70/142.99 tff(39,plain,
% 142.70/142.99 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(40,plain,
% 142.70/142.99 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(41,plain,
% 142.70/142.99 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[40, 39])).
% 142.70/142.99 tff(42,plain,
% 142.70/142.99 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[41, 38, 37])).
% 142.70/142.99 tff(43,plain,
% 142.70/142.99 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 142.70/142.99 inference(tautology,[status(thm)],[])).
% 142.70/142.99 tff(44,plain,
% 142.70/142.99 (m2_lattice4(B!1, A!0)),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[43, 42])).
% 142.70/142.99 tff(45,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(46,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[45])).
% 142.70/142.99 tff(47,plain,
% 142.70/142.99 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(48,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[47])).
% 142.70/142.99 tff(49,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(50,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[49])).
% 142.70/142.99 tff(51,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(transitivity,[status(thm)],[50, 48])).
% 142.70/142.99 tff(52,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(53,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[52])).
% 142.70/142.99 tff(54,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(55,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(56,plain,
% 142.70/142.99 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[55])).
% 142.70/142.99 tff(57,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 142.70/142.99 tff(58,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[57, 56])).
% 142.70/142.99 tff(59,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[58, 54])).
% 142.70/142.99 tff(60,plain,(
% 142.70/142.99 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(skolemize,[status(sab)],[59])).
% 142.70/142.99 tff(61,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[60, 53])).
% 142.70/142.99 tff(62,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[61, 51])).
% 142.70/142.99 tff(63,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[62, 46])).
% 142.70/142.99 tff(64,plain,
% 142.70/142.99 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(65,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(66,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[65, 64])).
% 142.70/142.99 tff(67,plain,
% 142.70/142.99 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[66, 33, 32, 31, 63])).
% 142.70/142.99 tff(68,plain,
% 142.70/142.99 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(69,plain,
% 142.70/142.99 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(70,plain,
% 142.70/142.99 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[69, 68])).
% 142.70/142.99 tff(71,plain,
% 142.70/142.99 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[70, 67, 44])).
% 142.70/142.99 tff(72,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(73,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[72])).
% 142.70/142.99 tff(74,plain,
% 142.70/142.99 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(75,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[74])).
% 142.70/142.99 tff(76,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(77,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[76])).
% 142.70/142.99 tff(78,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(transitivity,[status(thm)],[77, 75])).
% 142.70/142.99 tff(79,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(80,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[79])).
% 142.70/142.99 tff(81,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(82,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(83,plain,
% 142.70/142.99 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[82])).
% 142.70/142.99 tff(84,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d6_filter_2')).
% 142.70/142.99 tff(85,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[84, 83])).
% 142.70/142.99 tff(86,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[85, 81])).
% 142.70/142.99 tff(87,plain,(
% 142.70/142.99 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(skolemize,[status(sab)],[86])).
% 142.70/142.99 tff(88,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[87, 80])).
% 142.70/142.99 tff(89,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[88, 78])).
% 142.70/142.99 tff(90,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[89, 73])).
% 142.70/142.99 tff(91,plain,
% 142.70/142.99 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(92,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(93,plain,
% 142.70/142.99 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[92, 91])).
% 142.70/142.99 tff(94,plain,
% 142.70/142.99 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[93, 33, 32, 31, 90])).
% 142.70/142.99 tff(95,plain,
% 142.70/142.99 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(96,plain,
% 142.70/142.99 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 142.70/142.99 inference(quant_inst,[status(thm)],[])).
% 142.70/142.99 tff(97,plain,
% 142.70/142.99 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[96, 95])).
% 142.70/142.99 tff(98,plain,
% 142.70/142.99 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[97, 94])).
% 142.70/142.99 tff(99,plain,
% 142.70/142.99 (k7_filter_2(A!0, B!1) = B!1),
% 142.70/142.99 inference(unit_resolution,[status(thm)],[98, 71])).
% 142.70/142.99 tff(100,plain,
% 142.70/142.99 (r2_hidden(C!2, k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, B!1)),
% 142.70/142.99 inference(monotonicity,[status(thm)],[99])).
% 142.70/142.99 tff(101,plain,
% 142.70/142.99 (r2_hidden(C!2, B!1) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1))),
% 142.70/142.99 inference(symmetry,[status(thm)],[100])).
% 142.70/142.99 tff(102,plain,
% 142.70/142.99 ((~r2_hidden(C!2, B!1)) <=> (~r2_hidden(C!2, k7_filter_2(A!0, B!1)))),
% 142.70/142.99 inference(monotonicity,[status(thm)],[101])).
% 142.70/142.99 tff(103,assumption,(~r2_hidden(C!2, B!1)), introduced(assumption)).
% 142.70/142.99 tff(104,plain,
% 142.70/142.99 (~r2_hidden(C!2, k7_filter_2(A!0, B!1))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[103, 102])).
% 142.70/142.99 tff(105,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(106,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[105])).
% 142.70/142.99 tff(107,plain,
% 142.70/142.99 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(108,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[107])).
% 142.70/142.99 tff(109,plain,
% 142.70/142.99 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(110,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[109])).
% 142.70/142.99 tff(111,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(transitivity,[status(thm)],[110, 108])).
% 142.70/142.99 tff(112,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(113,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[112])).
% 142.70/142.99 tff(114,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(rewrite,[status(thm)],[])).
% 142.70/142.99 tff(115,plain,
% 142.70/142.99 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))))),
% 142.70/142.99 inference(bind,[status(th)],[])).
% 142.70/142.99 tff(116,plain,
% 142.70/142.99 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(quant_intro,[status(thm)],[115])).
% 142.70/142.99 tff(117,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','l70_filter_2')).
% 142.70/142.99 tff(118,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[117, 116])).
% 142.70/142.99 tff(119,plain,
% 142.70/142.99 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[118, 114])).
% 142.70/142.99 tff(120,plain,(
% 142.70/142.99 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/142.99 inference(skolemize,[status(sab)],[119])).
% 142.70/142.99 tff(121,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[120, 113])).
% 142.70/142.99 tff(122,plain,
% 142.70/142.99 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/142.99 inference(modus_ponens,[status(thm)],[121, 111])).
% 142.70/142.99 tff(123,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[122, 106])).
% 142.70/143.00 tff(124,plain,
% 142.70/143.00 (v17_lattices(A!0)),
% 142.70/143.00 inference(and_elim,[status(thm)],[30])).
% 142.70/143.00 tff(125,plain,
% 142.70/143.00 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B))))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(126,plain,
% 142.70/143.00 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B))))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(127,plain,
% 142.70/143.00 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k7_lattices(k1_lattice2(A), k5_filter_2(A, B)) = k7_lattices(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[126, 125])).
% 142.70/143.00 tff(128,plain,
% 142.70/143.00 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[127, 33, 32, 124, 31, 123])).
% 142.70/143.00 tff(129,plain,
% 142.70/143.00 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1))))),
% 142.70/143.00 inference(and_elim,[status(thm)],[30])).
% 142.70/143.00 tff(130,plain,
% 142.70/143.00 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 142.70/143.00 inference(or_elim,[status(thm)],[129])).
% 142.70/143.00 tff(131,plain,
% 142.70/143.00 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2)) = k7_lattices(A!0, C!2)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2)) = k7_lattices(A!0, C!2)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(132,plain,
% 142.70/143.00 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2)) = k7_lattices(A!0, C!2)))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(133,plain,
% 142.70/143.00 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k7_lattices(A!0, B)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2)) = k7_lattices(A!0, C!2))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[132, 131])).
% 142.70/143.00 tff(134,plain,
% 142.70/143.00 (k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2)) = k7_lattices(A!0, C!2)),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[133, 130, 128])).
% 142.70/143.00 tff(135,plain,
% 142.70/143.00 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(136,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[135])).
% 142.70/143.00 tff(137,plain,
% 142.70/143.00 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(138,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[137])).
% 142.70/143.00 tff(139,plain,
% 142.70/143.00 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(140,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[139])).
% 142.70/143.00 tff(141,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(transitivity,[status(thm)],[140, 138])).
% 142.70/143.00 tff(142,plain,
% 142.70/143.00 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(143,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[142])).
% 142.70/143.00 tff(144,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(145,plain,
% 142.70/143.00 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(146,plain,
% 142.70/143.00 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[145])).
% 142.70/143.00 tff(147,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d4_filter_2')).
% 142.70/143.00 tff(148,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[147, 146])).
% 142.70/143.00 tff(149,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[148, 144])).
% 142.70/143.00 tff(150,plain,(
% 142.70/143.00 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(skolemize,[status(sab)],[149])).
% 142.70/143.00 tff(151,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[150, 143])).
% 142.70/143.00 tff(152,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[151, 141])).
% 142.70/143.00 tff(153,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[152, 136])).
% 142.70/143.00 tff(154,plain,
% 142.70/143.00 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(155,plain,
% 142.70/143.00 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(156,plain,
% 142.70/143.00 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[155, 154])).
% 142.70/143.00 tff(157,plain,
% 142.70/143.00 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[156, 33, 32, 31, 153])).
% 142.70/143.00 tff(158,plain,
% 142.70/143.00 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(159,plain,
% 142.70/143.00 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(160,plain,
% 142.70/143.00 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k5_filter_2(A!0, C!2) = C!2)),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[159, 158])).
% 142.70/143.00 tff(161,plain,
% 142.70/143.00 (k5_filter_2(A!0, C!2) = C!2),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[160, 130, 157])).
% 142.70/143.00 tff(162,plain,
% 142.70/143.00 (C!2 = k5_filter_2(A!0, C!2)),
% 142.70/143.00 inference(symmetry,[status(thm)],[161])).
% 142.70/143.00 tff(163,plain,
% 142.70/143.00 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(164,plain,
% 142.70/143.00 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[163])).
% 142.70/143.00 tff(165,plain,
% 142.70/143.00 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(166,plain,
% 142.70/143.00 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(167,plain,
% 142.70/143.00 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[166])).
% 142.70/143.00 tff(168,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 142.70/143.00 tff(169,plain,
% 142.70/143.00 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[168, 167])).
% 142.70/143.00 tff(170,plain,
% 142.70/143.00 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[169, 165])).
% 142.70/143.00 tff(171,plain,(
% 142.70/143.00 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(skolemize,[status(sab)],[170])).
% 142.70/143.00 tff(172,plain,
% 142.70/143.00 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[171, 164])).
% 142.70/143.00 tff(173,plain,
% 142.70/143.00 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(174,plain,
% 142.70/143.00 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(175,plain,
% 142.70/143.00 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[174, 173])).
% 142.70/143.00 tff(176,plain,
% 142.70/143.00 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[175, 31, 172])).
% 142.70/143.00 tff(177,plain,
% 142.70/143.00 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 142.70/143.00 inference(symmetry,[status(thm)],[176])).
% 142.70/143.00 tff(178,plain,
% 142.70/143.00 (k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k7_lattices(k1_lattice2(A!0), k5_filter_2(A!0, C!2))),
% 142.70/143.00 inference(monotonicity,[status(thm)],[177, 162])).
% 142.70/143.00 tff(179,plain,
% 142.70/143.00 (k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k7_lattices(A!0, C!2)),
% 142.70/143.00 inference(transitivity,[status(thm)],[178, 134])).
% 142.70/143.00 tff(180,plain,
% 142.70/143.00 (r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(k7_lattices(A!0, C!2), B!1)),
% 142.70/143.00 inference(monotonicity,[status(thm)],[179, 99])).
% 142.70/143.00 tff(181,plain,
% 142.70/143.00 (r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1))),
% 142.70/143.00 inference(symmetry,[status(thm)],[180])).
% 142.70/143.00 tff(182,plain,
% 142.70/143.00 ((~r2_hidden(k7_lattices(A!0, C!2), B!1)) <=> (~r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)))),
% 142.70/143.00 inference(monotonicity,[status(thm)],[181])).
% 142.70/143.00 tff(183,plain,
% 142.70/143.00 (r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1)),
% 142.70/143.00 inference(or_elim,[status(thm)],[129])).
% 142.70/143.00 tff(184,plain,
% 142.70/143.00 ((~r2_hidden(k7_lattices(A!0, C!2), B!1)) | r2_hidden(C!2, B!1) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1)))),
% 142.70/143.00 inference(tautology,[status(thm)],[])).
% 142.70/143.00 tff(185,plain,
% 142.70/143.00 ((~r2_hidden(k7_lattices(A!0, C!2), B!1)) | r2_hidden(C!2, B!1)),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[184, 183])).
% 142.70/143.00 tff(186,plain,
% 142.70/143.00 (~r2_hidden(k7_lattices(A!0, C!2), B!1)),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[185, 103])).
% 142.70/143.00 tff(187,plain,
% 142.70/143.00 (~r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[186, 182])).
% 142.70/143.00 tff(188,plain,
% 142.70/143.00 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(189,plain,
% 142.70/143.00 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[188])).
% 142.70/143.00 tff(190,plain,
% 142.70/143.00 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(191,plain,
% 142.70/143.00 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[190])).
% 142.70/143.00 tff(192,plain,
% 142.70/143.00 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(193,plain,
% 142.70/143.00 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(194,plain,
% 142.70/143.00 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[193])).
% 142.70/143.00 tff(195,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 142.70/143.00 tff(196,plain,
% 142.70/143.00 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[195, 194])).
% 142.70/143.00 tff(197,plain,
% 142.70/143.00 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[196, 192])).
% 142.70/143.00 tff(198,plain,(
% 142.70/143.00 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 142.70/143.00 inference(skolemize,[status(sab)],[197])).
% 142.70/143.00 tff(199,plain,
% 142.70/143.00 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[198, 191])).
% 142.70/143.00 tff(200,plain,
% 142.70/143.00 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[199, 189])).
% 142.70/143.00 tff(201,plain,
% 142.70/143.00 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(202,plain,
% 142.70/143.00 ((v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(203,plain,
% 142.70/143.00 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))))),
% 142.70/143.00 inference(monotonicity,[status(thm)],[202])).
% 142.70/143.00 tff(204,plain,
% 142.70/143.00 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 142.70/143.00 inference(transitivity,[status(thm)],[203, 201])).
% 142.70/143.00 tff(205,plain,
% 142.70/143.00 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 142.70/143.00 inference(quant_inst,[status(thm)],[])).
% 142.70/143.00 tff(206,plain,
% 142.70/143.00 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[205, 204])).
% 142.70/143.00 tff(207,plain,
% 142.70/143.00 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 142.70/143.00 inference(unit_resolution,[status(thm)],[206, 33, 32, 31, 38, 200])).
% 142.70/143.00 tff(208,plain,
% 142.70/143.00 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 142.70/143.00 inference(symmetry,[status(thm)],[207])).
% 142.70/143.00 tff(209,plain,
% 142.70/143.00 (v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.00 inference(monotonicity,[status(thm)],[208, 177])).
% 142.70/143.00 tff(210,plain,
% 142.70/143.00 (v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) <=> v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.00 inference(symmetry,[status(thm)],[209])).
% 142.70/143.00 tff(211,plain,
% 142.70/143.00 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(212,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[211])).
% 142.70/143.00 tff(213,plain,
% 142.70/143.00 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(214,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[213])).
% 142.70/143.00 tff(215,plain,
% 142.70/143.00 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(216,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[215])).
% 142.70/143.00 tff(217,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(transitivity,[status(thm)],[216, 214])).
% 142.70/143.00 tff(218,plain,
% 142.70/143.00 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(219,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[218])).
% 142.70/143.00 tff(220,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(221,plain,
% 142.70/143.00 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))))),
% 142.70/143.00 inference(bind,[status(th)],[])).
% 142.70/143.00 tff(222,plain,
% 142.70/143.00 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(quant_intro,[status(thm)],[221])).
% 142.70/143.00 tff(223,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t33_filter_2')).
% 142.70/143.00 tff(224,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[223, 222])).
% 142.70/143.00 tff(225,plain,
% 142.70/143.00 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[224, 220])).
% 142.70/143.00 tff(226,plain,(
% 142.70/143.00 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(skolemize,[status(sab)],[225])).
% 142.70/143.00 tff(227,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[226, 219])).
% 142.70/143.00 tff(228,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[227, 217])).
% 142.70/143.00 tff(229,plain,
% 142.70/143.00 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.00 inference(modus_ponens,[status(thm)],[228, 212])).
% 142.70/143.00 tff(230,plain,
% 142.70/143.00 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 142.70/143.00 inference(rewrite,[status(thm)],[])).
% 142.70/143.00 tff(231,plain,
% 142.70/143.00 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(232,plain,
% 142.70/143.01 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[231, 230])).
% 142.70/143.01 tff(233,plain,
% 142.70/143.01 (![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[232, 33, 32, 31, 229])).
% 142.70/143.01 tff(234,plain,
% 142.70/143.01 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(B!1, A!0)) | (r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(B!1, A!0)) | (r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(235,plain,
% 142.70/143.01 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(B!1, A!0)) | (r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(236,plain,
% 142.70/143.01 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(B!1, A!0)) | (r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[235, 234])).
% 142.70/143.01 tff(237,plain,
% 142.70/143.01 (r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[236, 38, 233])).
% 142.70/143.01 tff(238,plain,
% 142.70/143.01 (r2_filter_2(A!0, B!1)),
% 142.70/143.01 inference(and_elim,[status(thm)],[30])).
% 142.70/143.01 tff(239,plain,
% 142.70/143.01 ((~(r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) | (~r2_filter_2(A!0, B!1)) | v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(240,plain,
% 142.70/143.01 ((~(r2_filter_2(A!0, B!1) <=> v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) | v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[239, 238])).
% 142.70/143.01 tff(241,plain,
% 142.70/143.01 (v1_filter_0(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[240, 237])).
% 142.70/143.01 tff(242,plain,
% 142.70/143.01 (v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[241, 210])).
% 142.70/143.01 tff(243,plain,
% 142.70/143.01 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 142.70/143.01 inference(monotonicity,[status(thm)],[177])).
% 142.70/143.01 tff(244,plain,
% 142.70/143.01 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.01 inference(symmetry,[status(thm)],[243])).
% 142.70/143.01 tff(245,plain,
% 142.70/143.01 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(246,plain,
% 142.70/143.01 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[245])).
% 142.70/143.01 tff(247,plain,
% 142.70/143.01 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(248,plain,
% 142.70/143.01 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[247])).
% 142.70/143.01 tff(249,plain,
% 142.70/143.01 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(250,plain,
% 142.70/143.01 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(251,plain,
% 142.70/143.01 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[250])).
% 142.70/143.01 tff(252,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 142.70/143.01 tff(253,plain,
% 142.70/143.01 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[252, 251])).
% 142.70/143.01 tff(254,plain,
% 142.70/143.01 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[253, 249])).
% 142.70/143.01 tff(255,plain,(
% 142.70/143.01 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 142.70/143.01 inference(skolemize,[status(sab)],[254])).
% 142.70/143.01 tff(256,plain,
% 142.70/143.01 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[255, 248])).
% 142.70/143.01 tff(257,plain,
% 142.70/143.01 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[256, 246])).
% 142.70/143.01 tff(258,plain,
% 142.70/143.01 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(259,plain,
% 142.70/143.01 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(260,plain,
% 142.70/143.01 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[259, 258])).
% 142.70/143.01 tff(261,plain,
% 142.70/143.01 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[260, 33, 32, 31, 257])).
% 142.70/143.01 tff(262,plain,
% 142.70/143.01 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(263,plain,
% 142.70/143.01 (v10_lattices(k1_lattice2(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[262, 261])).
% 142.70/143.01 tff(264,plain,
% 142.70/143.01 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[263, 244])).
% 142.70/143.01 tff(265,plain,
% 142.70/143.01 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 142.70/143.01 inference(monotonicity,[status(thm)],[177])).
% 142.70/143.01 tff(266,plain,
% 142.70/143.01 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.01 inference(symmetry,[status(thm)],[265])).
% 142.70/143.01 tff(267,plain,
% 142.70/143.01 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.01 inference(monotonicity,[status(thm)],[266])).
% 142.70/143.01 tff(268,plain,
% 142.70/143.01 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(269,plain,
% 142.70/143.01 (~v3_struct_0(k1_lattice2(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[268, 261])).
% 142.70/143.01 tff(270,plain,
% 142.70/143.01 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[269, 267])).
% 142.70/143.01 tff(271,plain,
% 142.70/143.01 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(272,plain,
% 142.70/143.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[271])).
% 142.70/143.01 tff(273,plain,
% 142.70/143.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(274,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 142.70/143.01 tff(275,plain,
% 142.70/143.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[274, 273])).
% 142.70/143.01 tff(276,plain,(
% 142.70/143.01 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 142.70/143.01 inference(skolemize,[status(sab)],[275])).
% 142.70/143.01 tff(277,plain,
% 142.70/143.01 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[276, 272])).
% 142.70/143.01 tff(278,plain,
% 142.70/143.01 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(279,plain,
% 142.70/143.01 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[278, 277])).
% 142.70/143.01 tff(280,plain,
% 142.70/143.01 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(281,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[280])).
% 142.70/143.01 tff(282,plain,
% 142.70/143.01 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(283,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[282])).
% 142.70/143.01 tff(284,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(285,plain,
% 142.70/143.01 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(286,plain,
% 142.70/143.01 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[285])).
% 142.70/143.01 tff(287,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 142.70/143.01 tff(288,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[287, 286])).
% 142.70/143.01 tff(289,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[288, 284])).
% 142.70/143.01 tff(290,plain,(
% 142.70/143.01 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 142.70/143.01 inference(skolemize,[status(sab)],[289])).
% 142.70/143.01 tff(291,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[290, 283])).
% 142.70/143.01 tff(292,plain,
% 142.70/143.01 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[291, 281])).
% 142.70/143.01 tff(293,plain,
% 142.70/143.01 (((~![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)))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(294,plain,
% 142.70/143.01 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(295,plain,
% 142.70/143.01 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[294, 293])).
% 142.70/143.01 tff(296,plain,
% 142.70/143.01 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[295, 31, 292])).
% 142.70/143.01 tff(297,plain,
% 142.70/143.01 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(298,plain,
% 142.70/143.01 (l1_lattices(A!0)),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[297, 296])).
% 142.70/143.01 tff(299,plain,
% 142.70/143.01 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(300,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[299])).
% 142.70/143.01 tff(301,plain,
% 142.70/143.01 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(302,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[301])).
% 142.70/143.01 tff(303,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(304,plain,
% 142.70/143.01 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(305,plain,
% 142.70/143.01 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[304])).
% 142.70/143.01 tff(306,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 142.70/143.01 tff(307,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[306, 305])).
% 142.70/143.01 tff(308,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[307, 303])).
% 142.70/143.01 tff(309,plain,(
% 142.70/143.01 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(skolemize,[status(sab)],[308])).
% 142.70/143.01 tff(310,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[309, 302])).
% 142.70/143.01 tff(311,plain,
% 142.70/143.01 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[310, 300])).
% 142.70/143.01 tff(312,plain,
% 142.70/143.01 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(313,plain,
% 142.70/143.01 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(314,plain,
% 142.70/143.01 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[313, 312])).
% 142.70/143.01 tff(315,plain,
% 142.70/143.01 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[314, 311])).
% 142.70/143.01 tff(316,plain,
% 142.70/143.01 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[315, 298])).
% 142.70/143.01 tff(317,plain,
% 142.70/143.01 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(318,plain,
% 142.70/143.01 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[317, 316])).
% 142.70/143.01 tff(319,plain,
% 142.70/143.01 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(320,plain,
% 142.70/143.01 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[319, 318])).
% 142.70/143.01 tff(321,plain,
% 142.70/143.01 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[320, 279])).
% 142.70/143.01 tff(322,plain,
% 142.70/143.01 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(323,plain,
% 142.70/143.01 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[322, 277])).
% 142.70/143.01 tff(324,plain,
% 142.70/143.01 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 142.70/143.01 inference(tautology,[status(thm)],[])).
% 142.70/143.01 tff(325,plain,
% 142.70/143.01 (l2_lattices(A!0)),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[324, 296])).
% 142.70/143.01 tff(326,plain,
% 142.70/143.01 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(327,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[326])).
% 142.70/143.01 tff(328,plain,
% 142.70/143.01 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(329,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[328])).
% 142.70/143.01 tff(330,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(331,plain,
% 142.70/143.01 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(bind,[status(th)],[])).
% 142.70/143.01 tff(332,plain,
% 142.70/143.01 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(quant_intro,[status(thm)],[331])).
% 142.70/143.01 tff(333,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 142.70/143.01 tff(334,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[333, 332])).
% 142.70/143.01 tff(335,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[334, 330])).
% 142.70/143.01 tff(336,plain,(
% 142.70/143.01 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 142.70/143.01 inference(skolemize,[status(sab)],[335])).
% 142.70/143.01 tff(337,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[336, 329])).
% 142.70/143.01 tff(338,plain,
% 142.70/143.01 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[337, 327])).
% 142.70/143.01 tff(339,plain,
% 142.70/143.01 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 142.70/143.01 inference(rewrite,[status(thm)],[])).
% 142.70/143.01 tff(340,plain,
% 142.70/143.01 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 142.70/143.01 inference(quant_inst,[status(thm)],[])).
% 142.70/143.01 tff(341,plain,
% 142.70/143.01 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 142.70/143.01 inference(modus_ponens,[status(thm)],[340, 339])).
% 142.70/143.01 tff(342,plain,
% 142.70/143.01 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[341, 338])).
% 142.70/143.01 tff(343,plain,
% 142.70/143.01 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 142.70/143.01 inference(unit_resolution,[status(thm)],[342, 325])).
% 142.70/143.01 tff(344,plain,
% 142.70/143.01 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(345,plain,
% 142.70/143.02 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[344, 343])).
% 142.70/143.02 tff(346,plain,
% 142.70/143.02 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(347,plain,
% 142.70/143.02 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[346, 345])).
% 142.70/143.02 tff(348,plain,
% 142.70/143.02 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[347, 323])).
% 142.70/143.02 tff(349,plain,
% 142.70/143.02 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(350,plain,
% 142.70/143.02 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[349, 343])).
% 142.70/143.02 tff(351,plain,
% 142.70/143.02 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(352,plain,
% 142.70/143.02 (v1_funct_1(u2_lattices(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[351, 343])).
% 142.70/143.02 tff(353,plain,
% 142.70/143.02 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(354,plain,
% 142.70/143.02 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[353, 316])).
% 142.70/143.02 tff(355,plain,
% 142.70/143.02 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(356,plain,
% 142.70/143.02 (v1_funct_1(u1_lattices(A!0))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[355, 316])).
% 142.70/143.02 tff(357,plain,
% 142.70/143.02 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(358,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[357])).
% 142.70/143.02 tff(359,plain,
% 142.70/143.02 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(360,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[359])).
% 142.70/143.02 tff(361,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(362,plain,
% 142.70/143.02 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(363,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[362])).
% 142.70/143.02 tff(364,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 142.70/143.02 tff(365,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[364, 363])).
% 142.70/143.02 tff(366,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[365, 361])).
% 142.70/143.02 tff(367,plain,(
% 142.70/143.02 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 142.70/143.02 inference(skolemize,[status(sab)],[366])).
% 142.70/143.02 tff(368,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[367, 360])).
% 142.70/143.02 tff(369,plain,
% 142.70/143.02 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[368, 358])).
% 142.70/143.02 tff(370,plain,
% 142.70/143.02 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(371,plain,
% 142.70/143.02 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(372,plain,
% 142.70/143.02 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(373,plain,
% 142.70/143.02 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(monotonicity,[status(thm)],[372])).
% 142.70/143.02 tff(374,plain,
% 142.70/143.02 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(transitivity,[status(thm)],[373, 371])).
% 142.70/143.02 tff(375,plain,
% 142.70/143.02 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 142.70/143.02 inference(monotonicity,[status(thm)],[374])).
% 142.70/143.02 tff(376,plain,
% 142.70/143.02 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(transitivity,[status(thm)],[375, 370])).
% 142.70/143.02 tff(377,plain,
% 142.70/143.02 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 142.70/143.02 inference(quant_inst,[status(thm)],[])).
% 142.70/143.02 tff(378,plain,
% 142.70/143.02 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[377, 376])).
% 142.70/143.02 tff(379,plain,
% 142.70/143.02 ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[378, 369, 356, 354, 352, 350])).
% 142.70/143.02 tff(380,plain,
% 142.70/143.02 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[379, 348, 321])).
% 142.70/143.02 tff(381,plain,
% 142.70/143.02 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.02 inference(tautology,[status(thm)],[])).
% 142.70/143.02 tff(382,plain,
% 142.70/143.02 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[381, 380])).
% 142.70/143.02 tff(383,plain,
% 142.70/143.02 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(384,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[383])).
% 142.70/143.02 tff(385,plain,
% 142.70/143.02 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(386,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[385])).
% 142.70/143.02 tff(387,plain,
% 142.70/143.02 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(388,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[387])).
% 142.70/143.02 tff(389,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(transitivity,[status(thm)],[388, 386])).
% 142.70/143.02 tff(390,plain,
% 142.70/143.02 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(391,plain,
% 142.70/143.02 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[390])).
% 142.70/143.02 tff(392,plain,
% 142.70/143.02 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(393,plain,
% 142.70/143.02 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(394,plain,
% 142.70/143.02 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[393])).
% 142.70/143.02 tff(395,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 142.70/143.02 tff(396,plain,
% 142.70/143.02 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[395, 394])).
% 142.70/143.02 tff(397,plain,
% 142.70/143.02 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[396, 392])).
% 142.70/143.02 tff(398,plain,(
% 142.70/143.02 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(skolemize,[status(sab)],[397])).
% 142.70/143.02 tff(399,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[398, 391])).
% 142.70/143.02 tff(400,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[399, 389])).
% 142.70/143.02 tff(401,plain,
% 142.70/143.02 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[400, 384])).
% 142.70/143.02 tff(402,plain,
% 142.70/143.02 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 142.70/143.02 inference(rewrite,[status(thm)],[])).
% 142.70/143.02 tff(403,plain,
% 142.70/143.02 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 142.70/143.02 inference(quant_inst,[status(thm)],[])).
% 142.70/143.02 tff(404,plain,
% 142.70/143.02 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.02 inference(modus_ponens,[status(thm)],[403, 402])).
% 142.70/143.02 tff(405,plain,
% 142.70/143.02 (![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[404, 401, 382, 270, 264])).
% 142.70/143.02 tff(406,plain,
% 142.70/143.02 ((~![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.02 inference(quant_inst,[status(thm)],[])).
% 142.70/143.02 tff(407,plain,
% 142.70/143.02 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.02 inference(unit_resolution,[status(thm)],[406, 405])).
% 142.70/143.02 tff(408,plain,
% 142.70/143.02 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.02 inference(monotonicity,[status(thm)],[208, 177])).
% 142.70/143.02 tff(409,plain,
% 142.70/143.02 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.02 inference(symmetry,[status(thm)],[408])).
% 142.70/143.02 tff(410,plain,
% 142.70/143.02 (^[A: $i, B: $i] : refl((m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(411,plain,
% 142.70/143.02 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[410])).
% 142.70/143.02 tff(412,plain,
% 142.70/143.02 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 142.70/143.02 inference(bind,[status(th)],[])).
% 142.70/143.02 tff(413,plain,
% 142.70/143.02 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.02 inference(quant_intro,[status(thm)],[412])).
% 142.70/143.02 tff(414,plain,
% 142.70/143.02 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 142.70/143.03 inference(rewrite,[status(thm)],[])).
% 142.70/143.03 tff(415,plain,
% 142.70/143.03 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(416,plain,
% 142.70/143.03 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[415])).
% 142.70/143.03 tff(417,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 142.70/143.03 tff(418,plain,
% 142.70/143.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[417, 416])).
% 142.70/143.03 tff(419,plain,
% 142.70/143.03 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[418, 414])).
% 142.70/143.03 tff(420,plain,(
% 142.70/143.03 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 142.70/143.03 inference(skolemize,[status(sab)],[419])).
% 142.70/143.03 tff(421,plain,
% 142.70/143.03 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[420, 413])).
% 142.70/143.03 tff(422,plain,
% 142.70/143.03 (![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[421, 411])).
% 142.70/143.03 tff(423,plain,
% 142.70/143.03 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 142.70/143.03 inference(rewrite,[status(thm)],[])).
% 142.70/143.03 tff(424,plain,
% 142.70/143.03 ((m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 142.70/143.03 inference(rewrite,[status(thm)],[])).
% 142.70/143.03 tff(425,plain,
% 142.70/143.03 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 142.70/143.03 inference(monotonicity,[status(thm)],[424])).
% 142.70/143.03 tff(426,plain,
% 142.70/143.03 (((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 142.70/143.03 inference(transitivity,[status(thm)],[425, 423])).
% 142.70/143.03 tff(427,plain,
% 142.70/143.03 ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 142.70/143.03 inference(quant_inst,[status(thm)],[])).
% 142.70/143.03 tff(428,plain,
% 142.70/143.03 ((~![A: $i, B: $i] : (m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[427, 426])).
% 142.70/143.03 tff(429,plain,
% 142.70/143.03 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 142.70/143.03 inference(unit_resolution,[status(thm)],[428, 33, 32, 31, 38, 422])).
% 142.70/143.03 tff(430,plain,
% 142.70/143.03 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[429, 409])).
% 142.70/143.03 tff(431,plain,
% 142.70/143.03 ((~(m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.03 inference(tautology,[status(thm)],[])).
% 142.70/143.03 tff(432,plain,
% 142.70/143.03 (m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.03 inference(unit_resolution,[status(thm)],[431, 430, 407])).
% 142.70/143.03 tff(433,plain,
% 142.70/143.03 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v17_lattices(k1_lattice2(A!0))),
% 142.70/143.03 inference(monotonicity,[status(thm)],[177])).
% 142.70/143.03 tff(434,plain,
% 142.70/143.03 (v17_lattices(k1_lattice2(A!0)) <=> v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.03 inference(symmetry,[status(thm)],[433])).
% 142.70/143.03 tff(435,plain,
% 142.70/143.03 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(436,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[435])).
% 142.70/143.03 tff(437,plain,
% 142.70/143.03 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(438,plain,
% 142.70/143.03 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[437])).
% 142.70/143.03 tff(439,plain,
% 142.70/143.03 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 142.70/143.03 inference(rewrite,[status(thm)],[])).
% 142.70/143.03 tff(440,plain,
% 142.70/143.03 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)))), (((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))))), ((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)))), ((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))))), (((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)))), (((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))))), ((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)))), ((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))))), (((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)))), (((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))))), ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)))), ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))))), (((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))), (((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(441,plain,
% 142.70/143.03 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[440])).
% 142.70/143.03 tff(442,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ((((((((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) & v11_lattices(k1_lattice2(A))) & v12_lattices(k1_lattice2(A))) & v13_lattices(k1_lattice2(A))) & v14_lattices(k1_lattice2(A))) & v15_lattices(k1_lattice2(A))) & v16_lattices(k1_lattice2(A))) & v17_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc4_filter_2')).
% 142.70/143.03 tff(443,plain,
% 142.70/143.03 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[442, 441])).
% 142.70/143.03 tff(444,plain,
% 142.70/143.03 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[443, 439])).
% 142.70/143.03 tff(445,plain,(
% 142.70/143.03 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) & v11_lattices(k1_lattice2(A)) & v12_lattices(k1_lattice2(A)) & v13_lattices(k1_lattice2(A)) & v14_lattices(k1_lattice2(A)) & v15_lattices(k1_lattice2(A)) & v16_lattices(k1_lattice2(A)) & v17_lattices(k1_lattice2(A))))),
% 142.70/143.03 inference(skolemize,[status(sab)],[444])).
% 142.70/143.03 tff(446,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[445, 438])).
% 142.70/143.03 tff(447,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[446, 436])).
% 142.70/143.03 tff(448,plain,
% 142.70/143.03 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))),
% 142.70/143.03 inference(rewrite,[status(thm)],[])).
% 142.70/143.03 tff(449,plain,
% 142.70/143.03 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))))),
% 142.70/143.03 inference(quant_inst,[status(thm)],[])).
% 142.70/143.03 tff(450,plain,
% 142.70/143.03 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))) | (~v11_lattices(k1_lattice2(A))) | (~v12_lattices(k1_lattice2(A))) | (~v13_lattices(k1_lattice2(A))) | (~v14_lattices(k1_lattice2(A))) | (~v15_lattices(k1_lattice2(A))) | (~v16_lattices(k1_lattice2(A))) | (~v17_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v17_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0)))))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[449, 448])).
% 142.70/143.03 tff(451,plain,
% 142.70/143.03 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0))))),
% 142.70/143.03 inference(unit_resolution,[status(thm)],[450, 33, 32, 124, 31, 447])).
% 142.70/143.03 tff(452,plain,
% 142.70/143.03 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))) | (~v11_lattices(k1_lattice2(A!0))) | (~v12_lattices(k1_lattice2(A!0))) | (~v13_lattices(k1_lattice2(A!0))) | (~v14_lattices(k1_lattice2(A!0))) | (~v15_lattices(k1_lattice2(A!0))) | (~v16_lattices(k1_lattice2(A!0))) | (~v17_lattices(k1_lattice2(A!0)))) | v17_lattices(k1_lattice2(A!0))),
% 142.70/143.03 inference(tautology,[status(thm)],[])).
% 142.70/143.03 tff(453,plain,
% 142.70/143.03 (v17_lattices(k1_lattice2(A!0))),
% 142.70/143.03 inference(unit_resolution,[status(thm)],[452, 451])).
% 142.70/143.03 tff(454,plain,
% 142.70/143.03 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.03 inference(modus_ponens,[status(thm)],[453, 434])).
% 142.70/143.03 tff(455,plain,
% 142.70/143.03 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite((![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) <=> ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), (![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), ((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))) | (~v10_lattices(A)) | (~v17_lattices(A))))), rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), ((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(456,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[455])).
% 142.70/143.03 tff(457,plain,
% 142.70/143.03 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(458,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.03 inference(quant_intro,[status(thm)],[457])).
% 142.70/143.03 tff(459,plain,
% 142.70/143.03 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))))),
% 142.70/143.03 inference(bind,[status(th)],[])).
% 142.70/143.03 tff(460,plain,
% 142.70/143.03 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[459])).
% 142.70/143.04 tff(461,plain,
% 142.70/143.04 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.04 inference(transitivity,[status(thm)],[460, 458])).
% 142.70/143.04 tff(462,plain,
% 142.70/143.04 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))))),
% 142.70/143.04 inference(bind,[status(th)],[])).
% 142.70/143.04 tff(463,plain,
% 142.70/143.04 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[462])).
% 142.70/143.04 tff(464,plain,
% 142.70/143.04 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(465,plain,
% 142.70/143.04 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(rewrite((r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))) <=> (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))), rewrite((~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))) <=> (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))), ((r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))) <=> (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))), ((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))) <=> (m1_subset_1(C, u1_struct_0(A)) => (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))), ((m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))))), ((v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))))) <=> (v1_filter_0(B, A) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), rewrite((v1_filter_0(B, A) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))) <=> ((~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))))), ((v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))))) <=> ((~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))), ((m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))) <=> (m1_filter_0(B, A) => ((~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))))))), rewrite((m1_filter_0(B, A) => ((~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))))) <=> (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))), ((m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))) <=> (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))))), (![B: $i] : (m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))) <=> ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))))),
% 142.70/143.04 inference(bind,[status(th)],[])).
% 142.70/143.04 tff(466,plain,
% 142.70/143.04 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[465])).
% 142.70/143.04 tff(467,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => (v1_filter_0(B, A) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (r2_hidden(C, B) <=> (~r2_hidden(k7_lattices(A, C), B)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t59_filter_0')).
% 142.70/143.04 tff(468,plain,
% 142.70/143.04 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[467, 466])).
% 142.70/143.04 tff(469,plain,
% 142.70/143.04 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[468, 464])).
% 142.70/143.04 tff(470,plain,(
% 142.70/143.04 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))))),
% 142.70/143.04 inference(skolemize,[status(sab)],[469])).
% 142.70/143.04 tff(471,plain,
% 142.70/143.04 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[470, 463])).
% 142.70/143.04 tff(472,plain,
% 142.70/143.04 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B)))) | (~m1_filter_0(B, A)) | (~v1_filter_0(B, A))) | (~v10_lattices(A)) | (~v17_lattices(A)))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[471, 461])).
% 142.70/143.04 tff(473,plain,
% 142.70/143.04 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[472, 456])).
% 142.70/143.04 tff(474,plain,
% 142.70/143.04 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B))))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(475,plain,
% 142.70/143.04 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B))))))),
% 142.70/143.04 inference(quant_inst,[status(thm)],[])).
% 142.70/143.04 tff(476,plain,
% 142.70/143.04 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~v1_filter_0(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~(r2_hidden(k7_lattices(A, C), B) <=> r2_hidden(C, B))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[475, 474])).
% 142.70/143.04 tff(477,plain,
% 142.70/143.04 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))),
% 142.70/143.04 inference(unit_resolution,[status(thm)],[476, 473, 382, 270, 264, 454])).
% 142.70/143.04 tff(478,plain,
% 142.70/143.04 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1))))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(479,plain,
% 142.70/143.04 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1))))))),
% 142.70/143.04 inference(quant_inst,[status(thm)],[])).
% 142.70/143.04 tff(480,plain,
% 142.70/143.04 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), B) <=> r2_hidden(C, B)))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[479, 478])).
% 142.70/143.04 tff(481,plain,
% 142.70/143.04 ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))),
% 142.70/143.04 inference(unit_resolution,[status(thm)],[480, 477])).
% 142.70/143.04 tff(482,plain,
% 142.70/143.04 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))),
% 142.70/143.04 inference(unit_resolution,[status(thm)],[481, 432, 242])).
% 142.70/143.04 tff(483,plain,
% 142.70/143.04 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 142.70/143.04 inference(monotonicity,[status(thm)],[176])).
% 142.70/143.04 tff(484,plain,
% 142.70/143.04 (m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.04 inference(monotonicity,[status(thm)],[161, 483])).
% 142.70/143.04 tff(485,plain,
% 142.70/143.04 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 142.70/143.04 inference(bind,[status(th)],[])).
% 142.70/143.04 tff(486,plain,
% 142.70/143.04 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[485])).
% 142.70/143.04 tff(487,plain,
% 142.70/143.04 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 142.70/143.04 inference(bind,[status(th)],[])).
% 142.70/143.04 tff(488,plain,
% 142.70/143.04 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[487])).
% 142.70/143.04 tff(489,plain,
% 142.70/143.04 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(490,plain,
% 142.70/143.04 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))))),
% 142.70/143.04 inference(bind,[status(th)],[])).
% 142.70/143.04 tff(491,plain,
% 142.70/143.04 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 142.70/143.04 inference(quant_intro,[status(thm)],[490])).
% 142.70/143.04 tff(492,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 142.70/143.04 tff(493,plain,
% 142.70/143.04 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[492, 491])).
% 142.70/143.04 tff(494,plain,
% 142.70/143.04 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[493, 489])).
% 142.70/143.04 tff(495,plain,(
% 142.70/143.04 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 142.70/143.04 inference(skolemize,[status(sab)],[494])).
% 142.70/143.04 tff(496,plain,
% 142.70/143.04 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[495, 488])).
% 142.70/143.04 tff(497,plain,
% 142.70/143.04 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[496, 486])).
% 142.70/143.04 tff(498,plain,
% 142.70/143.04 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(499,plain,
% 142.70/143.04 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(500,plain,
% 142.70/143.04 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))))),
% 142.70/143.04 inference(monotonicity,[status(thm)],[499])).
% 142.70/143.04 tff(501,plain,
% 142.70/143.04 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))))),
% 142.70/143.04 inference(transitivity,[status(thm)],[500, 498])).
% 142.70/143.04 tff(502,plain,
% 142.70/143.04 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 142.70/143.04 inference(quant_inst,[status(thm)],[])).
% 142.70/143.04 tff(503,plain,
% 142.70/143.04 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[502, 501])).
% 142.70/143.04 tff(504,plain,
% 142.70/143.04 (m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 142.70/143.04 inference(unit_resolution,[status(thm)],[503, 33, 32, 31, 130, 497])).
% 142.70/143.04 tff(505,plain,
% 142.70/143.04 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[504, 484])).
% 142.70/143.04 tff(506,plain,
% 142.70/143.04 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1)))))),
% 142.70/143.04 inference(rewrite,[status(thm)],[])).
% 142.70/143.04 tff(507,plain,
% 142.70/143.04 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1)))))),
% 142.70/143.04 inference(quant_inst,[status(thm)],[])).
% 142.70/143.04 tff(508,plain,
% 142.70/143.04 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C), k7_filter_2(A!0, B!1)) <=> r2_hidden(C, k7_filter_2(A!0, B!1)))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1))))),
% 142.70/143.04 inference(modus_ponens,[status(thm)],[507, 506])).
% 142.70/143.04 tff(509,plain,
% 142.70/143.04 (~(r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1)))),
% 142.70/143.04 inference(unit_resolution,[status(thm)],[508, 505, 482])).
% 142.70/143.04 tff(510,plain,
% 142.70/143.04 ((r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1))) | r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) | r2_hidden(C!2, k7_filter_2(A!0, B!1))),
% 143.51/143.84 inference(tautology,[status(thm)],[])).
% 143.51/143.84 tff(511,plain,
% 143.51/143.84 (r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) | r2_hidden(C!2, k7_filter_2(A!0, B!1))),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[510, 509])).
% 143.51/143.84 tff(512,plain,
% 143.51/143.84 ($false),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[511, 187, 104])).
% 143.51/143.84 tff(513,plain,(r2_hidden(C!2, B!1)), inference(lemma,lemma(discharge,[]))).
% 143.51/143.84 tff(514,plain,
% 143.51/143.84 (r2_hidden(C!2, k7_filter_2(A!0, B!1))),
% 143.51/143.84 inference(modus_ponens,[status(thm)],[513, 101])).
% 143.51/143.84 tff(515,plain,
% 143.51/143.84 (r2_hidden(k7_lattices(A!0, C!2), B!1) | (~r2_hidden(C!2, B!1)) | (~(r2_hidden(k7_lattices(A!0, C!2), B!1) <=> r2_hidden(C!2, B!1)))),
% 143.51/143.84 inference(tautology,[status(thm)],[])).
% 143.51/143.84 tff(516,plain,
% 143.51/143.84 (r2_hidden(k7_lattices(A!0, C!2), B!1) | (~r2_hidden(C!2, B!1))),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[515, 183])).
% 143.51/143.84 tff(517,plain,
% 143.51/143.84 (r2_hidden(k7_lattices(A!0, C!2), B!1)),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[516, 513])).
% 143.51/143.84 tff(518,plain,
% 143.51/143.84 (r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1))),
% 143.51/143.84 inference(modus_ponens,[status(thm)],[517, 181])).
% 143.51/143.84 tff(519,plain,
% 143.51/143.84 ((r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1)) <=> r2_hidden(C!2, k7_filter_2(A!0, B!1))) | (~r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1))) | (~r2_hidden(C!2, k7_filter_2(A!0, B!1)))),
% 143.51/143.84 inference(tautology,[status(thm)],[])).
% 143.51/143.84 tff(520,plain,
% 143.51/143.84 ((~r2_hidden(k7_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2), k7_filter_2(A!0, B!1))) | (~r2_hidden(C!2, k7_filter_2(A!0, B!1)))),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[519, 509])).
% 143.51/143.84 tff(521,plain,
% 143.51/143.84 ($false),
% 143.51/143.84 inference(unit_resolution,[status(thm)],[520, 518, 514])).
% 143.51/143.84 % SZS output end Proof
% 143.51/143.84 % E exiting
%------------------------------------------------------------------------------