%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT324+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 36.73s 36.90s
% Output : Proof 36.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT324+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Thu Jun 19 20:18:35 EDT 2025
% 0.13/0.33 % CPUTime :
% 36.73/36.90 % SZS status Theorem
% 36.73/36.90 % SZS output start Proof
% 36.73/36.90 tff(v1_filter_0_type, type, (
% 36.73/36.90 v1_filter_0: ( $i * $i ) > $o)).
% 36.73/36.90 tff(k1_lattice2_type, type, (
% 36.73/36.90 k1_lattice2: $i > $i)).
% 36.73/36.90 tff(tptp_fun_A_0_type, type, (
% 36.73/36.90 tptp_fun_A_0: $i)).
% 36.73/36.90 tff(k15_filter_2_type, type, (
% 36.73/36.90 k15_filter_2: ( $i * $i ) > $i)).
% 36.73/36.90 tff(tptp_fun_D_31_type, type, (
% 36.73/36.90 tptp_fun_D_31: ( $i * $i * $i ) > $i)).
% 36.73/36.90 tff(g3_lattices_type, type, (
% 36.73/36.90 g3_lattices: ( $i * $i * $i ) > $i)).
% 36.73/36.90 tff(u2_lattices_type, type, (
% 36.73/36.90 u2_lattices: $i > $i)).
% 36.73/36.90 tff(u1_lattices_type, type, (
% 36.73/36.90 u1_lattices: $i > $i)).
% 36.73/36.90 tff(u1_struct_0_type, type, (
% 36.73/36.90 u1_struct_0: $i > $i)).
% 36.73/36.90 tff(tptp_fun_B_1_type, type, (
% 36.73/36.90 tptp_fun_B_1: $i)).
% 36.73/36.90 tff(tptp_fun_C_2_type, type, (
% 36.73/36.90 tptp_fun_C_2: $i)).
% 36.73/36.90 tff(l3_lattices_type, type, (
% 36.73/36.90 l3_lattices: $i > $o)).
% 36.73/36.90 tff(r2_hidden_type, type, (
% 36.73/36.90 r2_hidden: ( $i * $i ) > $o)).
% 36.73/36.90 tff(r2_filter_2_type, type, (
% 36.73/36.90 r2_filter_2: ( $i * $i ) > $o)).
% 36.73/36.90 tff(m2_filter_2_type, type, (
% 36.73/36.90 m2_filter_2: ( $i * $i ) > $o)).
% 36.73/36.90 tff(m1_subset_1_type, type, (
% 36.73/36.90 m1_subset_1: ( $i * $i ) > $o)).
% 36.73/36.90 tff(v17_lattices_type, type, (
% 36.73/36.90 v17_lattices: $i > $o)).
% 36.73/36.90 tff(v10_lattices_type, type, (
% 36.73/36.90 v10_lattices: $i > $o)).
% 36.73/36.90 tff(v3_struct_0_type, type, (
% 36.73/36.90 v3_struct_0: $i > $o)).
% 36.73/36.90 tff(k7_filter_2_type, type, (
% 36.73/36.90 k7_filter_2: ( $i * $i ) > $i)).
% 36.73/36.90 tff(k1_zfmisc_1_type, type, (
% 36.73/36.90 k1_zfmisc_1: $i > $i)).
% 36.73/36.90 tff(v3_lattices_type, type, (
% 36.73/36.90 v3_lattices: $i > $o)).
% 36.73/36.90 tff(m1_relset_1_type, type, (
% 36.73/36.90 m1_relset_1: ( $i * $i * $i ) > $o)).
% 36.73/36.90 tff(k2_zfmisc_1_type, type, (
% 36.73/36.90 k2_zfmisc_1: ( $i * $i ) > $i)).
% 36.73/36.90 tff(m2_relset_1_type, type, (
% 36.73/36.90 m2_relset_1: ( $i * $i * $i ) > $o)).
% 36.73/36.90 tff(v1_funct_2_type, type, (
% 36.73/36.90 v1_funct_2: ( $i * $i * $i ) > $o)).
% 36.73/36.90 tff(v1_funct_1_type, type, (
% 36.73/36.90 v1_funct_1: $i > $o)).
% 36.73/36.90 tff(l1_lattices_type, type, (
% 36.73/36.90 l1_lattices: $i > $o)).
% 36.73/36.90 tff(l2_lattices_type, type, (
% 36.73/36.90 l2_lattices: $i > $o)).
% 36.73/36.90 tff(v1_xboole_0_type, type, (
% 36.73/36.90 v1_xboole_0: $i > $o)).
% 36.73/36.90 tff(m1_filter_0_type, type, (
% 36.73/36.90 m1_filter_0: ( $i * $i ) > $o)).
% 36.73/36.90 tff(k5_filter_2_type, type, (
% 36.73/36.90 k5_filter_2: ( $i * $i ) > $i)).
% 36.73/36.90 tff(v16_lattices_type, type, (
% 36.73/36.90 v16_lattices: $i > $o)).
% 36.73/36.90 tff(v15_lattices_type, type, (
% 36.73/36.90 v15_lattices: $i > $o)).
% 36.73/36.90 tff(v14_lattices_type, type, (
% 36.73/36.90 v14_lattices: $i > $o)).
% 36.73/36.90 tff(v13_lattices_type, type, (
% 36.73/36.90 v13_lattices: $i > $o)).
% 36.73/36.90 tff(v12_lattices_type, type, (
% 36.73/36.90 v12_lattices: $i > $o)).
% 36.73/36.90 tff(v11_lattices_type, type, (
% 36.73/36.90 v11_lattices: $i > $o)).
% 36.73/36.90 tff(v9_lattices_type, type, (
% 36.73/36.90 v9_lattices: $i > $o)).
% 36.73/36.90 tff(v8_lattices_type, type, (
% 36.73/36.90 v8_lattices: $i > $o)).
% 36.73/36.90 tff(v7_lattices_type, type, (
% 36.73/36.90 v7_lattices: $i > $o)).
% 36.73/36.90 tff(v6_lattices_type, type, (
% 36.73/36.90 v6_lattices: $i > $o)).
% 36.73/36.90 tff(v5_lattices_type, type, (
% 36.73/36.90 v5_lattices: $i > $o)).
% 36.73/36.90 tff(v4_lattices_type, type, (
% 36.73/36.90 v4_lattices: $i > $o)).
% 36.73/36.90 tff(k14_filter_2_type, type, (
% 36.73/36.90 k14_filter_2: ( $i * $i ) > $i)).
% 36.73/36.90 tff(k8_filter_2_type, type, (
% 36.73/36.90 k8_filter_2: ( $i * $i ) > $i)).
% 36.73/36.90 tff(1,plain,
% 36.73/36.90 (^[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)))))),
% 36.73/36.90 inference(bind,[status(th)],[])).
% 36.73/36.90 tff(2,plain,
% 36.73/36.90 (![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))))),
% 36.73/36.90 inference(quant_intro,[status(thm)],[1])).
% 36.73/36.90 tff(3,plain,
% 36.73/36.90 (![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))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(4,plain,
% 36.73/36.90 (^[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)))))),
% 36.73/36.90 inference(bind,[status(th)],[])).
% 36.73/36.90 tff(5,plain,
% 36.73/36.90 (![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))))),
% 36.73/36.90 inference(quant_intro,[status(thm)],[4])).
% 36.73/36.90 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 36.73/36.90 tff(7,plain,
% 36.73/36.90 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 36.73/36.90 inference(modus_ponens,[status(thm)],[6, 5])).
% 36.73/36.90 tff(8,plain,
% 36.73/36.90 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 36.73/36.90 inference(modus_ponens,[status(thm)],[7, 3])).
% 36.73/36.90 tff(9,plain,(
% 36.73/36.90 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 36.73/36.90 inference(skolemize,[status(sab)],[8])).
% 36.73/36.90 tff(10,plain,
% 36.73/36.90 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 36.73/36.90 inference(modus_ponens,[status(thm)],[9, 2])).
% 36.73/36.90 tff(11,plain,
% 36.73/36.90 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(12,plain,
% 36.73/36.90 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(13,plain,
% 36.73/36.90 ((m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(14,plain,
% 36.73/36.90 (((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))) <=> ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(15,plain,
% 36.73/36.90 ((m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 36.73/36.90 inference(monotonicity,[status(thm)],[14])).
% 36.73/36.90 tff(16,plain,
% 36.73/36.90 ((m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(transitivity,[status(thm)],[15, 13])).
% 36.73/36.90 tff(17,plain,
% 36.73/36.90 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 36.73/36.90 inference(monotonicity,[status(thm)],[16])).
% 36.73/36.90 tff(18,plain,
% 36.73/36.90 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(transitivity,[status(thm)],[17, 12])).
% 36.73/36.90 tff(19,plain,
% 36.73/36.90 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))))),
% 36.73/36.90 inference(monotonicity,[status(thm)],[18])).
% 36.73/36.90 tff(20,plain,
% 36.73/36.90 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (m1_subset_1(C!2, u1_struct_0(A!0)) & ((~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))))),
% 36.73/36.90 inference(transitivity,[status(thm)],[19, 11])).
% 36.73/36.90 tff(21,plain,
% 36.73/36.90 ((~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))) <=> (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))),
% 36.73/36.90 inference(rewrite,[status(thm)],[])).
% 36.73/36.90 tff(22,plain,
% 36.73/36.90 ((~![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)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m2_filter_2(D, A) => (~(r2_filter_2(A, D) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))) <=> (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(23,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)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m2_filter_2(D, A) => (~(r2_filter_2(A, D) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t60_filter_2')).
% 36.73/36.91 tff(24,plain,
% 36.73/36.91 (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[23, 22])).
% 36.73/36.91 tff(25,plain,
% 36.73/36.91 (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[24, 21])).
% 36.73/36.91 tff(26,plain,
% 36.73/36.91 (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[25, 21])).
% 36.73/36.91 tff(27,plain,
% 36.73/36.91 (~![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m2_filter_2(D, A)) | (~(r2_filter_2(A, D) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[26, 21])).
% 36.73/36.91 tff(28,plain,
% 36.73/36.91 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & m1_subset_1(C!2, u1_struct_0(A!0)) & (~(B!1 = C!2)) & ![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[27, 20])).
% 36.73/36.91 tff(29,plain,
% 36.73/36.91 (l3_lattices(A!0)),
% 36.73/36.91 inference(and_elim,[status(thm)],[28])).
% 36.73/36.91 tff(30,plain,
% 36.73/36.91 (((~![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))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(31,plain,
% 36.73/36.91 ((~![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))))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(32,plain,
% 36.73/36.91 ((~![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)))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[31, 30])).
% 36.73/36.91 tff(33,plain,
% 36.73/36.91 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[32, 29, 10])).
% 36.73/36.91 tff(34,plain,
% 36.73/36.91 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 36.73/36.91 inference(symmetry,[status(thm)],[33])).
% 36.73/36.91 tff(35,plain,
% 36.73/36.91 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 36.73/36.91 inference(monotonicity,[status(thm)],[34])).
% 36.73/36.91 tff(36,plain,
% 36.73/36.91 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.91 inference(monotonicity,[status(thm)],[35])).
% 36.73/36.91 tff(37,plain,
% 36.73/36.91 (k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.91 inference(symmetry,[status(thm)],[36])).
% 36.73/36.91 tff(38,plain,
% 36.73/36.91 (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)))),
% 36.73/36.91 inference(symmetry,[status(thm)],[35])).
% 36.73/36.91 tff(39,plain,
% 36.73/36.91 (g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.91 inference(monotonicity,[status(thm)],[38])).
% 36.73/36.91 tff(40,plain,
% 36.73/36.91 (g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.91 inference(symmetry,[status(thm)],[39])).
% 36.73/36.91 tff(41,plain,
% 36.73/36.91 (^[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)))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(42,plain,
% 36.73/36.91 (![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))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[41])).
% 36.73/36.91 tff(43,plain,
% 36.73/36.91 (![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))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(44,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 36.73/36.91 tff(45,plain,
% 36.73/36.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[44, 43])).
% 36.73/36.91 tff(46,plain,(
% 36.73/36.91 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 36.73/36.91 inference(skolemize,[status(sab)],[45])).
% 36.73/36.91 tff(47,plain,
% 36.73/36.91 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[46, 42])).
% 36.73/36.91 tff(48,plain,
% 36.73/36.91 ((~![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)))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(49,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[48, 47])).
% 36.73/36.91 tff(50,plain,
% 36.73/36.91 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(51,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[50])).
% 36.73/36.91 tff(52,plain,
% 36.73/36.91 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(53,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[52])).
% 36.73/36.91 tff(54,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(55,plain,
% 36.73/36.91 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(56,plain,
% 36.73/36.91 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[55])).
% 36.73/36.91 tff(57,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 36.73/36.91 tff(58,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[57, 56])).
% 36.73/36.91 tff(59,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[58, 54])).
% 36.73/36.91 tff(60,plain,(
% 36.73/36.91 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 36.73/36.91 inference(skolemize,[status(sab)],[59])).
% 36.73/36.91 tff(61,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[60, 53])).
% 36.73/36.91 tff(62,plain,
% 36.73/36.91 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[61, 51])).
% 36.73/36.91 tff(63,plain,
% 36.73/36.91 (((~![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)))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(64,plain,
% 36.73/36.91 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(65,plain,
% 36.73/36.91 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[64, 63])).
% 36.73/36.91 tff(66,plain,
% 36.73/36.91 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[65, 29, 62])).
% 36.73/36.91 tff(67,plain,
% 36.73/36.91 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(68,plain,
% 36.73/36.91 (l1_lattices(A!0)),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[67, 66])).
% 36.73/36.91 tff(69,plain,
% 36.73/36.91 (^[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)))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(70,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[69])).
% 36.73/36.91 tff(71,plain,
% 36.73/36.91 (^[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)))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(72,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[71])).
% 36.73/36.91 tff(73,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(74,plain,
% 36.73/36.91 (^[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))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(75,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[74])).
% 36.73/36.91 tff(76,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/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 36.73/36.91 tff(77,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[76, 75])).
% 36.73/36.91 tff(78,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[77, 73])).
% 36.73/36.91 tff(79,plain,(
% 36.73/36.91 ![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))))),
% 36.73/36.91 inference(skolemize,[status(sab)],[78])).
% 36.73/36.91 tff(80,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[79, 72])).
% 36.73/36.91 tff(81,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[80, 70])).
% 36.73/36.91 tff(82,plain,
% 36.73/36.91 (((~![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))))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(83,plain,
% 36.73/36.91 ((~![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))))))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(84,plain,
% 36.73/36.91 ((~![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)))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[83, 82])).
% 36.73/36.91 tff(85,plain,
% 36.73/36.91 ((~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)))))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[84, 81])).
% 36.73/36.91 tff(86,plain,
% 36.73/36.91 (~((~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))))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[85, 68])).
% 36.73/36.91 tff(87,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(88,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[87, 86])).
% 36.73/36.91 tff(89,plain,
% 36.73/36.91 ((~(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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(90,plain,
% 36.73/36.91 ((~(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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[89, 88])).
% 36.73/36.91 tff(91,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[90, 49])).
% 36.73/36.91 tff(92,plain,
% 36.73/36.91 ((~![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)))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(93,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[92, 47])).
% 36.73/36.91 tff(94,plain,
% 36.73/36.91 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(95,plain,
% 36.73/36.91 (l2_lattices(A!0)),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[94, 66])).
% 36.73/36.91 tff(96,plain,
% 36.73/36.91 (^[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)))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(97,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[96])).
% 36.73/36.91 tff(98,plain,
% 36.73/36.91 (^[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)))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(99,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[98])).
% 36.73/36.91 tff(100,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(101,plain,
% 36.73/36.91 (^[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))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(102,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[101])).
% 36.73/36.91 tff(103,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/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 36.73/36.91 tff(104,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[103, 102])).
% 36.73/36.91 tff(105,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[104, 100])).
% 36.73/36.91 tff(106,plain,(
% 36.73/36.91 ![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))))),
% 36.73/36.91 inference(skolemize,[status(sab)],[105])).
% 36.73/36.91 tff(107,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[106, 99])).
% 36.73/36.91 tff(108,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[107, 97])).
% 36.73/36.91 tff(109,plain,
% 36.73/36.91 (((~![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))))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(110,plain,
% 36.73/36.91 ((~![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))))))),
% 36.73/36.91 inference(quant_inst,[status(thm)],[])).
% 36.73/36.91 tff(111,plain,
% 36.73/36.91 ((~![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)))))),
% 36.73/36.91 inference(modus_ponens,[status(thm)],[110, 109])).
% 36.73/36.91 tff(112,plain,
% 36.73/36.91 ((~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)))))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[111, 108])).
% 36.73/36.91 tff(113,plain,
% 36.73/36.91 (~((~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))))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[112, 95])).
% 36.73/36.91 tff(114,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(115,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[114, 113])).
% 36.73/36.91 tff(116,plain,
% 36.73/36.91 ((~(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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(117,plain,
% 36.73/36.91 ((~(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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[116, 115])).
% 36.73/36.91 tff(118,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[117, 93])).
% 36.73/36.91 tff(119,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(120,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[119, 113])).
% 36.73/36.91 tff(121,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(122,plain,
% 36.73/36.91 (v1_funct_1(u2_lattices(A!0))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[121, 113])).
% 36.73/36.91 tff(123,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(124,plain,
% 36.73/36.91 (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))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[123, 86])).
% 36.73/36.91 tff(125,plain,
% 36.73/36.91 (((~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))),
% 36.73/36.91 inference(tautology,[status(thm)],[])).
% 36.73/36.91 tff(126,plain,
% 36.73/36.91 (v1_funct_1(u1_lattices(A!0))),
% 36.73/36.91 inference(unit_resolution,[status(thm)],[125, 86])).
% 36.73/36.91 tff(127,plain,
% 36.73/36.91 (^[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)))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(128,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[127])).
% 36.73/36.91 tff(129,plain,
% 36.73/36.91 (^[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))))))))),
% 36.73/36.91 inference(bind,[status(th)],[])).
% 36.73/36.91 tff(130,plain,
% 36.73/36.91 (![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))))))),
% 36.73/36.91 inference(quant_intro,[status(thm)],[129])).
% 36.73/36.91 tff(131,plain,
% 36.73/36.91 (![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))))),
% 36.73/36.91 inference(rewrite,[status(thm)],[])).
% 36.73/36.91 tff(132,plain,
% 36.73/36.91 (^[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))))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(133,plain,
% 36.73/36.92 (![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))))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[132])).
% 36.73/36.92 tff(134,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/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 36.73/36.92 tff(135,plain,
% 36.73/36.92 (![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))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[134, 133])).
% 36.73/36.92 tff(136,plain,
% 36.73/36.92 (![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))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[135, 131])).
% 36.73/36.92 tff(137,plain,(
% 36.73/36.92 ![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))))),
% 36.73/36.92 inference(skolemize,[status(sab)],[136])).
% 36.73/36.92 tff(138,plain,
% 36.73/36.92 (![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))))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[137, 130])).
% 36.73/36.92 tff(139,plain,
% 36.73/36.92 (![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))))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[138, 128])).
% 36.73/36.92 tff(140,plain,
% 36.73/36.92 (((~![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)))))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(141,plain,
% 36.73/36.92 (((~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)))))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(142,plain,
% 36.73/36.92 ((~((~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))))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(143,plain,
% 36.73/36.92 (((~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)))))))),
% 36.73/36.92 inference(monotonicity,[status(thm)],[142])).
% 36.73/36.92 tff(144,plain,
% 36.73/36.92 (((~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)))))))),
% 36.73/36.92 inference(transitivity,[status(thm)],[143, 141])).
% 36.73/36.92 tff(145,plain,
% 36.73/36.92 (((~![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))))))))),
% 36.73/36.92 inference(monotonicity,[status(thm)],[144])).
% 36.73/36.92 tff(146,plain,
% 36.73/36.92 (((~![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)))))))),
% 36.73/36.92 inference(transitivity,[status(thm)],[145, 140])).
% 36.73/36.92 tff(147,plain,
% 36.73/36.92 ((~![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)))))))),
% 36.73/36.92 inference(quant_inst,[status(thm)],[])).
% 36.73/36.92 tff(148,plain,
% 36.73/36.92 ((~![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))))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[147, 146])).
% 36.73/36.92 tff(149,plain,
% 36.73/36.92 ((~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))))))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[148, 139, 126, 124, 122, 120])).
% 36.73/36.92 tff(150,plain,
% 36.73/36.92 (~((~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)))))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[149, 118, 91])).
% 36.73/36.92 tff(151,plain,
% 36.73/36.92 (((~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)))),
% 36.73/36.92 inference(tautology,[status(thm)],[])).
% 36.73/36.92 tff(152,plain,
% 36.73/36.92 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[151, 150])).
% 36.73/36.92 tff(153,plain,
% 36.73/36.92 (((~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)))),
% 36.73/36.92 inference(tautology,[status(thm)],[])).
% 36.73/36.92 tff(154,plain,
% 36.73/36.92 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[153, 150])).
% 36.73/36.92 tff(155,plain,
% 36.73/36.92 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(156,plain,
% 36.73/36.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[155])).
% 36.73/36.92 tff(157,plain,
% 36.73/36.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(158,plain,
% 36.73/36.92 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(159,plain,
% 36.73/36.92 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[158])).
% 36.73/36.92 tff(160,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 36.73/36.92 tff(161,plain,
% 36.73/36.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[160, 159])).
% 36.73/36.92 tff(162,plain,
% 36.73/36.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[161, 157])).
% 36.73/36.92 tff(163,plain,(
% 36.73/36.92 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(skolemize,[status(sab)],[162])).
% 36.73/36.92 tff(164,plain,
% 36.73/36.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[163, 156])).
% 36.73/36.92 tff(165,plain,
% 36.73/36.92 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(166,plain,
% 36.73/36.92 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(167,plain,
% 36.73/36.92 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.73/36.92 inference(monotonicity,[status(thm)],[166])).
% 36.73/36.92 tff(168,plain,
% 36.73/36.92 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.73/36.92 inference(transitivity,[status(thm)],[167, 165])).
% 36.73/36.92 tff(169,plain,
% 36.73/36.92 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.73/36.92 inference(quant_inst,[status(thm)],[])).
% 36.73/36.92 tff(170,plain,
% 36.73/36.92 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.73/36.92 inference(modus_ponens,[status(thm)],[169, 168])).
% 36.73/36.92 tff(171,plain,
% 36.73/36.92 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[170, 164])).
% 36.73/36.92 tff(172,plain,
% 36.73/36.92 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.92 inference(unit_resolution,[status(thm)],[171, 154, 152])).
% 36.73/36.92 tff(173,plain,
% 36.73/36.92 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.92 inference(transitivity,[status(thm)],[172, 40])).
% 36.73/36.92 tff(174,plain,
% 36.73/36.92 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(175,plain,
% 36.73/36.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[174])).
% 36.73/36.92 tff(176,plain,
% 36.73/36.92 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(177,plain,
% 36.73/36.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[176])).
% 36.73/36.92 tff(178,plain,
% 36.73/36.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.92 inference(transitivity,[status(thm)],[177, 175])).
% 36.73/36.92 tff(179,plain,
% 36.73/36.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 36.73/36.92 inference(bind,[status(th)],[])).
% 36.73/36.92 tff(180,plain,
% 36.73/36.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.92 inference(quant_intro,[status(thm)],[179])).
% 36.73/36.92 tff(181,plain,
% 36.73/36.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 36.73/36.92 inference(rewrite,[status(thm)],[])).
% 36.73/36.92 tff(182,plain,
% 36.73/36.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(183,plain,
% 36.73/36.93 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[182])).
% 36.73/36.93 tff(184,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 36.73/36.93 tff(185,plain,
% 36.73/36.93 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[184, 183])).
% 36.73/36.93 tff(186,plain,
% 36.73/36.93 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[185, 181])).
% 36.73/36.93 tff(187,plain,(
% 36.73/36.93 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 36.73/36.93 inference(skolemize,[status(sab)],[186])).
% 36.73/36.93 tff(188,plain,
% 36.73/36.93 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[187, 180])).
% 36.73/36.93 tff(189,plain,
% 36.73/36.93 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[188, 178])).
% 36.73/36.93 tff(190,plain,
% 36.73/36.93 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(191,plain,
% 36.73/36.93 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(192,plain,
% 36.73/36.93 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 36.73/36.93 inference(monotonicity,[status(thm)],[191])).
% 36.73/36.93 tff(193,plain,
% 36.73/36.93 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 36.73/36.93 inference(transitivity,[status(thm)],[192, 190])).
% 36.73/36.93 tff(194,plain,
% 36.73/36.93 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 36.73/36.93 inference(quant_inst,[status(thm)],[])).
% 36.73/36.93 tff(195,plain,
% 36.73/36.93 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[194, 193])).
% 36.73/36.93 tff(196,plain,
% 36.73/36.93 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[195, 189, 126, 124, 122, 120])).
% 36.73/36.93 tff(197,plain,
% 36.73/36.93 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[196, 118, 91])).
% 36.73/36.93 tff(198,plain,
% 36.73/36.93 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(199,plain,
% 36.73/36.93 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 36.73/36.93 inference(quant_inst,[status(thm)],[])).
% 36.73/36.93 tff(200,plain,
% 36.73/36.93 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[199, 198])).
% 36.73/36.93 tff(201,plain,
% 36.73/36.93 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[200, 197])).
% 36.73/36.93 tff(202,plain,
% 36.73/36.93 (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[201, 173])).
% 36.73/36.93 tff(203,plain,
% 36.73/36.93 (((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.93 inference(tautology,[status(thm)],[])).
% 36.73/36.93 tff(204,plain,
% 36.73/36.93 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[203, 202])).
% 36.73/36.93 tff(205,plain,
% 36.73/36.93 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.93 inference(monotonicity,[status(thm)],[204])).
% 36.73/36.93 tff(206,plain,
% 36.73/36.93 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.93 inference(transitivity,[status(thm)],[205, 37])).
% 36.73/36.93 tff(207,plain,
% 36.73/36.93 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.73/36.93 inference(monotonicity,[status(thm)],[206])).
% 36.73/36.93 tff(208,plain,
% 36.73/36.93 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 36.73/36.93 inference(symmetry,[status(thm)],[207])).
% 36.73/36.93 tff(209,plain,
% 36.73/36.93 (^[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))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(210,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[209])).
% 36.73/36.93 tff(211,plain,
% 36.73/36.93 (^[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))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(212,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[211])).
% 36.73/36.93 tff(213,plain,
% 36.73/36.93 (^[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))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(214,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[213])).
% 36.73/36.93 tff(215,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(transitivity,[status(thm)],[214, 212])).
% 36.73/36.93 tff(216,plain,
% 36.73/36.93 (^[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)))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(217,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[216])).
% 36.73/36.93 tff(218,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(219,plain,
% 36.73/36.93 (^[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)))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(220,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[219])).
% 36.73/36.93 tff(221,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/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 36.73/36.93 tff(222,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[221, 220])).
% 36.73/36.93 tff(223,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[222, 218])).
% 36.73/36.93 tff(224,plain,(
% 36.73/36.93 ![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)))),
% 36.73/36.93 inference(skolemize,[status(sab)],[223])).
% 36.73/36.93 tff(225,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[224, 217])).
% 36.73/36.93 tff(226,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[225, 215])).
% 36.73/36.93 tff(227,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[226, 210])).
% 36.73/36.93 tff(228,plain,
% 36.73/36.93 (v10_lattices(A!0)),
% 36.73/36.93 inference(and_elim,[status(thm)],[28])).
% 36.73/36.93 tff(229,plain,
% 36.73/36.93 (~v3_struct_0(A!0)),
% 36.73/36.93 inference(and_elim,[status(thm)],[28])).
% 36.73/36.93 tff(230,plain,
% 36.73/36.93 (((~![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)))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(231,plain,
% 36.73/36.93 ((~![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)))),
% 36.73/36.93 inference(quant_inst,[status(thm)],[])).
% 36.73/36.93 tff(232,plain,
% 36.73/36.93 ((~![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))),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[231, 230])).
% 36.73/36.93 tff(233,plain,
% 36.73/36.93 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[232, 229, 228, 29, 227])).
% 36.73/36.93 tff(234,plain,
% 36.73/36.93 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 36.73/36.93 inference(and_elim,[status(thm)],[28])).
% 36.73/36.93 tff(235,plain,
% 36.73/36.93 (((~![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))),
% 36.73/36.93 inference(rewrite,[status(thm)],[])).
% 36.73/36.93 tff(236,plain,
% 36.73/36.93 ((~![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))),
% 36.73/36.93 inference(quant_inst,[status(thm)],[])).
% 36.73/36.93 tff(237,plain,
% 36.73/36.93 ((~![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)),
% 36.73/36.93 inference(modus_ponens,[status(thm)],[236, 235])).
% 36.73/36.93 tff(238,plain,
% 36.73/36.93 (k5_filter_2(A!0, C!2) = C!2),
% 36.73/36.93 inference(unit_resolution,[status(thm)],[237, 234, 233])).
% 36.73/36.93 tff(239,plain,
% 36.73/36.93 (C!2 = k5_filter_2(A!0, C!2)),
% 36.73/36.93 inference(symmetry,[status(thm)],[238])).
% 36.73/36.93 tff(240,plain,
% 36.73/36.93 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.93 inference(monotonicity,[status(thm)],[239, 35])).
% 36.73/36.93 tff(241,plain,
% 36.73/36.93 (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))))),
% 36.73/36.93 inference(symmetry,[status(thm)],[240])).
% 36.73/36.93 tff(242,plain,
% 36.73/36.93 (^[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))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(243,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.93 inference(quant_intro,[status(thm)],[242])).
% 36.73/36.93 tff(244,plain,
% 36.73/36.93 (^[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)))))),
% 36.73/36.93 inference(bind,[status(th)],[])).
% 36.73/36.93 tff(245,plain,
% 36.73/36.93 (![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)))),
% 36.73/36.94 inference(quant_intro,[status(thm)],[244])).
% 36.73/36.94 tff(246,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(247,plain,
% 36.73/36.94 (^[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))))))),
% 36.73/36.94 inference(bind,[status(th)],[])).
% 36.73/36.94 tff(248,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(quant_intro,[status(thm)],[247])).
% 36.73/36.94 tff(249,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/sandbox2/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 36.73/36.94 tff(250,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[249, 248])).
% 36.73/36.94 tff(251,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[250, 246])).
% 36.73/36.94 tff(252,plain,(
% 36.73/36.94 ![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))))),
% 36.73/36.94 inference(skolemize,[status(sab)],[251])).
% 36.73/36.94 tff(253,plain,
% 36.73/36.94 (![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)))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[252, 245])).
% 36.73/36.94 tff(254,plain,
% 36.73/36.94 (![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)))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[253, 243])).
% 36.73/36.94 tff(255,plain,
% 36.73/36.94 (((~![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))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(256,plain,
% 36.73/36.94 ((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))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(257,plain,
% 36.73/36.94 (((~![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)))))),
% 36.73/36.94 inference(monotonicity,[status(thm)],[256])).
% 36.73/36.94 tff(258,plain,
% 36.73/36.94 (((~![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))))),
% 36.73/36.94 inference(transitivity,[status(thm)],[257, 255])).
% 36.73/36.94 tff(259,plain,
% 36.73/36.94 ((~![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)))),
% 36.73/36.94 inference(quant_inst,[status(thm)],[])).
% 36.73/36.94 tff(260,plain,
% 36.73/36.94 ((~![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)))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[259, 258])).
% 36.73/36.94 tff(261,plain,
% 36.73/36.94 (m1_subset_1(k5_filter_2(A!0, C!2), u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.94 inference(unit_resolution,[status(thm)],[260, 229, 228, 29, 234, 254])).
% 36.73/36.94 tff(262,plain,
% 36.73/36.94 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[261, 241])).
% 36.73/36.94 tff(263,plain,
% 36.73/36.94 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 36.73/36.94 inference(and_elim,[status(thm)],[28])).
% 36.73/36.94 tff(264,plain,
% 36.73/36.94 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(265,plain,
% 36.73/36.94 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 36.73/36.94 inference(quant_inst,[status(thm)],[])).
% 36.73/36.94 tff(266,plain,
% 36.73/36.94 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[265, 264])).
% 36.73/36.94 tff(267,plain,
% 36.73/36.94 (k5_filter_2(A!0, B!1) = B!1),
% 36.73/36.94 inference(unit_resolution,[status(thm)],[266, 263, 233])).
% 36.73/36.94 tff(268,plain,
% 36.73/36.94 (B!1 = k5_filter_2(A!0, B!1)),
% 36.73/36.94 inference(symmetry,[status(thm)],[267])).
% 36.73/36.94 tff(269,plain,
% 36.73/36.94 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.94 inference(monotonicity,[status(thm)],[268, 35])).
% 36.73/36.94 tff(270,plain,
% 36.73/36.94 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.94 inference(symmetry,[status(thm)],[269])).
% 36.73/36.94 tff(271,plain,
% 36.73/36.94 (((~![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(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), 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(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(272,plain,
% 36.73/36.94 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(273,plain,
% 36.73/36.94 (((~![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, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | 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(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))))),
% 36.73/36.94 inference(monotonicity,[status(thm)],[272])).
% 36.73/36.94 tff(274,plain,
% 36.73/36.94 (((~![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, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | 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(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 36.73/36.94 inference(transitivity,[status(thm)],[273, 271])).
% 36.73/36.94 tff(275,plain,
% 36.73/36.94 ((~![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, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 36.73/36.94 inference(quant_inst,[status(thm)],[])).
% 36.73/36.94 tff(276,plain,
% 36.73/36.94 ((~![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(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[275, 274])).
% 36.73/36.94 tff(277,plain,
% 36.73/36.94 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 36.73/36.94 inference(unit_resolution,[status(thm)],[276, 229, 228, 29, 263, 254])).
% 36.73/36.94 tff(278,plain,
% 36.73/36.94 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[277, 270])).
% 36.73/36.94 tff(279,plain,
% 36.73/36.94 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v17_lattices(k1_lattice2(A!0))),
% 36.73/36.94 inference(monotonicity,[status(thm)],[34])).
% 36.73/36.94 tff(280,plain,
% 36.73/36.94 (v17_lattices(k1_lattice2(A!0)) <=> v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.94 inference(symmetry,[status(thm)],[279])).
% 36.73/36.94 tff(281,plain,
% 36.73/36.94 (^[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)))))))),
% 36.73/36.94 inference(bind,[status(th)],[])).
% 36.73/36.94 tff(282,plain,
% 36.73/36.94 (![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))))))),
% 36.73/36.94 inference(quant_intro,[status(thm)],[281])).
% 36.73/36.94 tff(283,plain,
% 36.73/36.94 (^[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))))))))),
% 36.73/36.94 inference(bind,[status(th)],[])).
% 36.73/36.94 tff(284,plain,
% 36.73/36.94 (![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))))))),
% 36.73/36.94 inference(quant_intro,[status(thm)],[283])).
% 36.73/36.94 tff(285,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(286,plain,
% 36.73/36.94 (^[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))))))),
% 36.73/36.94 inference(bind,[status(th)],[])).
% 36.73/36.94 tff(287,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(quant_intro,[status(thm)],[286])).
% 36.73/36.94 tff(288,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/sandbox2/benchmark/theBenchmark.p','fc4_filter_2')).
% 36.73/36.94 tff(289,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[288, 287])).
% 36.73/36.94 tff(290,plain,
% 36.73/36.94 (![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))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[289, 285])).
% 36.73/36.94 tff(291,plain,(
% 36.73/36.94 ![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))))),
% 36.73/36.94 inference(skolemize,[status(sab)],[290])).
% 36.73/36.94 tff(292,plain,
% 36.73/36.94 (![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))))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[291, 284])).
% 36.73/36.94 tff(293,plain,
% 36.73/36.94 (![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))))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[292, 282])).
% 36.73/36.94 tff(294,plain,
% 36.73/36.94 (v17_lattices(A!0)),
% 36.73/36.94 inference(and_elim,[status(thm)],[28])).
% 36.73/36.94 tff(295,plain,
% 36.73/36.94 (((~![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))))))),
% 36.73/36.94 inference(rewrite,[status(thm)],[])).
% 36.73/36.94 tff(296,plain,
% 36.73/36.94 ((~![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))))))),
% 36.73/36.94 inference(quant_inst,[status(thm)],[])).
% 36.73/36.94 tff(297,plain,
% 36.73/36.94 ((~![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)))))),
% 36.73/36.94 inference(modus_ponens,[status(thm)],[296, 295])).
% 36.73/36.94 tff(298,plain,
% 36.73/36.94 (~(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))))),
% 36.73/36.95 inference(unit_resolution,[status(thm)],[297, 229, 228, 294, 29, 293])).
% 36.73/36.95 tff(299,plain,
% 36.73/36.95 ((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))),
% 36.73/36.95 inference(tautology,[status(thm)],[])).
% 36.73/36.95 tff(300,plain,
% 36.73/36.95 (v17_lattices(k1_lattice2(A!0))),
% 36.73/36.95 inference(unit_resolution,[status(thm)],[299, 298])).
% 36.73/36.95 tff(301,plain,
% 36.73/36.95 (v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[300, 280])).
% 36.73/36.95 tff(302,plain,
% 36.73/36.95 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 36.73/36.95 inference(monotonicity,[status(thm)],[34])).
% 36.73/36.95 tff(303,plain,
% 36.73/36.95 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.95 inference(symmetry,[status(thm)],[302])).
% 36.73/36.95 tff(304,plain,
% 36.73/36.95 (^[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)))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(305,plain,
% 36.73/36.95 (![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))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[304])).
% 36.73/36.95 tff(306,plain,
% 36.73/36.95 (^[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))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(307,plain,
% 36.73/36.95 (![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))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[306])).
% 36.73/36.95 tff(308,plain,
% 36.73/36.95 (![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))))),
% 36.73/36.95 inference(rewrite,[status(thm)],[])).
% 36.73/36.95 tff(309,plain,
% 36.73/36.95 (^[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))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(310,plain,
% 36.73/36.95 (![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))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[309])).
% 36.73/36.95 tff(311,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/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 36.73/36.95 tff(312,plain,
% 36.73/36.95 (![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))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[311, 310])).
% 36.73/36.95 tff(313,plain,
% 36.73/36.95 (![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))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[312, 308])).
% 36.73/36.95 tff(314,plain,(
% 36.73/36.95 ![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))))),
% 36.73/36.95 inference(skolemize,[status(sab)],[313])).
% 36.73/36.95 tff(315,plain,
% 36.73/36.95 (![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))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[314, 307])).
% 36.73/36.95 tff(316,plain,
% 36.73/36.95 (![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))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[315, 305])).
% 36.73/36.95 tff(317,plain,
% 36.73/36.95 (((~![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))))))),
% 36.73/36.95 inference(rewrite,[status(thm)],[])).
% 36.73/36.95 tff(318,plain,
% 36.73/36.95 ((~![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))))))),
% 36.73/36.95 inference(quant_inst,[status(thm)],[])).
% 36.73/36.95 tff(319,plain,
% 36.73/36.95 ((~![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)))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[318, 317])).
% 36.73/36.95 tff(320,plain,
% 36.73/36.95 (~(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))))),
% 36.73/36.95 inference(unit_resolution,[status(thm)],[319, 229, 228, 29, 316])).
% 36.73/36.95 tff(321,plain,
% 36.73/36.95 ((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))),
% 36.73/36.95 inference(tautology,[status(thm)],[])).
% 36.73/36.95 tff(322,plain,
% 36.73/36.95 (v10_lattices(k1_lattice2(A!0))),
% 36.73/36.95 inference(unit_resolution,[status(thm)],[321, 320])).
% 36.73/36.95 tff(323,plain,
% 36.73/36.95 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[322, 303])).
% 36.73/36.95 tff(324,plain,
% 36.73/36.95 (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))),
% 36.73/36.95 inference(monotonicity,[status(thm)],[34])).
% 36.73/36.95 tff(325,plain,
% 36.73/36.95 (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)))),
% 36.73/36.95 inference(symmetry,[status(thm)],[324])).
% 36.73/36.95 tff(326,plain,
% 36.73/36.95 ((~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))))),
% 36.73/36.95 inference(monotonicity,[status(thm)],[325])).
% 36.73/36.95 tff(327,plain,
% 36.73/36.95 ((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)))),
% 36.73/36.95 inference(tautology,[status(thm)],[])).
% 36.73/36.95 tff(328,plain,
% 36.73/36.95 (~v3_struct_0(k1_lattice2(A!0))),
% 36.73/36.95 inference(unit_resolution,[status(thm)],[327, 320])).
% 36.73/36.95 tff(329,plain,
% 36.73/36.95 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[328, 326])).
% 36.73/36.95 tff(330,plain,
% 36.73/36.95 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(331,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, 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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[330])).
% 36.73/36.95 tff(332,plain,
% 36.73/36.95 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(333,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, 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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[332])).
% 36.73/36.95 tff(334,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, 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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(transitivity,[status(thm)],[333, 331])).
% 36.73/36.95 tff(335,plain,
% 36.73/36.95 (^[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))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(336,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, 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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[335])).
% 36.73/36.95 tff(337,plain,
% 36.73/36.95 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((B = C) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(338,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((B = C) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))) <=> ![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[337])).
% 36.73/36.95 tff(339,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))) <=> ![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.95 inference(rewrite,[status(thm)],[])).
% 36.73/36.95 tff(340,plain,
% 36.73/36.95 (^[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(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite((~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))) <=> (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))), ((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))), ((m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D)))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))))),
% 36.73/36.95 inference(bind,[status(th)],[])).
% 36.73/36.95 tff(341,plain,
% 36.73/36.95 (![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)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D))))))))))) <=> ![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.95 inference(quant_intro,[status(thm)],[340])).
% 36.73/36.95 tff(342,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)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (~((~(B = C)) & ![D: $i] : (m1_filter_0(D, A) => (~(v1_filter_0(D, A) & ((r2_hidden(B, D) & (~r2_hidden(C, D))) | ((~r2_hidden(B, D)) & r2_hidden(C, D)))))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t60_filter_0')).
% 36.73/36.95 tff(343,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[342, 341])).
% 36.73/36.95 tff(344,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~((~(B = C)) & ![D: $i] : ((~m1_filter_0(D, A)) | (~(v1_filter_0(D, A) & (((~r2_hidden(B, D)) & r2_hidden(C, D)) | (r2_hidden(B, D) & (~r2_hidden(C, D))))))))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[343, 339])).
% 36.73/36.95 tff(345,plain,(
% 36.73/36.95 ![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))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((B = C) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))))),
% 36.73/36.95 inference(skolemize,[status(sab)],[344])).
% 36.73/36.95 tff(346,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~(v1_filter_0(tptp_fun_D_31(C, B, A), A) & (((~r2_hidden(B, tptp_fun_D_31(C, B, A))) & r2_hidden(C, tptp_fun_D_31(C, B, A))) | (r2_hidden(B, tptp_fun_D_31(C, B, A)) & (~r2_hidden(C, tptp_fun_D_31(C, B, A))))))))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[345, 338])).
% 36.73/36.95 tff(347,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[346, 336])).
% 36.73/36.95 tff(348,plain,
% 36.73/36.95 (![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, B, A)))))))))))),
% 36.73/36.95 inference(modus_ponens,[status(thm)],[347, 334])).
% 36.73/36.95 tff(349,plain,
% 36.73/36.95 (((~![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, 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)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, 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)) | (~v17_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, 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)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))))),
% 36.73/36.95 inference(rewrite,[status(thm)],[])).
% 36.73/36.95 tff(350,plain,
% 36.73/36.95 ((~![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, 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)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))))),
% 36.80/36.96 inference(quant_inst,[status(thm)],[])).
% 36.80/36.96 tff(351,plain,
% 36.80/36.96 ((~![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))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(A))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~v1_filter_0(tptp_fun_D_31(C, B, A), A)) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, A)) | (~r2_hidden(C, tptp_fun_D_31(C, B, A))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, A))) | r2_hidden(C, tptp_fun_D_31(C, 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)))) | (~v17_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 36.80/36.96 inference(modus_ponens,[status(thm)],[350, 349])).
% 36.80/36.96 tff(352,plain,
% 36.80/36.96 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 36.80/36.96 inference(unit_resolution,[status(thm)],[351, 348, 154, 329, 323, 301])).
% 36.80/36.96 tff(353,plain,
% 36.80/36.96 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 36.80/36.96 inference(rewrite,[status(thm)],[])).
% 36.80/36.96 tff(354,plain,
% 36.80/36.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))),
% 36.80/36.96 inference(quant_inst,[status(thm)],[])).
% 36.80/36.96 tff(355,plain,
% 36.80/36.96 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 36.80/36.96 inference(modus_ponens,[status(thm)],[354, 353])).
% 36.80/36.96 tff(356,plain,
% 36.80/36.96 ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 36.80/36.96 inference(unit_resolution,[status(thm)],[355, 352])).
% 36.80/36.96 tff(357,plain,
% 36.80/36.96 (![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 36.80/36.96 inference(unit_resolution,[status(thm)],[356, 278])).
% 36.80/36.96 tff(358,plain,
% 36.80/36.96 (~(B!1 = C!2)),
% 36.80/36.96 inference(and_elim,[status(thm)],[28])).
% 36.80/36.96 tff(359,plain,
% 36.80/36.96 (((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | ((B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) <=> ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | (B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 36.80/36.96 inference(rewrite,[status(thm)],[])).
% 36.80/36.96 tff(360,plain,
% 36.80/36.96 ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | ((B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))),
% 36.80/36.96 inference(quant_inst,[status(thm)],[])).
% 36.80/36.96 tff(361,plain,
% 36.80/36.96 ((~![C: $i] : ((B!1 = C) | (~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C, tptp_fun_D_31(C, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))))) | (B!1 = C!2) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 36.80/36.96 inference(modus_ponens,[status(thm)],[360, 359])).
% 36.80/36.96 tff(362,plain,
% 36.80/36.96 (~((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.80/36.96 inference(unit_resolution,[status(thm)],[361, 358, 357, 262])).
% 36.80/36.96 tff(363,plain,
% 36.80/36.96 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.80/36.96 inference(tautology,[status(thm)],[])).
% 36.80/36.96 tff(364,plain,
% 36.80/36.96 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.80/36.96 inference(unit_resolution,[status(thm)],[363, 362])).
% 36.80/36.96 tff(365,plain,
% 36.80/36.96 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 36.80/36.96 inference(bind,[status(th)],[])).
% 36.80/36.96 tff(366,plain,
% 36.80/36.96 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.96 inference(quant_intro,[status(thm)],[365])).
% 36.80/36.96 tff(367,plain,
% 36.80/36.96 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 36.80/36.96 inference(bind,[status(th)],[])).
% 36.80/36.96 tff(368,plain,
% 36.80/36.96 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.96 inference(quant_intro,[status(thm)],[367])).
% 36.80/36.96 tff(369,plain,
% 36.80/36.96 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.96 inference(transitivity,[status(thm)],[368, 366])).
% 36.80/36.96 tff(370,plain,
% 36.80/36.96 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 36.80/36.96 inference(bind,[status(th)],[])).
% 36.80/36.96 tff(371,plain,
% 36.80/36.96 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.96 inference(quant_intro,[status(thm)],[370])).
% 36.80/36.96 tff(372,plain,
% 36.80/36.96 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 36.80/36.96 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(373,plain,
% 36.80/36.97 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(374,plain,
% 36.80/36.97 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[373])).
% 36.80/36.97 tff(375,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 36.80/36.97 tff(376,plain,
% 36.80/36.97 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[375, 374])).
% 36.80/36.97 tff(377,plain,
% 36.80/36.97 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[376, 372])).
% 36.80/36.97 tff(378,plain,(
% 36.80/36.97 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 36.80/36.97 inference(skolemize,[status(sab)],[377])).
% 36.80/36.97 tff(379,plain,
% 36.80/36.97 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[378, 371])).
% 36.80/36.97 tff(380,plain,
% 36.80/36.97 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[379, 369])).
% 36.80/36.97 tff(381,plain,
% 36.80/36.97 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(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_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(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_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(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_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 36.80/36.97 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(382,plain,
% 36.80/36.97 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(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_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 36.80/36.97 inference(quant_inst,[status(thm)],[])).
% 36.80/36.97 tff(383,plain,
% 36.80/36.97 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(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_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[382, 381])).
% 36.80/36.97 tff(384,plain,
% 36.80/36.97 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[383, 380, 154, 329, 323])).
% 36.80/36.97 tff(385,plain,
% 36.80/36.97 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(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_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.80/36.97 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(386,plain,
% 36.80/36.97 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.80/36.97 inference(quant_inst,[status(thm)],[])).
% 36.80/36.97 tff(387,plain,
% 36.80/36.97 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[386, 385])).
% 36.80/36.97 tff(388,plain,
% 36.80/36.97 (~(v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[387, 384, 364])).
% 36.80/36.97 tff(389,plain,
% 36.80/36.97 ((v1_xboole_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.80/36.97 inference(tautology,[status(thm)],[])).
% 36.80/36.97 tff(390,plain,
% 36.80/36.97 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[389, 388])).
% 36.80/36.97 tff(391,plain,
% 36.80/36.97 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[390, 208])).
% 36.80/36.97 tff(392,plain,
% 36.80/36.97 (^[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))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(393,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[392])).
% 36.80/36.97 tff(394,plain,
% 36.80/36.97 (^[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))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(395,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[394])).
% 36.80/36.97 tff(396,plain,
% 36.80/36.97 (^[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))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(397,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[396])).
% 36.80/36.97 tff(398,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(transitivity,[status(thm)],[397, 395])).
% 36.80/36.97 tff(399,plain,
% 36.80/36.97 (^[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)))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(400,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[399])).
% 36.80/36.97 tff(401,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(402,plain,
% 36.80/36.97 (^[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)))))),
% 36.80/36.97 inference(bind,[status(th)],[])).
% 36.80/36.97 tff(403,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(quant_intro,[status(thm)],[402])).
% 36.80/36.97 tff(404,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/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 36.80/36.97 tff(405,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[404, 403])).
% 36.80/36.97 tff(406,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[405, 401])).
% 36.80/36.97 tff(407,plain,(
% 36.80/36.97 ![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)))),
% 36.80/36.97 inference(skolemize,[status(sab)],[406])).
% 36.80/36.97 tff(408,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[407, 400])).
% 36.80/36.97 tff(409,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[408, 398])).
% 36.80/36.97 tff(410,plain,
% 36.80/36.97 (![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)))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[409, 393])).
% 36.80/36.97 tff(411,plain,
% 36.80/36.97 (((~![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)))),
% 36.80/36.97 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(412,plain,
% 36.80/36.97 ((~![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)))),
% 36.80/36.97 inference(quant_inst,[status(thm)],[])).
% 36.80/36.97 tff(413,plain,
% 36.80/36.97 ((~![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))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[412, 411])).
% 36.80/36.97 tff(414,plain,
% 36.80/36.97 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[413, 229, 228, 29, 410])).
% 36.80/36.97 tff(415,plain,
% 36.80/36.97 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.80/36.97 inference(rewrite,[status(thm)],[])).
% 36.80/36.97 tff(416,plain,
% 36.80/36.97 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.80/36.97 inference(quant_inst,[status(thm)],[])).
% 36.80/36.97 tff(417,plain,
% 36.80/36.97 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.80/36.97 inference(modus_ponens,[status(thm)],[416, 415])).
% 36.80/36.97 tff(418,plain,
% 36.80/36.97 ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[417, 414])).
% 36.80/36.97 tff(419,plain,
% 36.80/36.97 (k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.80/36.97 inference(unit_resolution,[status(thm)],[418, 391])).
% 36.80/36.97 tff(420,plain,
% 36.80/36.97 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)) <=> m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.97 inference(monotonicity,[status(thm)],[33])).
% 36.82/36.97 tff(421,plain,
% 36.82/36.97 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 36.82/36.97 inference(symmetry,[status(thm)],[420])).
% 36.82/36.97 tff(422,plain,
% 36.82/36.97 (m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 36.82/36.97 inference(modus_ponens,[status(thm)],[364, 421])).
% 36.82/36.97 tff(423,plain,
% 36.82/36.97 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 36.82/36.97 inference(bind,[status(th)],[])).
% 36.82/36.97 tff(424,plain,
% 36.82/36.97 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.97 inference(quant_intro,[status(thm)],[423])).
% 36.82/36.97 tff(425,plain,
% 36.82/36.97 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 36.82/36.97 inference(bind,[status(th)],[])).
% 36.82/36.97 tff(426,plain,
% 36.82/36.97 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.97 inference(quant_intro,[status(thm)],[425])).
% 36.82/36.97 tff(427,plain,
% 36.82/36.97 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 36.82/36.97 inference(rewrite,[status(thm)],[])).
% 36.82/36.97 tff(428,plain,
% 36.82/36.97 (^[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_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))))),
% 36.82/36.97 inference(bind,[status(th)],[])).
% 36.82/36.97 tff(429,plain,
% 36.82/36.97 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 36.82/36.97 inference(quant_intro,[status(thm)],[428])).
% 36.82/36.97 tff(430,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k14_filter_2')).
% 36.82/36.97 tff(431,plain,
% 36.82/36.97 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 36.82/36.97 inference(modus_ponens,[status(thm)],[430, 429])).
% 36.82/36.97 tff(432,plain,
% 36.82/36.97 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 36.82/36.97 inference(modus_ponens,[status(thm)],[431, 427])).
% 36.82/36.97 tff(433,plain,(
% 36.82/36.97 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 36.82/36.97 inference(skolemize,[status(sab)],[432])).
% 36.82/36.97 tff(434,plain,
% 36.82/36.97 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.97 inference(modus_ponens,[status(thm)],[433, 426])).
% 36.82/36.97 tff(435,plain,
% 36.82/36.97 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.97 inference(modus_ponens,[status(thm)],[434, 424])).
% 36.82/36.97 tff(436,plain,
% 36.82/36.97 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.97 inference(rewrite,[status(thm)],[])).
% 36.82/36.97 tff(437,plain,
% 36.82/36.97 ((v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.97 inference(rewrite,[status(thm)],[])).
% 36.82/36.97 tff(438,plain,
% 36.82/36.97 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.82/36.97 inference(monotonicity,[status(thm)],[437])).
% 36.82/36.97 tff(439,plain,
% 36.82/36.97 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.97 inference(transitivity,[status(thm)],[438, 436])).
% 36.82/36.97 tff(440,plain,
% 36.82/36.97 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 36.82/36.98 inference(quant_inst,[status(thm)],[])).
% 36.82/36.98 tff(441,plain,
% 36.82/36.98 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[440, 439])).
% 36.82/36.98 tff(442,plain,
% 36.82/36.98 ((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[441, 229, 228, 29, 435])).
% 36.82/36.98 tff(443,plain,
% 36.82/36.98 (k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[442, 422])).
% 36.82/36.98 tff(444,plain,
% 36.82/36.98 (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(symmetry,[status(thm)],[443])).
% 36.82/36.98 tff(445,plain,
% 36.82/36.98 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.98 inference(monotonicity,[status(thm)],[37])).
% 36.82/36.98 tff(446,plain,
% 36.82/36.98 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 36.82/36.98 inference(symmetry,[status(thm)],[445])).
% 36.82/36.98 tff(447,plain,
% 36.82/36.98 (m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[390, 446])).
% 36.82/36.98 tff(448,plain,
% 36.82/36.98 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(449,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[448])).
% 36.82/36.98 tff(450,plain,
% 36.82/36.98 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(451,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[450])).
% 36.82/36.98 tff(452,plain,
% 36.82/36.98 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(453,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[452])).
% 36.82/36.98 tff(454,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(transitivity,[status(thm)],[453, 451])).
% 36.82/36.98 tff(455,plain,
% 36.82/36.98 (^[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))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(456,plain,
% 36.82/36.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[455])).
% 36.82/36.98 tff(457,plain,
% 36.82/36.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(458,plain,
% 36.82/36.98 (^[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((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A)))) => (k8_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(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_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(k1_lattice2(A))))) | (k8_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(k1_lattice2(A)))) => (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(459,plain,
% 36.82/36.98 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_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(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[458])).
% 36.82/36.98 tff(460,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(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_filter_2')).
% 36.82/36.98 tff(461,plain,
% 36.82/36.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[460, 459])).
% 36.82/36.98 tff(462,plain,
% 36.82/36.98 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[461, 457])).
% 36.82/36.98 tff(463,plain,(
% 36.82/36.98 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(skolemize,[status(sab)],[462])).
% 36.82/36.98 tff(464,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[463, 456])).
% 36.82/36.98 tff(465,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[464, 454])).
% 36.82/36.98 tff(466,plain,
% 36.82/36.98 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[465, 449])).
% 36.82/36.98 tff(467,plain,
% 36.82/36.98 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A!0))))) | (k8_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(k1_lattice2(A))))) | (k8_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(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(468,plain,
% 36.82/36.98 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 36.82/36.98 inference(quant_inst,[status(thm)],[])).
% 36.82/36.98 tff(469,plain,
% 36.82/36.98 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_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(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[468, 467])).
% 36.82/36.98 tff(470,plain,
% 36.82/36.98 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[469, 229, 228, 29, 466])).
% 36.82/36.98 tff(471,plain,
% 36.82/36.98 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(472,plain,
% 36.82/36.98 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.98 inference(quant_inst,[status(thm)],[])).
% 36.82/36.98 tff(473,plain,
% 36.82/36.98 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[472, 471])).
% 36.82/36.98 tff(474,plain,
% 36.82/36.98 ((~m1_subset_1(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[473, 470])).
% 36.82/36.98 tff(475,plain,
% 36.82/36.98 (k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[474, 447])).
% 36.82/36.98 tff(476,plain,
% 36.82/36.98 (tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k8_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(symmetry,[status(thm)],[475])).
% 36.82/36.98 tff(477,plain,
% 36.82/36.98 (tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.98 inference(transitivity,[status(thm)],[476, 444])).
% 36.82/36.98 tff(478,plain,
% 36.82/36.98 (m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0) <=> m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 36.82/36.98 inference(monotonicity,[status(thm)],[477])).
% 36.82/36.98 tff(479,plain,
% 36.82/36.98 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) <=> m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 36.82/36.98 inference(symmetry,[status(thm)],[478])).
% 36.82/36.98 tff(480,plain,
% 36.82/36.98 (^[A: $i, B: $i] : refl((m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(481,plain,
% 36.82/36.98 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[480])).
% 36.82/36.98 tff(482,plain,
% 36.82/36.98 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(483,plain,
% 36.82/36.98 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[482])).
% 36.82/36.98 tff(484,plain,
% 36.82/36.98 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(485,plain,
% 36.82/36.98 (^[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_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(486,plain,
% 36.82/36.98 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[485])).
% 36.82/36.98 tff(487,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k14_filter_2')).
% 36.82/36.98 tff(488,plain,
% 36.82/36.98 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[487, 486])).
% 36.82/36.98 tff(489,plain,
% 36.82/36.98 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[488, 484])).
% 36.82/36.98 tff(490,plain,(
% 36.82/36.98 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 36.82/36.98 inference(skolemize,[status(sab)],[489])).
% 36.82/36.98 tff(491,plain,
% 36.82/36.98 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[490, 483])).
% 36.82/36.98 tff(492,plain,
% 36.82/36.98 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[491, 481])).
% 36.82/36.98 tff(493,plain,
% 36.82/36.98 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(494,plain,
% 36.82/36.98 ((m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(495,plain,
% 36.82/36.98 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))))),
% 36.82/36.98 inference(monotonicity,[status(thm)],[494])).
% 36.82/36.98 tff(496,plain,
% 36.82/36.98 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 36.82/36.98 inference(transitivity,[status(thm)],[495, 493])).
% 36.82/36.98 tff(497,plain,
% 36.82/36.98 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 36.82/36.98 inference(quant_inst,[status(thm)],[])).
% 36.82/36.98 tff(498,plain,
% 36.82/36.98 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[497, 496])).
% 36.82/36.98 tff(499,plain,
% 36.82/36.98 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[498, 229, 228, 29, 492])).
% 36.82/36.98 tff(500,plain,
% 36.82/36.98 (m2_filter_2(k14_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 36.82/36.98 inference(unit_resolution,[status(thm)],[499, 422])).
% 36.82/36.98 tff(501,plain,
% 36.82/36.98 (m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[500, 479])).
% 36.82/36.98 tff(502,plain,
% 36.82/36.98 (^[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))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(503,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[502])).
% 36.82/36.98 tff(504,plain,
% 36.82/36.98 (^[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)))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(505,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[504])).
% 36.82/36.98 tff(506,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(507,plain,
% 36.82/36.98 (^[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)))))),
% 36.82/36.98 inference(bind,[status(th)],[])).
% 36.82/36.98 tff(508,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(quant_intro,[status(thm)],[507])).
% 36.82/36.98 tff(509,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/sandbox2/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 36.82/36.98 tff(510,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[509, 508])).
% 36.82/36.98 tff(511,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[510, 506])).
% 36.82/36.98 tff(512,plain,(
% 36.82/36.98 ![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)))),
% 36.82/36.98 inference(skolemize,[status(sab)],[511])).
% 36.82/36.98 tff(513,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[512, 505])).
% 36.82/36.98 tff(514,plain,
% 36.82/36.98 (![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)))),
% 36.82/36.98 inference(modus_ponens,[status(thm)],[513, 503])).
% 36.82/36.98 tff(515,plain,
% 36.82/36.98 (((~![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) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_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) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(516,plain,
% 36.82/36.98 ((v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.98 inference(rewrite,[status(thm)],[])).
% 36.82/36.98 tff(517,plain,
% 36.82/36.98 (((~![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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), 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) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.82/36.98 inference(monotonicity,[status(thm)],[516])).
% 36.82/36.98 tff(518,plain,
% 36.82/36.98 (((~![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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), 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) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.98 inference(transitivity,[status(thm)],[517, 515])).
% 36.82/36.98 tff(519,plain,
% 36.82/36.98 ((~![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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 36.82/36.99 inference(quant_inst,[status(thm)],[])).
% 36.82/36.99 tff(520,plain,
% 36.82/36.99 ((~![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) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[519, 518])).
% 36.82/36.99 tff(521,plain,
% 36.82/36.99 (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.82/36.99 inference(unit_resolution,[status(thm)],[520, 229, 228, 29, 514, 501])).
% 36.82/36.99 tff(522,plain,
% 36.82/36.99 (k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.99 inference(transitivity,[status(thm)],[521, 419])).
% 36.82/36.99 tff(523,plain,
% 36.82/36.99 (v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)) <=> v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.99 inference(monotonicity,[status(thm)],[522, 33])).
% 36.82/36.99 tff(524,plain,
% 36.82/36.99 (v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 36.82/36.99 inference(symmetry,[status(thm)],[523])).
% 36.82/36.99 tff(525,plain,
% 36.82/36.99 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.99 inference(tautology,[status(thm)],[])).
% 36.82/36.99 tff(526,plain,
% 36.82/36.99 (v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 36.82/36.99 inference(unit_resolution,[status(thm)],[525, 362])).
% 36.82/36.99 tff(527,plain,
% 36.82/36.99 (v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[526, 524])).
% 36.82/36.99 tff(528,plain,
% 36.82/36.99 (^[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))))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(529,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[528])).
% 36.82/36.99 tff(530,plain,
% 36.82/36.99 (^[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))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(531,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[530])).
% 36.82/36.99 tff(532,plain,
% 36.82/36.99 (^[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))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(533,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[532])).
% 36.82/36.99 tff(534,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(transitivity,[status(thm)],[533, 531])).
% 36.82/36.99 tff(535,plain,
% 36.82/36.99 (^[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_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)))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(536,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[535])).
% 36.82/36.99 tff(537,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(rewrite,[status(thm)],[])).
% 36.82/36.99 tff(538,plain,
% 36.82/36.99 (^[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_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)))))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(539,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[538])).
% 36.82/36.99 tff(540,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/sandbox2/benchmark/theBenchmark.p','t33_filter_2')).
% 36.82/36.99 tff(541,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[540, 539])).
% 36.82/36.99 tff(542,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[541, 537])).
% 36.82/36.99 tff(543,plain,(
% 36.82/36.99 ![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)))))),
% 36.82/36.99 inference(skolemize,[status(sab)],[542])).
% 36.82/36.99 tff(544,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[543, 536])).
% 36.82/36.99 tff(545,plain,
% 36.82/36.99 (![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)))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[544, 534])).
% 36.82/36.99 tff(546,plain,
% 36.82/36.99 (![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)))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[545, 529])).
% 36.82/36.99 tff(547,plain,
% 36.82/36.99 (((~![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)))))),
% 36.82/36.99 inference(rewrite,[status(thm)],[])).
% 36.82/36.99 tff(548,plain,
% 36.82/36.99 ((~![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)))))),
% 36.82/36.99 inference(quant_inst,[status(thm)],[])).
% 36.82/36.99 tff(549,plain,
% 36.82/36.99 ((~![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))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[548, 547])).
% 36.82/36.99 tff(550,plain,
% 36.82/36.99 (![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))))),
% 36.82/36.99 inference(unit_resolution,[status(thm)],[549, 229, 228, 29, 546])).
% 36.82/36.99 tff(551,plain,
% 36.82/36.99 (((~![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(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), 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(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 36.82/36.99 inference(rewrite,[status(thm)],[])).
% 36.82/36.99 tff(552,plain,
% 36.82/36.99 ((~![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(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 36.82/36.99 inference(quant_inst,[status(thm)],[])).
% 36.82/36.99 tff(553,plain,
% 36.82/36.99 ((~![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(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[552, 551])).
% 36.82/36.99 tff(554,plain,
% 36.82/36.99 (r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 36.82/36.99 inference(unit_resolution,[status(thm)],[553, 550, 501])).
% 36.82/36.99 tff(555,plain,
% 36.82/36.99 (((~m1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) | ((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 36.82/36.99 inference(tautology,[status(thm)],[])).
% 36.82/36.99 tff(556,plain,
% 36.82/36.99 ((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 36.82/36.99 inference(unit_resolution,[status(thm)],[555, 362])).
% 36.82/36.99 tff(557,plain,
% 36.82/36.99 (^[D: $i] : refl(((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(558,plain,
% 36.82/36.99 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))) <=> ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[557])).
% 36.82/36.99 tff(559,plain,
% 36.82/36.99 (^[D: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) <=> (~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D))))), rewrite((r2_hidden(B!1, D) & (~r2_hidden(C!2, D))) <=> (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))), ((((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))), rewrite(((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))), ((((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))) <=> ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))), ((r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))) <=> (r2_filter_2(A!0, D) & ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), rewrite((r2_filter_2(A!0, D) & ((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))) <=> (~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))), ((r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))) <=> (~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))), ((~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))) <=> (~(~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))))), rewrite((~(~((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))) <=> ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), ((~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))) <=> ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D)))))))), (((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))), rewrite(((~m2_filter_2(D, A!0)) | ((~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))), (((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))))),
% 36.82/36.99 inference(bind,[status(th)],[])).
% 36.82/36.99 tff(560,plain,
% 36.82/36.99 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D))))))) <=> ![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 36.82/36.99 inference(quant_intro,[status(thm)],[559])).
% 36.82/36.99 tff(561,plain,
% 36.82/36.99 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~(r2_filter_2(A!0, D) & (((~r2_hidden(B!1, D)) & r2_hidden(C!2, D)) | (r2_hidden(B!1, D) & (~r2_hidden(C!2, D)))))))),
% 36.82/36.99 inference(and_elim,[status(thm)],[28])).
% 36.82/36.99 tff(562,plain,
% 36.82/36.99 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[561, 560])).
% 36.82/36.99 tff(563,plain,
% 36.82/36.99 (![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[562, 558])).
% 36.82/36.99 tff(564,plain,
% 36.82/36.99 (((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.82/36.99 inference(rewrite,[status(thm)],[])).
% 36.82/36.99 tff(565,plain,
% 36.82/36.99 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | ((~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 36.82/36.99 inference(quant_inst,[status(thm)],[])).
% 36.82/36.99 tff(566,plain,
% 36.82/36.99 ((~![D: $i] : ((~m2_filter_2(D, A!0)) | (~r2_filter_2(A!0, D)) | (~((~(r2_hidden(B!1, D) | (~r2_hidden(C!2, D)))) | (~((~r2_hidden(B!1, D)) | r2_hidden(C!2, D))))))) | (~m2_filter_2(tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~(r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~((~r2_hidden(B!1, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(C!2, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 36.82/36.99 inference(modus_ponens,[status(thm)],[565, 564])).
% 36.82/36.99 tff(567,plain,
% 36.82/36.99 (~r2_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 36.96/37.15 inference(unit_resolution,[status(thm)],[566, 563, 556, 501])).
% 36.96/37.15 tff(568,plain,
% 36.96/37.15 ((~(r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 36.96/37.15 inference(tautology,[status(thm)],[])).
% 36.96/37.15 tff(569,plain,
% 36.96/37.15 ((~(r2_filter_2(A!0, tptp_fun_D_31(C!2, 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, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 36.96/37.15 inference(unit_resolution,[status(thm)],[568, 567])).
% 36.96/37.15 tff(570,plain,
% 36.96/37.15 (~v1_filter_0(k15_filter_2(A!0, tptp_fun_D_31(C!2, B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 36.96/37.15 inference(unit_resolution,[status(thm)],[569, 554])).
% 36.96/37.15 tff(571,plain,
% 36.96/37.15 ($false),
% 36.96/37.15 inference(unit_resolution,[status(thm)],[570, 527])).
% 36.96/37.15 % SZS output end Proof
% 36.96/37.16 % E exiting
%------------------------------------------------------------------------------