%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT309+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.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 05:14:17 AM UTC 2025
% Result : Theorem 5.04s 5.27s
% Output : Proof 5.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : LAT309+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n011.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Thu Jun 19 20:11:56 EDT 2025
% 0.12/0.35 % CPUTime :
% 5.04/5.27 % SZS status Theorem
% 5.04/5.27 % SZS output start Proof
% 5.04/5.27 tff(v1_filter_0_type, type, (
% 5.04/5.27 v1_filter_0: ( $i * $i ) > $o)).
% 5.04/5.27 tff(k1_lattice2_type, type, (
% 5.04/5.27 k1_lattice2: $i > $i)).
% 5.04/5.27 tff(tptp_fun_A_0_type, type, (
% 5.04/5.27 tptp_fun_A_0: $i)).
% 5.04/5.27 tff(k15_filter_2_type, type, (
% 5.04/5.27 k15_filter_2: ( $i * $i ) > $i)).
% 5.04/5.27 tff(tptp_fun_C_27_type, type, (
% 5.04/5.27 tptp_fun_C_27: ( $i * $i ) > $i)).
% 5.04/5.27 tff(g3_lattices_type, type, (
% 5.04/5.27 g3_lattices: ( $i * $i * $i ) > $i)).
% 5.04/5.27 tff(u2_lattices_type, type, (
% 5.04/5.27 u2_lattices: $i > $i)).
% 5.04/5.27 tff(u1_lattices_type, type, (
% 5.04/5.27 u1_lattices: $i > $i)).
% 5.04/5.27 tff(u1_struct_0_type, type, (
% 5.04/5.27 u1_struct_0: $i > $i)).
% 5.04/5.27 tff(tptp_fun_B_1_type, type, (
% 5.04/5.27 tptp_fun_B_1: $i)).
% 5.04/5.27 tff(l3_lattices_type, type, (
% 5.04/5.27 l3_lattices: $i > $o)).
% 5.04/5.27 tff(r2_filter_2_type, type, (
% 5.04/5.27 r2_filter_2: ( $i * $i ) > $o)).
% 5.04/5.27 tff(r2_hidden_type, type, (
% 5.04/5.27 r2_hidden: ( $i * $i ) > $o)).
% 5.04/5.27 tff(m2_filter_2_type, type, (
% 5.04/5.27 m2_filter_2: ( $i * $i ) > $o)).
% 5.04/5.27 tff(k6_lattices_type, type, (
% 5.04/5.27 k6_lattices: $i > $i)).
% 5.04/5.27 tff(v14_lattices_type, type, (
% 5.04/5.27 v14_lattices: $i > $o)).
% 5.04/5.27 tff(m1_subset_1_type, type, (
% 5.04/5.27 m1_subset_1: ( $i * $i ) > $o)).
% 5.04/5.27 tff(v10_lattices_type, type, (
% 5.04/5.27 v10_lattices: $i > $o)).
% 5.04/5.27 tff(v3_struct_0_type, type, (
% 5.04/5.27 v3_struct_0: $i > $o)).
% 5.04/5.27 tff(k7_filter_2_type, type, (
% 5.04/5.27 k7_filter_2: ( $i * $i ) > $i)).
% 5.04/5.27 tff(k1_zfmisc_1_type, type, (
% 5.04/5.27 k1_zfmisc_1: $i > $i)).
% 5.04/5.27 tff(v3_lattices_type, type, (
% 5.04/5.27 v3_lattices: $i > $o)).
% 5.04/5.27 tff(m1_relset_1_type, type, (
% 5.04/5.27 m1_relset_1: ( $i * $i * $i ) > $o)).
% 5.04/5.27 tff(k2_zfmisc_1_type, type, (
% 5.04/5.27 k2_zfmisc_1: ( $i * $i ) > $i)).
% 5.04/5.27 tff(m2_relset_1_type, type, (
% 5.04/5.27 m2_relset_1: ( $i * $i * $i ) > $o)).
% 5.04/5.27 tff(v1_funct_2_type, type, (
% 5.04/5.27 v1_funct_2: ( $i * $i * $i ) > $o)).
% 5.04/5.27 tff(v1_funct_1_type, type, (
% 5.04/5.27 v1_funct_1: $i > $o)).
% 5.04/5.27 tff(l1_lattices_type, type, (
% 5.04/5.27 l1_lattices: $i > $o)).
% 5.04/5.27 tff(l2_lattices_type, type, (
% 5.04/5.27 l2_lattices: $i > $o)).
% 5.04/5.27 tff(v1_xboole_0_type, type, (
% 5.04/5.27 v1_xboole_0: $i > $o)).
% 5.04/5.27 tff(m1_filter_0_type, type, (
% 5.04/5.27 m1_filter_0: ( $i * $i ) > $o)).
% 5.04/5.27 tff(k5_lattices_type, type, (
% 5.04/5.27 k5_lattices: $i > $i)).
% 5.04/5.27 tff(k5_filter_2_type, type, (
% 5.04/5.27 k5_filter_2: ( $i * $i ) > $i)).
% 5.04/5.27 tff(v13_lattices_type, type, (
% 5.04/5.27 v13_lattices: $i > $o)).
% 5.04/5.27 tff(v9_lattices_type, type, (
% 5.04/5.27 v9_lattices: $i > $o)).
% 5.04/5.27 tff(v8_lattices_type, type, (
% 5.04/5.27 v8_lattices: $i > $o)).
% 5.04/5.27 tff(v7_lattices_type, type, (
% 5.04/5.27 v7_lattices: $i > $o)).
% 5.04/5.27 tff(v6_lattices_type, type, (
% 5.04/5.27 v6_lattices: $i > $o)).
% 5.04/5.27 tff(v5_lattices_type, type, (
% 5.04/5.27 v5_lattices: $i > $o)).
% 5.04/5.27 tff(v4_lattices_type, type, (
% 5.04/5.27 v4_lattices: $i > $o)).
% 5.04/5.27 tff(k14_filter_2_type, type, (
% 5.04/5.27 k14_filter_2: ( $i * $i ) > $i)).
% 5.04/5.27 tff(k8_filter_2_type, type, (
% 5.04/5.27 k8_filter_2: ( $i * $i ) > $i)).
% 5.04/5.27 tff(1,plain,
% 5.04/5.27 (^[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)))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(2,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[1])).
% 5.04/5.27 tff(3,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(4,plain,
% 5.04/5.27 (^[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)))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(5,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[4])).
% 5.04/5.27 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')).
% 5.04/5.27 tff(7,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[6, 5])).
% 5.04/5.27 tff(8,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[7, 3])).
% 5.04/5.27 tff(9,plain,(
% 5.04/5.27 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 5.04/5.27 inference(skolemize,[status(sab)],[8])).
% 5.04/5.27 tff(10,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[9, 2])).
% 5.04/5.27 tff(11,plain,
% 5.04/5.27 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(12,plain,
% 5.04/5.27 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(13,plain,
% 5.04/5.27 ((v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))) <=> (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(14,plain,
% 5.04/5.27 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[13])).
% 5.04/5.27 tff(15,plain,
% 5.04/5.27 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 5.04/5.27 inference(transitivity,[status(thm)],[14, 12])).
% 5.04/5.27 tff(16,plain,
% 5.04/5.27 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[15])).
% 5.04/5.27 tff(17,plain,
% 5.04/5.27 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 5.04/5.27 inference(transitivity,[status(thm)],[16, 11])).
% 5.04/5.27 tff(18,plain,
% 5.04/5.27 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C)))))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(19,plain,
% 5.04/5.27 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((v14_lattices(A) & (~(B = k6_lattices(A)))) & ![C: $i] : (m2_filter_2(C, A) => (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C)))))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((v14_lattices(A) & (~(B = k6_lattices(A)))) & ![C: $i] : (m2_filter_2(C, A) => (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_filter_2')).
% 5.04/5.27 tff(21,plain,
% 5.04/5.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[20, 19])).
% 5.04/5.27 tff(22,plain,
% 5.04/5.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[21, 18])).
% 5.04/5.27 tff(23,plain,
% 5.04/5.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[22, 18])).
% 5.04/5.27 tff(24,plain,
% 5.04/5.27 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[23, 18])).
% 5.04/5.27 tff(25,plain,
% 5.04/5.27 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[24, 17])).
% 5.04/5.27 tff(26,plain,
% 5.04/5.27 (l3_lattices(A!0)),
% 5.04/5.27 inference(and_elim,[status(thm)],[25])).
% 5.04/5.27 tff(27,plain,
% 5.04/5.27 (((~![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))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(28,plain,
% 5.04/5.27 ((~![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))))),
% 5.04/5.27 inference(quant_inst,[status(thm)],[])).
% 5.04/5.27 tff(29,plain,
% 5.04/5.27 ((~![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)))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[28, 27])).
% 5.04/5.27 tff(30,plain,
% 5.04/5.27 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[29, 26, 10])).
% 5.04/5.27 tff(31,plain,
% 5.04/5.27 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 5.04/5.27 inference(symmetry,[status(thm)],[30])).
% 5.04/5.27 tff(32,plain,
% 5.04/5.27 (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))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[31])).
% 5.04/5.27 tff(33,plain,
% 5.04/5.27 (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)))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[32])).
% 5.04/5.27 tff(34,plain,
% 5.04/5.27 (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))))),
% 5.04/5.27 inference(symmetry,[status(thm)],[33])).
% 5.04/5.27 tff(35,plain,
% 5.04/5.27 (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)))),
% 5.04/5.27 inference(symmetry,[status(thm)],[32])).
% 5.04/5.27 tff(36,plain,
% 5.04/5.27 (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))))),
% 5.04/5.27 inference(monotonicity,[status(thm)],[35])).
% 5.04/5.27 tff(37,plain,
% 5.04/5.27 (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))))),
% 5.04/5.27 inference(symmetry,[status(thm)],[36])).
% 5.04/5.27 tff(38,plain,
% 5.04/5.27 (^[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)))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(39,plain,
% 5.04/5.27 (![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))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[38])).
% 5.04/5.27 tff(40,plain,
% 5.04/5.27 (![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))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(41,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')).
% 5.04/5.27 tff(42,plain,
% 5.04/5.27 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[41, 40])).
% 5.04/5.27 tff(43,plain,(
% 5.04/5.27 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 5.04/5.27 inference(skolemize,[status(sab)],[42])).
% 5.04/5.27 tff(44,plain,
% 5.04/5.27 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[43, 39])).
% 5.04/5.27 tff(45,plain,
% 5.04/5.27 ((~![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)))),
% 5.04/5.27 inference(quant_inst,[status(thm)],[])).
% 5.04/5.27 tff(46,plain,
% 5.04/5.27 (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))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[45, 44])).
% 5.04/5.27 tff(47,plain,
% 5.04/5.27 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(48,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[47])).
% 5.04/5.27 tff(49,plain,
% 5.04/5.27 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(50,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[49])).
% 5.04/5.27 tff(51,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(52,plain,
% 5.04/5.27 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(53,plain,
% 5.04/5.27 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[52])).
% 5.04/5.27 tff(54,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 5.04/5.27 tff(55,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[54, 53])).
% 5.04/5.27 tff(56,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[55, 51])).
% 5.04/5.27 tff(57,plain,(
% 5.04/5.27 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 5.04/5.27 inference(skolemize,[status(sab)],[56])).
% 5.04/5.27 tff(58,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[57, 50])).
% 5.04/5.27 tff(59,plain,
% 5.04/5.27 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[58, 48])).
% 5.04/5.27 tff(60,plain,
% 5.04/5.27 (((~![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)))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(61,plain,
% 5.04/5.27 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 5.04/5.27 inference(quant_inst,[status(thm)],[])).
% 5.04/5.27 tff(62,plain,
% 5.04/5.27 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[61, 60])).
% 5.04/5.27 tff(63,plain,
% 5.04/5.27 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[62, 26, 59])).
% 5.04/5.27 tff(64,plain,
% 5.04/5.27 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 5.04/5.27 inference(tautology,[status(thm)],[])).
% 5.04/5.27 tff(65,plain,
% 5.04/5.27 (l1_lattices(A!0)),
% 5.04/5.27 inference(unit_resolution,[status(thm)],[64, 63])).
% 5.04/5.27 tff(66,plain,
% 5.04/5.27 (^[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)))))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(67,plain,
% 5.04/5.27 (![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))))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[66])).
% 5.04/5.27 tff(68,plain,
% 5.04/5.27 (^[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)))))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(69,plain,
% 5.04/5.27 (![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))))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[68])).
% 5.04/5.27 tff(70,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(71,plain,
% 5.04/5.27 (^[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))))))),
% 5.04/5.27 inference(bind,[status(th)],[])).
% 5.04/5.27 tff(72,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(quant_intro,[status(thm)],[71])).
% 5.04/5.27 tff(73,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')).
% 5.04/5.27 tff(74,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[73, 72])).
% 5.04/5.27 tff(75,plain,
% 5.04/5.27 (![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))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[74, 70])).
% 5.04/5.27 tff(76,plain,(
% 5.04/5.27 ![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))))),
% 5.04/5.27 inference(skolemize,[status(sab)],[75])).
% 5.04/5.27 tff(77,plain,
% 5.04/5.27 (![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))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[76, 69])).
% 5.04/5.27 tff(78,plain,
% 5.04/5.27 (![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))))))),
% 5.04/5.27 inference(modus_ponens,[status(thm)],[77, 67])).
% 5.04/5.27 tff(79,plain,
% 5.04/5.27 (((~![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))))))),
% 5.04/5.27 inference(rewrite,[status(thm)],[])).
% 5.04/5.27 tff(80,plain,
% 5.04/5.27 ((~![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))))))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(81,plain,
% 5.04/5.28 ((~![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)))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[80, 79])).
% 5.04/5.28 tff(82,plain,
% 5.04/5.28 ((~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)))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[81, 78])).
% 5.04/5.28 tff(83,plain,
% 5.04/5.28 (~((~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))))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[82, 65])).
% 5.04/5.28 tff(84,plain,
% 5.04/5.28 (((~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))),
% 5.04/5.28 inference(tautology,[status(thm)],[])).
% 5.04/5.28 tff(85,plain,
% 5.04/5.28 (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))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[84, 83])).
% 5.04/5.28 tff(86,plain,
% 5.04/5.28 ((~(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))),
% 5.04/5.28 inference(tautology,[status(thm)],[])).
% 5.04/5.28 tff(87,plain,
% 5.04/5.28 ((~(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))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[86, 85])).
% 5.04/5.28 tff(88,plain,
% 5.04/5.28 (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))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[87, 46])).
% 5.04/5.28 tff(89,plain,
% 5.04/5.28 ((~![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)))),
% 5.04/5.28 inference(quant_inst,[status(thm)],[])).
% 5.04/5.28 tff(90,plain,
% 5.04/5.28 (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))),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[89, 44])).
% 5.04/5.28 tff(91,plain,
% 5.04/5.28 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 5.04/5.28 inference(tautology,[status(thm)],[])).
% 5.04/5.28 tff(92,plain,
% 5.04/5.28 (l2_lattices(A!0)),
% 5.04/5.28 inference(unit_resolution,[status(thm)],[91, 63])).
% 5.04/5.28 tff(93,plain,
% 5.04/5.28 (^[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)))))))),
% 5.04/5.28 inference(bind,[status(th)],[])).
% 5.04/5.28 tff(94,plain,
% 5.04/5.28 (![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))))))),
% 5.04/5.28 inference(quant_intro,[status(thm)],[93])).
% 5.04/5.28 tff(95,plain,
% 5.04/5.28 (^[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)))))))),
% 5.04/5.28 inference(bind,[status(th)],[])).
% 5.04/5.28 tff(96,plain,
% 5.04/5.28 (![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))))))),
% 5.04/5.28 inference(quant_intro,[status(thm)],[95])).
% 5.04/5.28 tff(97,plain,
% 5.04/5.28 (![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))))),
% 5.04/5.28 inference(rewrite,[status(thm)],[])).
% 5.04/5.28 tff(98,plain,
% 5.04/5.28 (^[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))))))),
% 5.04/5.28 inference(bind,[status(th)],[])).
% 5.04/5.28 tff(99,plain,
% 5.04/5.28 (![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))))),
% 5.04/5.28 inference(quant_intro,[status(thm)],[98])).
% 5.04/5.28 tff(100,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')).
% 5.04/5.28 tff(101,plain,
% 5.04/5.28 (![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))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[100, 99])).
% 5.04/5.28 tff(102,plain,
% 5.04/5.28 (![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))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[101, 97])).
% 5.04/5.28 tff(103,plain,(
% 5.04/5.28 ![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))))),
% 5.04/5.28 inference(skolemize,[status(sab)],[102])).
% 5.04/5.28 tff(104,plain,
% 5.04/5.28 (![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))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[103, 96])).
% 5.04/5.28 tff(105,plain,
% 5.04/5.28 (![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))))))),
% 5.04/5.28 inference(modus_ponens,[status(thm)],[104, 94])).
% 5.04/5.28 tff(106,plain,
% 5.04/5.28 (((~![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))))))),
% 5.12/5.28 inference(rewrite,[status(thm)],[])).
% 5.12/5.28 tff(107,plain,
% 5.12/5.28 ((~![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))))))),
% 5.12/5.28 inference(quant_inst,[status(thm)],[])).
% 5.12/5.28 tff(108,plain,
% 5.12/5.28 ((~![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)))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[107, 106])).
% 5.12/5.28 tff(109,plain,
% 5.12/5.28 ((~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)))))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[108, 105])).
% 5.12/5.28 tff(110,plain,
% 5.12/5.28 (~((~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))))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[109, 92])).
% 5.12/5.28 tff(111,plain,
% 5.12/5.28 (((~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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(112,plain,
% 5.12/5.28 (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))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[111, 110])).
% 5.12/5.28 tff(113,plain,
% 5.12/5.28 ((~(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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(114,plain,
% 5.12/5.28 ((~(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))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[113, 112])).
% 5.12/5.28 tff(115,plain,
% 5.12/5.28 (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))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[114, 90])).
% 5.12/5.28 tff(116,plain,
% 5.12/5.28 (((~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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(117,plain,
% 5.12/5.28 (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))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[116, 110])).
% 5.12/5.28 tff(118,plain,
% 5.12/5.28 (((~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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(119,plain,
% 5.12/5.28 (v1_funct_1(u2_lattices(A!0))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[118, 110])).
% 5.12/5.28 tff(120,plain,
% 5.12/5.28 (((~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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(121,plain,
% 5.12/5.28 (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))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[120, 83])).
% 5.12/5.28 tff(122,plain,
% 5.12/5.28 (((~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))),
% 5.12/5.28 inference(tautology,[status(thm)],[])).
% 5.12/5.28 tff(123,plain,
% 5.12/5.28 (v1_funct_1(u1_lattices(A!0))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[122, 83])).
% 5.12/5.28 tff(124,plain,
% 5.12/5.28 (^[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)))))))),
% 5.12/5.28 inference(bind,[status(th)],[])).
% 5.12/5.28 tff(125,plain,
% 5.12/5.28 (![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))))))),
% 5.12/5.28 inference(quant_intro,[status(thm)],[124])).
% 5.12/5.28 tff(126,plain,
% 5.12/5.28 (^[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))))))))),
% 5.12/5.28 inference(bind,[status(th)],[])).
% 5.12/5.28 tff(127,plain,
% 5.12/5.28 (![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))))))),
% 5.12/5.28 inference(quant_intro,[status(thm)],[126])).
% 5.12/5.28 tff(128,plain,
% 5.12/5.28 (![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))))),
% 5.12/5.28 inference(rewrite,[status(thm)],[])).
% 5.12/5.28 tff(129,plain,
% 5.12/5.28 (^[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))))))),
% 5.12/5.28 inference(bind,[status(th)],[])).
% 5.12/5.28 tff(130,plain,
% 5.12/5.28 (![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))))),
% 5.12/5.28 inference(quant_intro,[status(thm)],[129])).
% 5.12/5.28 tff(131,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')).
% 5.12/5.28 tff(132,plain,
% 5.12/5.28 (![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))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[131, 130])).
% 5.12/5.28 tff(133,plain,
% 5.12/5.28 (![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))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[132, 128])).
% 5.12/5.28 tff(134,plain,(
% 5.12/5.28 ![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))))),
% 5.12/5.28 inference(skolemize,[status(sab)],[133])).
% 5.12/5.28 tff(135,plain,
% 5.12/5.28 (![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))))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[134, 127])).
% 5.12/5.28 tff(136,plain,
% 5.12/5.28 (![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))))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[135, 125])).
% 5.12/5.28 tff(137,plain,
% 5.12/5.28 (((~![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)))))))),
% 5.12/5.28 inference(rewrite,[status(thm)],[])).
% 5.12/5.28 tff(138,plain,
% 5.12/5.28 (((~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)))))))),
% 5.12/5.28 inference(rewrite,[status(thm)],[])).
% 5.12/5.28 tff(139,plain,
% 5.12/5.28 ((~((~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))))))),
% 5.12/5.28 inference(rewrite,[status(thm)],[])).
% 5.12/5.28 tff(140,plain,
% 5.12/5.28 (((~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)))))))),
% 5.12/5.28 inference(monotonicity,[status(thm)],[139])).
% 5.12/5.28 tff(141,plain,
% 5.12/5.28 (((~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)))))))),
% 5.12/5.28 inference(transitivity,[status(thm)],[140, 138])).
% 5.12/5.28 tff(142,plain,
% 5.12/5.28 (((~![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))))))))),
% 5.12/5.28 inference(monotonicity,[status(thm)],[141])).
% 5.12/5.28 tff(143,plain,
% 5.12/5.28 (((~![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)))))))),
% 5.12/5.28 inference(transitivity,[status(thm)],[142, 137])).
% 5.12/5.28 tff(144,plain,
% 5.12/5.28 ((~![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)))))))),
% 5.12/5.28 inference(quant_inst,[status(thm)],[])).
% 5.12/5.28 tff(145,plain,
% 5.12/5.28 ((~![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))))))),
% 5.12/5.28 inference(modus_ponens,[status(thm)],[144, 143])).
% 5.12/5.28 tff(146,plain,
% 5.12/5.28 ((~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))))))),
% 5.12/5.28 inference(unit_resolution,[status(thm)],[145, 136, 123, 121, 119, 117])).
% 5.12/5.28 tff(147,plain,
% 5.12/5.28 (~((~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)))))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[146, 115, 88])).
% 5.12/5.29 tff(148,plain,
% 5.12/5.29 (((~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)))),
% 5.12/5.29 inference(tautology,[status(thm)],[])).
% 5.12/5.29 tff(149,plain,
% 5.12/5.29 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[148, 147])).
% 5.12/5.29 tff(150,plain,
% 5.12/5.29 (((~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)))),
% 5.12/5.29 inference(tautology,[status(thm)],[])).
% 5.12/5.29 tff(151,plain,
% 5.12/5.29 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[150, 147])).
% 5.12/5.29 tff(152,plain,
% 5.12/5.29 (^[A: $i] : refl(((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))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(153,plain,
% 5.12/5.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[152])).
% 5.12/5.29 tff(154,plain,
% 5.12/5.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(155,plain,
% 5.12/5.29 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))) | (~l3_lattices(A)) | (~v3_lattices(A)))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(156,plain,
% 5.12/5.29 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[155])).
% 5.12/5.29 tff(157,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')).
% 5.12/5.29 tff(158,plain,
% 5.12/5.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[157, 156])).
% 5.12/5.29 tff(159,plain,
% 5.12/5.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[158, 154])).
% 5.12/5.29 tff(160,plain,(
% 5.12/5.29 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(skolemize,[status(sab)],[159])).
% 5.12/5.29 tff(161,plain,
% 5.12/5.29 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[160, 153])).
% 5.12/5.29 tff(162,plain,
% 5.12/5.29 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))) | (~l3_lattices(A)) | (~v3_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))))))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(163,plain,
% 5.12/5.29 (((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))))) | (~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))))) <=> ((~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))))))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(164,plain,
% 5.12/5.29 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))))) | (~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)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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)))))))),
% 5.12/5.29 inference(monotonicity,[status(thm)],[163])).
% 5.12/5.29 tff(165,plain,
% 5.12/5.29 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))))) | (~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)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))))))),
% 5.12/5.29 inference(transitivity,[status(thm)],[164, 162])).
% 5.12/5.29 tff(166,plain,
% 5.12/5.29 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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))))) | (~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)))))),
% 5.12/5.29 inference(quant_inst,[status(thm)],[])).
% 5.12/5.29 tff(167,plain,
% 5.12/5.29 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_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)))))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[166, 165])).
% 5.12/5.29 tff(168,plain,
% 5.12/5.29 ((~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)))))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[167, 161])).
% 5.12/5.29 tff(169,plain,
% 5.12/5.29 (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))))),
% 5.12/5.29 inference(unit_resolution,[status(thm)],[168, 151, 149])).
% 5.12/5.29 tff(170,plain,
% 5.12/5.29 (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))))),
% 5.12/5.29 inference(transitivity,[status(thm)],[169, 37])).
% 5.12/5.29 tff(171,plain,
% 5.12/5.29 (^[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)))))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(172,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[171])).
% 5.12/5.29 tff(173,plain,
% 5.12/5.29 (^[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)))))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(174,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[173])).
% 5.12/5.29 tff(175,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(transitivity,[status(thm)],[174, 172])).
% 5.12/5.29 tff(176,plain,
% 5.12/5.29 (^[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))))))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(177,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[176])).
% 5.12/5.29 tff(178,plain,
% 5.12/5.29 (![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))))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(179,plain,
% 5.12/5.29 (^[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))))))),
% 5.12/5.29 inference(bind,[status(th)],[])).
% 5.12/5.29 tff(180,plain,
% 5.12/5.29 (![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))))),
% 5.12/5.29 inference(quant_intro,[status(thm)],[179])).
% 5.12/5.29 tff(181,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')).
% 5.12/5.29 tff(182,plain,
% 5.12/5.29 (![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))))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[181, 180])).
% 5.12/5.29 tff(183,plain,
% 5.12/5.29 (![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))))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[182, 178])).
% 5.12/5.29 tff(184,plain,(
% 5.12/5.29 ![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))))),
% 5.12/5.29 inference(skolemize,[status(sab)],[183])).
% 5.12/5.29 tff(185,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[184, 177])).
% 5.12/5.29 tff(186,plain,
% 5.12/5.29 (![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))))))),
% 5.12/5.29 inference(modus_ponens,[status(thm)],[185, 175])).
% 5.12/5.29 tff(187,plain,
% 5.12/5.29 (((~![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))))),
% 5.12/5.29 inference(rewrite,[status(thm)],[])).
% 5.12/5.29 tff(188,plain,
% 5.12/5.29 (((~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))))),
% 5.14/5.29 inference(rewrite,[status(thm)],[])).
% 5.14/5.29 tff(189,plain,
% 5.14/5.29 (((~![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)))))),
% 5.14/5.29 inference(monotonicity,[status(thm)],[188])).
% 5.14/5.29 tff(190,plain,
% 5.14/5.29 (((~![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))))),
% 5.14/5.29 inference(transitivity,[status(thm)],[189, 187])).
% 5.14/5.29 tff(191,plain,
% 5.14/5.29 ((~![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))))))),
% 5.14/5.29 inference(quant_inst,[status(thm)],[])).
% 5.14/5.29 tff(192,plain,
% 5.14/5.29 ((~![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)))),
% 5.14/5.29 inference(modus_ponens,[status(thm)],[191, 190])).
% 5.14/5.29 tff(193,plain,
% 5.14/5.29 (![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)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[192, 186, 123, 121, 119, 117])).
% 5.14/5.30 tff(194,plain,
% 5.14/5.30 (![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)))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[193, 115, 88])).
% 5.14/5.30 tff(195,plain,
% 5.14/5.30 (((~![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))))))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(196,plain,
% 5.14/5.30 ((~![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))))))))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(197,plain,
% 5.14/5.30 ((~![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)))))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[196, 195])).
% 5.14/5.30 tff(198,plain,
% 5.14/5.30 ((~(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)))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[197, 194])).
% 5.14/5.30 tff(199,plain,
% 5.14/5.30 (~((~(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))))))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[198, 170])).
% 5.14/5.30 tff(200,plain,
% 5.14/5.30 (((~(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)))),
% 5.14/5.30 inference(tautology,[status(thm)],[])).
% 5.14/5.30 tff(201,plain,
% 5.14/5.30 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[200, 199])).
% 5.14/5.30 tff(202,plain,
% 5.14/5.30 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[201])).
% 5.14/5.30 tff(203,plain,
% 5.14/5.30 (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))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[202, 34])).
% 5.14/5.30 tff(204,plain,
% 5.14/5.30 (m1_subset_1(tptp_fun_C_27(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_C_27(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)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[203])).
% 5.14/5.30 tff(205,plain,
% 5.14/5.30 (m1_subset_1(tptp_fun_C_27(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_C_27(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)))),
% 5.14/5.30 inference(symmetry,[status(thm)],[204])).
% 5.14/5.30 tff(206,plain,
% 5.14/5.30 (^[A: $i] : refl((v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(207,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[206])).
% 5.14/5.30 tff(208,plain,
% 5.14/5.30 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(209,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[208])).
% 5.14/5.30 tff(210,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(211,plain,
% 5.14/5.30 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(212,plain,
% 5.14/5.30 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[211])).
% 5.14/5.30 tff(213,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t79_lattice2')).
% 5.14/5.30 tff(214,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[213, 212])).
% 5.14/5.30 tff(215,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[214, 210])).
% 5.14/5.30 tff(216,plain,(
% 5.14/5.30 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(skolemize,[status(sab)],[215])).
% 5.14/5.30 tff(217,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[216, 209])).
% 5.14/5.30 tff(218,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[217, 207])).
% 5.14/5.30 tff(219,plain,
% 5.14/5.30 (v14_lattices(A!0)),
% 5.14/5.30 inference(and_elim,[status(thm)],[25])).
% 5.14/5.30 tff(220,plain,
% 5.14/5.30 (v10_lattices(A!0)),
% 5.14/5.30 inference(and_elim,[status(thm)],[25])).
% 5.14/5.30 tff(221,plain,
% 5.14/5.30 (~v3_struct_0(A!0)),
% 5.14/5.30 inference(and_elim,[status(thm)],[25])).
% 5.14/5.30 tff(222,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(223,plain,
% 5.14/5.30 ((v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(224,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[223])).
% 5.14/5.30 tff(225,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 5.14/5.30 inference(transitivity,[status(thm)],[224, 222])).
% 5.14/5.30 tff(226,plain,
% 5.14/5.30 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(227,plain,
% 5.14/5.30 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[226, 225])).
% 5.14/5.30 tff(228,plain,
% 5.14/5.30 (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[227, 221, 220, 26, 219, 218])).
% 5.14/5.30 tff(229,plain,
% 5.14/5.30 (k5_lattices(k1_lattice2(A!0)) = k6_lattices(A!0)),
% 5.14/5.30 inference(symmetry,[status(thm)],[228])).
% 5.14/5.30 tff(230,plain,
% 5.14/5.30 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[31])).
% 5.14/5.30 tff(231,plain,
% 5.14/5.30 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k6_lattices(A!0)),
% 5.14/5.30 inference(transitivity,[status(thm)],[230, 229])).
% 5.14/5.30 tff(232,plain,
% 5.14/5.30 ((B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> (B!1 = k6_lattices(A!0))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[231])).
% 5.14/5.30 tff(233,plain,
% 5.14/5.30 ((B!1 = k6_lattices(A!0)) <=> (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.14/5.30 inference(symmetry,[status(thm)],[232])).
% 5.14/5.30 tff(234,plain,
% 5.14/5.30 ((~(B!1 = k6_lattices(A!0))) <=> (~(B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[233])).
% 5.14/5.30 tff(235,plain,
% 5.14/5.30 (~(B!1 = k6_lattices(A!0))),
% 5.14/5.30 inference(and_elim,[status(thm)],[25])).
% 5.14/5.30 tff(236,plain,
% 5.14/5.30 (~(B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[235, 234])).
% 5.14/5.30 tff(237,plain,
% 5.14/5.30 (^[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))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(238,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[237])).
% 5.14/5.30 tff(239,plain,
% 5.14/5.30 (^[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))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(240,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[239])).
% 5.14/5.30 tff(241,plain,
% 5.14/5.30 (^[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))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(242,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[241])).
% 5.14/5.30 tff(243,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(transitivity,[status(thm)],[242, 240])).
% 5.14/5.30 tff(244,plain,
% 5.14/5.30 (^[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)))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(245,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[244])).
% 5.14/5.30 tff(246,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(247,plain,
% 5.14/5.30 (^[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)))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(248,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[247])).
% 5.14/5.30 tff(249,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')).
% 5.14/5.30 tff(250,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[249, 248])).
% 5.14/5.30 tff(251,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[250, 246])).
% 5.14/5.30 tff(252,plain,(
% 5.14/5.30 ![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)))),
% 5.14/5.30 inference(skolemize,[status(sab)],[251])).
% 5.14/5.30 tff(253,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[252, 245])).
% 5.14/5.30 tff(254,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[253, 243])).
% 5.14/5.30 tff(255,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[254, 238])).
% 5.14/5.30 tff(256,plain,
% 5.14/5.30 (((~![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)))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(257,plain,
% 5.14/5.30 ((~![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)))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(258,plain,
% 5.14/5.30 ((~![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))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[257, 256])).
% 5.14/5.30 tff(259,plain,
% 5.14/5.30 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[258, 221, 220, 26, 255])).
% 5.14/5.30 tff(260,plain,
% 5.14/5.30 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 5.14/5.30 inference(and_elim,[status(thm)],[25])).
% 5.14/5.30 tff(261,plain,
% 5.14/5.30 (((~![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))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(262,plain,
% 5.14/5.30 ((~![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))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(263,plain,
% 5.14/5.30 ((~![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)),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[262, 261])).
% 5.14/5.30 tff(264,plain,
% 5.14/5.30 (k5_filter_2(A!0, B!1) = B!1),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[263, 260, 259])).
% 5.14/5.30 tff(265,plain,
% 5.14/5.30 (B!1 = k5_filter_2(A!0, B!1)),
% 5.14/5.30 inference(symmetry,[status(thm)],[264])).
% 5.14/5.30 tff(266,plain,
% 5.14/5.30 (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)))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[265, 32])).
% 5.14/5.30 tff(267,plain,
% 5.14/5.30 (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))))),
% 5.14/5.30 inference(symmetry,[status(thm)],[266])).
% 5.14/5.30 tff(268,plain,
% 5.14/5.30 (^[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))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(269,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[268])).
% 5.14/5.30 tff(270,plain,
% 5.14/5.30 (^[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)))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(271,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[270])).
% 5.14/5.30 tff(272,plain,
% 5.14/5.30 (![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))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(273,plain,
% 5.14/5.30 (^[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))))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(274,plain,
% 5.14/5.30 (![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))))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[273])).
% 5.14/5.30 tff(275,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')).
% 5.14/5.30 tff(276,plain,
% 5.14/5.30 (![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))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[275, 274])).
% 5.14/5.30 tff(277,plain,
% 5.14/5.30 (![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))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[276, 272])).
% 5.14/5.30 tff(278,plain,(
% 5.14/5.30 ![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))))),
% 5.14/5.30 inference(skolemize,[status(sab)],[277])).
% 5.14/5.30 tff(279,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[278, 271])).
% 5.14/5.30 tff(280,plain,
% 5.14/5.30 (![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[279, 269])).
% 5.14/5.30 tff(281,plain,
% 5.14/5.30 (((~![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))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(282,plain,
% 5.14/5.30 ((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))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(283,plain,
% 5.14/5.30 (((~![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)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[282])).
% 5.14/5.30 tff(284,plain,
% 5.14/5.30 (((~![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))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[283, 281])).
% 5.14/5.30 tff(285,plain,
% 5.14/5.30 ((~![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)))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(286,plain,
% 5.14/5.30 ((~![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)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[285, 284])).
% 5.14/5.30 tff(287,plain,
% 5.14/5.30 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[286, 221, 220, 26, 260, 280])).
% 5.14/5.30 tff(288,plain,
% 5.14/5.30 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[287, 267])).
% 5.14/5.30 tff(289,plain,
% 5.14/5.30 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v13_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[31])).
% 5.14/5.30 tff(290,plain,
% 5.14/5.30 (v13_lattices(k1_lattice2(A!0)) <=> v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.14/5.30 inference(symmetry,[status(thm)],[289])).
% 5.14/5.30 tff(291,plain,
% 5.14/5.30 (^[A: $i] : refl((v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(292,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[291])).
% 5.14/5.30 tff(293,plain,
% 5.14/5.30 (^[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))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(294,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[293])).
% 5.14/5.30 tff(295,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(296,plain,
% 5.14/5.30 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))))),
% 5.14/5.30 inference(bind,[status(th)],[])).
% 5.14/5.30 tff(297,plain,
% 5.14/5.30 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(quant_intro,[status(thm)],[296])).
% 5.14/5.30 tff(298,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_lattice2')).
% 5.14/5.30 tff(299,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[298, 297])).
% 5.14/5.30 tff(300,plain,
% 5.14/5.30 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[299, 295])).
% 5.14/5.30 tff(301,plain,(
% 5.14/5.30 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 5.14/5.30 inference(skolemize,[status(sab)],[300])).
% 5.14/5.30 tff(302,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[301, 294])).
% 5.14/5.30 tff(303,plain,
% 5.14/5.30 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[302, 292])).
% 5.14/5.30 tff(304,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(305,plain,
% 5.14/5.30 ((v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 5.14/5.30 inference(rewrite,[status(thm)],[])).
% 5.14/5.30 tff(306,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[305])).
% 5.14/5.30 tff(307,plain,
% 5.14/5.30 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 5.14/5.30 inference(transitivity,[status(thm)],[306, 304])).
% 5.14/5.30 tff(308,plain,
% 5.14/5.30 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 5.14/5.30 inference(quant_inst,[status(thm)],[])).
% 5.14/5.30 tff(309,plain,
% 5.14/5.30 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[308, 307])).
% 5.14/5.30 tff(310,plain,
% 5.14/5.30 (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[309, 221, 220, 26, 303])).
% 5.14/5.30 tff(311,plain,
% 5.14/5.30 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | (~v14_lattices(A!0)) | v13_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(tautology,[status(thm)],[])).
% 5.14/5.30 tff(312,plain,
% 5.14/5.30 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | v13_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[311, 219])).
% 5.14/5.30 tff(313,plain,
% 5.14/5.30 (v13_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(unit_resolution,[status(thm)],[312, 310])).
% 5.14/5.30 tff(314,plain,
% 5.14/5.30 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.14/5.30 inference(modus_ponens,[status(thm)],[313, 290])).
% 5.14/5.30 tff(315,plain,
% 5.14/5.30 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 5.14/5.30 inference(monotonicity,[status(thm)],[31])).
% 5.14/5.30 tff(316,plain,
% 5.14/5.30 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.14/5.30 inference(symmetry,[status(thm)],[315])).
% 5.14/5.30 tff(317,plain,
% 5.14/5.30 (^[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)))))))),
% 5.14/5.31 inference(bind,[status(th)],[])).
% 5.14/5.31 tff(318,plain,
% 5.14/5.31 (![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))))))),
% 5.14/5.31 inference(quant_intro,[status(thm)],[317])).
% 5.14/5.31 tff(319,plain,
% 5.14/5.31 (^[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))))))))),
% 5.14/5.31 inference(bind,[status(th)],[])).
% 5.14/5.31 tff(320,plain,
% 5.14/5.31 (![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))))))),
% 5.14/5.31 inference(quant_intro,[status(thm)],[319])).
% 5.14/5.31 tff(321,plain,
% 5.14/5.31 (![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))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(322,plain,
% 5.14/5.31 (^[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))))))),
% 5.14/5.31 inference(bind,[status(th)],[])).
% 5.14/5.31 tff(323,plain,
% 5.14/5.31 (![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))))),
% 5.14/5.31 inference(quant_intro,[status(thm)],[322])).
% 5.14/5.31 tff(324,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')).
% 5.14/5.31 tff(325,plain,
% 5.14/5.31 (![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))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[324, 323])).
% 5.14/5.31 tff(326,plain,
% 5.14/5.31 (![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))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[325, 321])).
% 5.14/5.31 tff(327,plain,(
% 5.14/5.31 ![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))))),
% 5.14/5.31 inference(skolemize,[status(sab)],[326])).
% 5.14/5.31 tff(328,plain,
% 5.14/5.31 (![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))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[327, 320])).
% 5.14/5.31 tff(329,plain,
% 5.14/5.31 (![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))))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[328, 318])).
% 5.14/5.31 tff(330,plain,
% 5.14/5.31 (((~![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))))))),
% 5.14/5.31 inference(rewrite,[status(thm)],[])).
% 5.14/5.31 tff(331,plain,
% 5.14/5.31 ((~![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))))))),
% 5.14/5.31 inference(quant_inst,[status(thm)],[])).
% 5.14/5.31 tff(332,plain,
% 5.14/5.31 ((~![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)))))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[331, 330])).
% 5.14/5.31 tff(333,plain,
% 5.14/5.31 (~(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))))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[332, 221, 220, 26, 329])).
% 5.14/5.31 tff(334,plain,
% 5.14/5.31 ((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))),
% 5.14/5.31 inference(tautology,[status(thm)],[])).
% 5.14/5.31 tff(335,plain,
% 5.14/5.31 (v10_lattices(k1_lattice2(A!0))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[334, 333])).
% 5.14/5.31 tff(336,plain,
% 5.14/5.31 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[335, 316])).
% 5.14/5.31 tff(337,plain,
% 5.14/5.31 (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))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[31])).
% 5.14/5.31 tff(338,plain,
% 5.14/5.31 (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)))),
% 5.14/5.31 inference(symmetry,[status(thm)],[337])).
% 5.14/5.31 tff(339,plain,
% 5.14/5.31 ((~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))))),
% 5.14/5.31 inference(monotonicity,[status(thm)],[338])).
% 5.14/5.31 tff(340,plain,
% 5.14/5.31 ((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)))),
% 5.14/5.31 inference(tautology,[status(thm)],[])).
% 5.14/5.31 tff(341,plain,
% 5.14/5.31 (~v3_struct_0(k1_lattice2(A!0))),
% 5.14/5.31 inference(unit_resolution,[status(thm)],[340, 333])).
% 5.14/5.31 tff(342,plain,
% 5.14/5.31 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.14/5.31 inference(modus_ponens,[status(thm)],[341, 339])).
% 5.14/5.31 tff(343,plain,
% 5.14/5.31 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 5.14/5.31 inference(bind,[status(th)],[])).
% 5.14/5.31 tff(344,plain,
% 5.14/5.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.14/5.31 inference(quant_intro,[status(thm)],[343])).
% 5.14/5.31 tff(345,plain,
% 5.14/5.31 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 5.14/5.31 inference(bind,[status(th)],[])).
% 5.14/5.31 tff(346,plain,
% 5.14/5.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.14/5.31 inference(quant_intro,[status(thm)],[345])).
% 5.14/5.31 tff(347,plain,
% 5.14/5.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.14/5.31 inference(transitivity,[status(thm)],[346, 344])).
% 5.14/5.31 tff(348,plain,
% 5.14/5.31 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))), ((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), rewrite((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))), ((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 5.15/5.31 inference(bind,[status(th)],[])).
% 5.15/5.31 tff(349,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.15/5.31 inference(quant_intro,[status(thm)],[348])).
% 5.15/5.31 tff(350,plain,
% 5.15/5.31 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (B = k5_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 5.15/5.31 inference(bind,[status(th)],[])).
% 5.15/5.31 tff(351,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (B = k5_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 5.15/5.31 inference(quant_intro,[status(thm)],[350])).
% 5.15/5.31 tff(352,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 5.15/5.31 inference(rewrite,[status(thm)],[])).
% 5.15/5.31 tff(353,plain,
% 5.15/5.31 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))) <=> (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))))),
% 5.15/5.31 inference(bind,[status(th)],[])).
% 5.15/5.31 tff(354,plain,
% 5.15/5.31 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 5.15/5.31 inference(quant_intro,[status(thm)],[353])).
% 5.15/5.31 tff(355,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_filter_0')).
% 5.15/5.31 tff(356,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 5.15/5.31 inference(modus_ponens,[status(thm)],[355, 354])).
% 5.15/5.31 tff(357,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 5.15/5.31 inference(modus_ponens,[status(thm)],[356, 352])).
% 5.15/5.31 tff(358,plain,(
% 5.15/5.31 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (B = k5_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 5.15/5.31 inference(skolemize,[status(sab)],[357])).
% 5.15/5.31 tff(359,plain,
% 5.15/5.31 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 5.15/5.31 inference(modus_ponens,[status(thm)],[358, 351])).
% 5.15/5.31 tff(360,plain,
% 5.15/5.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.15/5.31 inference(modus_ponens,[status(thm)],[359, 349])).
% 5.15/5.31 tff(361,plain,
% 5.15/5.31 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 5.15/5.31 inference(modus_ponens,[status(thm)],[360, 347])).
% 5.15/5.31 tff(362,plain,
% 5.15/5.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))),
% 5.15/5.31 inference(rewrite,[status(thm)],[])).
% 5.15/5.31 tff(363,plain,
% 5.15/5.31 ((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] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_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)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) <=> (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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))),
% 5.16/5.31 inference(rewrite,[status(thm)],[])).
% 5.16/5.31 tff(364,plain,
% 5.16/5.31 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_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)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))))),
% 5.16/5.32 inference(monotonicity,[status(thm)],[363])).
% 5.16/5.32 tff(365,plain,
% 5.16/5.32 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_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)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))),
% 5.16/5.32 inference(transitivity,[status(thm)],[364, 362])).
% 5.16/5.32 tff(366,plain,
% 5.16/5.32 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_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)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))),
% 5.16/5.32 inference(quant_inst,[status(thm)],[])).
% 5.16/5.32 tff(367,plain,
% 5.16/5.32 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), 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] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(modus_ponens,[status(thm)],[366, 365])).
% 5.16/5.32 tff(368,plain,
% 5.16/5.32 (![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(unit_resolution,[status(thm)],[367, 361, 151, 342, 336])).
% 5.16/5.32 tff(369,plain,
% 5.16/5.32 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(rewrite,[status(thm)],[])).
% 5.16/5.32 tff(370,plain,
% 5.16/5.32 (((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B!1 = k5_lattices(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))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(rewrite,[status(thm)],[])).
% 5.16/5.32 tff(371,plain,
% 5.16/5.32 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B!1 = k5_lattices(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))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))))),
% 5.16/5.32 inference(monotonicity,[status(thm)],[370])).
% 5.16/5.32 tff(372,plain,
% 5.16/5.32 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B!1 = k5_lattices(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))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(transitivity,[status(thm)],[371, 369])).
% 5.16/5.32 tff(373,plain,
% 5.16/5.32 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B!1 = k5_lattices(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))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))),
% 5.16/5.32 inference(quant_inst,[status(thm)],[])).
% 5.16/5.32 tff(374,plain,
% 5.16/5.32 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))),
% 5.16/5.32 inference(modus_ponens,[status(thm)],[373, 372])).
% 5.16/5.32 tff(375,plain,
% 5.16/5.32 ((B!1 = k5_lattices(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))))) | (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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))))))),
% 5.16/5.32 inference(unit_resolution,[status(thm)],[374, 151, 342, 336, 368, 314])).
% 5.16/5.32 tff(376,plain,
% 5.16/5.32 (~((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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)))))),
% 5.16/5.32 inference(unit_resolution,[status(thm)],[375, 288, 236])).
% 5.16/5.32 tff(377,plain,
% 5.16/5.32 (((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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_C_27(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)))),
% 5.16/5.32 inference(tautology,[status(thm)],[])).
% 5.16/5.32 tff(378,plain,
% 5.16/5.32 (m1_filter_0(tptp_fun_C_27(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)))),
% 5.16/5.32 inference(unit_resolution,[status(thm)],[377, 376])).
% 5.16/5.32 tff(379,plain,
% 5.16/5.32 (^[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)))))))))),
% 5.16/5.32 inference(bind,[status(th)],[])).
% 5.16/5.32 tff(380,plain,
% 5.16/5.32 (![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))))))))),
% 5.16/5.32 inference(quant_intro,[status(thm)],[379])).
% 5.16/5.32 tff(381,plain,
% 5.16/5.32 (^[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)))))))))),
% 5.16/5.32 inference(bind,[status(th)],[])).
% 5.16/5.32 tff(382,plain,
% 5.16/5.32 (![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))))))))),
% 5.16/5.32 inference(quant_intro,[status(thm)],[381])).
% 5.16/5.32 tff(383,plain,
% 5.16/5.32 (![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))))))))),
% 5.16/5.32 inference(transitivity,[status(thm)],[382, 380])).
% 5.16/5.32 tff(384,plain,
% 5.16/5.32 (^[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))))))))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(385,plain,
% 5.16/5.33 (![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))))))))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[384])).
% 5.16/5.33 tff(386,plain,
% 5.16/5.33 (![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))))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(387,plain,
% 5.16/5.33 (^[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))))))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(388,plain,
% 5.16/5.33 (![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))))))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[387])).
% 5.16/5.33 tff(389,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')).
% 5.16/5.33 tff(390,plain,
% 5.16/5.33 (![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))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[389, 388])).
% 5.16/5.33 tff(391,plain,
% 5.16/5.33 (![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))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[390, 386])).
% 5.16/5.33 tff(392,plain,(
% 5.16/5.33 ![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))))))),
% 5.16/5.33 inference(skolemize,[status(sab)],[391])).
% 5.16/5.33 tff(393,plain,
% 5.16/5.33 (![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))))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[392, 385])).
% 5.16/5.33 tff(394,plain,
% 5.16/5.33 (![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))))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[393, 383])).
% 5.16/5.33 tff(395,plain,
% 5.16/5.33 (((~![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))))))))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(396,plain,
% 5.16/5.33 ((~![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))))))))))),
% 5.16/5.33 inference(quant_inst,[status(thm)],[])).
% 5.16/5.33 tff(397,plain,
% 5.16/5.33 ((~![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)))))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[396, 395])).
% 5.16/5.33 tff(398,plain,
% 5.16/5.33 (![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)))))))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[397, 394, 151, 342, 336])).
% 5.16/5.33 tff(399,plain,
% 5.16/5.33 (((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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)))))))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(400,plain,
% 5.16/5.33 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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)))))))))),
% 5.16/5.33 inference(quant_inst,[status(thm)],[])).
% 5.16/5.33 tff(401,plain,
% 5.16/5.33 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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))))))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[400, 399])).
% 5.16/5.33 tff(402,plain,
% 5.16/5.33 (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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)))))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[401, 398, 378])).
% 5.16/5.33 tff(403,plain,
% 5.16/5.33 ((v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(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_C_27(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)))))),
% 5.16/5.33 inference(tautology,[status(thm)],[])).
% 5.16/5.33 tff(404,plain,
% 5.16/5.33 (m1_subset_1(tptp_fun_C_27(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)))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[403, 402])).
% 5.16/5.33 tff(405,plain,
% 5.16/5.33 (m1_subset_1(tptp_fun_C_27(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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[404, 205])).
% 5.16/5.33 tff(406,plain,
% 5.16/5.33 (^[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))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(407,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[406])).
% 5.16/5.33 tff(408,plain,
% 5.16/5.33 (^[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))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(409,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[408])).
% 5.16/5.33 tff(410,plain,
% 5.16/5.33 (^[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))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(411,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[410])).
% 5.16/5.33 tff(412,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(transitivity,[status(thm)],[411, 409])).
% 5.16/5.33 tff(413,plain,
% 5.16/5.33 (^[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)))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(414,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[413])).
% 5.16/5.33 tff(415,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(416,plain,
% 5.16/5.33 (^[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)))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(417,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[416])).
% 5.16/5.33 tff(418,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')).
% 5.16/5.33 tff(419,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[418, 417])).
% 5.16/5.33 tff(420,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[419, 415])).
% 5.16/5.33 tff(421,plain,(
% 5.16/5.33 ![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)))),
% 5.16/5.33 inference(skolemize,[status(sab)],[420])).
% 5.16/5.33 tff(422,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[421, 414])).
% 5.16/5.33 tff(423,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[422, 412])).
% 5.16/5.33 tff(424,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[423, 407])).
% 5.16/5.33 tff(425,plain,
% 5.16/5.33 (((~![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)))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(426,plain,
% 5.16/5.33 ((~![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)))),
% 5.16/5.33 inference(quant_inst,[status(thm)],[])).
% 5.16/5.33 tff(427,plain,
% 5.16/5.33 ((~![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))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[426, 425])).
% 5.16/5.33 tff(428,plain,
% 5.16/5.33 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[427, 221, 220, 26, 424])).
% 5.16/5.33 tff(429,plain,
% 5.16/5.33 (((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(430,plain,
% 5.16/5.33 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.33 inference(quant_inst,[status(thm)],[])).
% 5.16/5.33 tff(431,plain,
% 5.16/5.33 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[430, 429])).
% 5.16/5.33 tff(432,plain,
% 5.16/5.33 ((~m1_subset_1(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[431, 428])).
% 5.16/5.33 tff(433,plain,
% 5.16/5.33 (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[432, 405])).
% 5.16/5.33 tff(434,plain,
% 5.16/5.33 (m1_filter_0(tptp_fun_C_27(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_C_27(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)))),
% 5.16/5.33 inference(monotonicity,[status(thm)],[30])).
% 5.16/5.33 tff(435,plain,
% 5.16/5.33 (m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 5.16/5.33 inference(symmetry,[status(thm)],[434])).
% 5.16/5.33 tff(436,plain,
% 5.16/5.33 (m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[378, 435])).
% 5.16/5.33 tff(437,plain,
% 5.16/5.33 (^[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)))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(438,plain,
% 5.16/5.33 (![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))))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[437])).
% 5.16/5.33 tff(439,plain,
% 5.16/5.33 (^[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))))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(440,plain,
% 5.16/5.33 (![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))))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[439])).
% 5.16/5.33 tff(441,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(442,plain,
% 5.16/5.33 (^[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)))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(443,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(quant_intro,[status(thm)],[442])).
% 5.16/5.33 tff(444,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')).
% 5.16/5.33 tff(445,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[444, 443])).
% 5.16/5.33 tff(446,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[445, 441])).
% 5.16/5.33 tff(447,plain,(
% 5.16/5.33 ![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)))),
% 5.16/5.33 inference(skolemize,[status(sab)],[446])).
% 5.16/5.33 tff(448,plain,
% 5.16/5.33 (![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))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[447, 440])).
% 5.16/5.33 tff(449,plain,
% 5.16/5.33 (![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))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[448, 438])).
% 5.16/5.33 tff(450,plain,
% 5.16/5.33 (((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(451,plain,
% 5.16/5.33 ((v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.33 inference(rewrite,[status(thm)],[])).
% 5.16/5.33 tff(452,plain,
% 5.16/5.33 (((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 5.16/5.33 inference(monotonicity,[status(thm)],[451])).
% 5.16/5.33 tff(453,plain,
% 5.16/5.33 (((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.33 inference(transitivity,[status(thm)],[452, 450])).
% 5.16/5.33 tff(454,plain,
% 5.16/5.33 ((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 5.16/5.33 inference(quant_inst,[status(thm)],[])).
% 5.16/5.33 tff(455,plain,
% 5.16/5.33 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[454, 453])).
% 5.16/5.33 tff(456,plain,
% 5.16/5.33 ((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[455, 221, 220, 26, 449])).
% 5.16/5.33 tff(457,plain,
% 5.16/5.33 (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.33 inference(unit_resolution,[status(thm)],[456, 436])).
% 5.16/5.33 tff(458,plain,
% 5.16/5.33 (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.33 inference(symmetry,[status(thm)],[457])).
% 5.16/5.33 tff(459,plain,
% 5.16/5.33 (m1_subset_1(tptp_fun_C_27(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_C_27(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)))))),
% 5.16/5.33 inference(monotonicity,[status(thm)],[34])).
% 5.16/5.33 tff(460,plain,
% 5.16/5.33 (m1_subset_1(tptp_fun_C_27(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_C_27(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))))),
% 5.16/5.33 inference(symmetry,[status(thm)],[459])).
% 5.16/5.33 tff(461,plain,
% 5.16/5.33 (m1_subset_1(tptp_fun_C_27(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))))),
% 5.16/5.33 inference(modus_ponens,[status(thm)],[404, 460])).
% 5.16/5.33 tff(462,plain,
% 5.16/5.33 (^[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))))),
% 5.16/5.33 inference(bind,[status(th)],[])).
% 5.16/5.33 tff(463,plain,
% 5.16/5.33 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[462])).
% 5.16/5.34 tff(464,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(465,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[464])).
% 5.16/5.34 tff(466,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(467,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[466])).
% 5.16/5.34 tff(468,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(transitivity,[status(thm)],[467, 465])).
% 5.16/5.34 tff(469,plain,
% 5.16/5.34 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~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)))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(470,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[469])).
% 5.16/5.34 tff(471,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(472,plain,
% 5.16/5.34 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : 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)))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(473,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[472])).
% 5.16/5.34 tff(474,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')).
% 5.16/5.34 tff(475,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[474, 473])).
% 5.16/5.34 tff(476,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[475, 471])).
% 5.16/5.34 tff(477,plain,(
% 5.16/5.34 ![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)))),
% 5.16/5.34 inference(skolemize,[status(sab)],[476])).
% 5.16/5.34 tff(478,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[477, 470])).
% 5.16/5.34 tff(479,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[478, 468])).
% 5.16/5.34 tff(480,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[479, 463])).
% 5.16/5.34 tff(481,plain,
% 5.16/5.34 (((~![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)))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(482,plain,
% 5.16/5.34 ((~![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)))),
% 5.16/5.34 inference(quant_inst,[status(thm)],[])).
% 5.16/5.34 tff(483,plain,
% 5.16/5.34 ((~![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))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[482, 481])).
% 5.16/5.34 tff(484,plain,
% 5.16/5.34 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[483, 221, 220, 26, 480])).
% 5.16/5.34 tff(485,plain,
% 5.16/5.34 (((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(486,plain,
% 5.16/5.34 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.34 inference(quant_inst,[status(thm)],[])).
% 5.16/5.34 tff(487,plain,
% 5.16/5.34 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[486, 485])).
% 5.16/5.34 tff(488,plain,
% 5.16/5.34 ((~m1_subset_1(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[487, 484])).
% 5.16/5.34 tff(489,plain,
% 5.16/5.34 (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[488, 461])).
% 5.16/5.34 tff(490,plain,
% 5.16/5.34 (tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.34 inference(symmetry,[status(thm)],[489])).
% 5.16/5.34 tff(491,plain,
% 5.16/5.34 (tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.34 inference(transitivity,[status(thm)],[490, 458])).
% 5.16/5.34 tff(492,plain,
% 5.16/5.34 (m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 5.16/5.34 inference(monotonicity,[status(thm)],[491])).
% 5.16/5.34 tff(493,plain,
% 5.16/5.34 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) <=> m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 5.16/5.34 inference(symmetry,[status(thm)],[492])).
% 5.16/5.34 tff(494,plain,
% 5.16/5.34 (^[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)))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(495,plain,
% 5.16/5.34 (![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))))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[494])).
% 5.16/5.34 tff(496,plain,
% 5.16/5.34 (^[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))))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(497,plain,
% 5.16/5.34 (![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))))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[496])).
% 5.16/5.34 tff(498,plain,
% 5.16/5.34 (![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))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(499,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(500,plain,
% 5.16/5.34 (![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))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[499])).
% 5.16/5.34 tff(501,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')).
% 5.16/5.34 tff(502,plain,
% 5.16/5.34 (![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))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[501, 500])).
% 5.16/5.34 tff(503,plain,
% 5.16/5.34 (![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))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[502, 498])).
% 5.16/5.34 tff(504,plain,(
% 5.16/5.34 ![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))),
% 5.16/5.34 inference(skolemize,[status(sab)],[503])).
% 5.16/5.34 tff(505,plain,
% 5.16/5.34 (![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))))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[504, 497])).
% 5.16/5.34 tff(506,plain,
% 5.16/5.34 (![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))))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[505, 495])).
% 5.16/5.34 tff(507,plain,
% 5.16/5.34 (((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(508,plain,
% 5.16/5.34 ((m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(509,plain,
% 5.16/5.34 (((~![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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))))),
% 5.16/5.34 inference(monotonicity,[status(thm)],[508])).
% 5.16/5.34 tff(510,plain,
% 5.16/5.34 (((~![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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 5.16/5.34 inference(transitivity,[status(thm)],[509, 507])).
% 5.16/5.34 tff(511,plain,
% 5.16/5.34 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 5.16/5.34 inference(quant_inst,[status(thm)],[])).
% 5.16/5.34 tff(512,plain,
% 5.16/5.34 ((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[511, 510])).
% 5.16/5.34 tff(513,plain,
% 5.16/5.34 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[512, 221, 220, 26, 506])).
% 5.16/5.34 tff(514,plain,
% 5.16/5.34 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[513, 436])).
% 5.16/5.34 tff(515,plain,
% 5.16/5.34 (m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[514, 493])).
% 5.16/5.34 tff(516,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(517,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[516])).
% 5.16/5.34 tff(518,plain,
% 5.16/5.34 (^[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)))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(519,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[518])).
% 5.16/5.34 tff(520,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(521,plain,
% 5.16/5.34 (^[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)))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(522,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[521])).
% 5.16/5.34 tff(523,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')).
% 5.16/5.34 tff(524,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[523, 522])).
% 5.16/5.34 tff(525,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[524, 520])).
% 5.16/5.34 tff(526,plain,(
% 5.16/5.34 ![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)))),
% 5.16/5.34 inference(skolemize,[status(sab)],[525])).
% 5.16/5.34 tff(527,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[526, 519])).
% 5.16/5.34 tff(528,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[527, 517])).
% 5.16/5.34 tff(529,plain,
% 5.16/5.34 (((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(530,plain,
% 5.16/5.34 ((v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.34 inference(rewrite,[status(thm)],[])).
% 5.16/5.34 tff(531,plain,
% 5.16/5.34 (((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 5.16/5.34 inference(monotonicity,[status(thm)],[530])).
% 5.16/5.34 tff(532,plain,
% 5.16/5.34 (((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.34 inference(transitivity,[status(thm)],[531, 529])).
% 5.16/5.34 tff(533,plain,
% 5.16/5.34 ((~![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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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)))),
% 5.16/5.34 inference(quant_inst,[status(thm)],[])).
% 5.16/5.34 tff(534,plain,
% 5.16/5.34 ((~![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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[533, 532])).
% 5.16/5.34 tff(535,plain,
% 5.16/5.34 (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[534, 221, 220, 26, 528, 515])).
% 5.16/5.34 tff(536,plain,
% 5.16/5.34 (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 5.16/5.34 inference(transitivity,[status(thm)],[535, 433])).
% 5.16/5.34 tff(537,plain,
% 5.16/5.34 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(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_C_27(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)))),
% 5.16/5.34 inference(monotonicity,[status(thm)],[536, 30])).
% 5.16/5.34 tff(538,plain,
% 5.16/5.34 (v1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 5.16/5.34 inference(symmetry,[status(thm)],[537])).
% 5.16/5.34 tff(539,plain,
% 5.16/5.34 (((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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_C_27(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)))),
% 5.16/5.34 inference(tautology,[status(thm)],[])).
% 5.16/5.34 tff(540,plain,
% 5.16/5.34 (v1_filter_0(tptp_fun_C_27(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)))),
% 5.16/5.34 inference(unit_resolution,[status(thm)],[539, 376])).
% 5.16/5.34 tff(541,plain,
% 5.16/5.34 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 5.16/5.34 inference(modus_ponens,[status(thm)],[540, 538])).
% 5.16/5.34 tff(542,plain,
% 5.16/5.34 (^[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))))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(543,plain,
% 5.16/5.34 (![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)))))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[542])).
% 5.16/5.34 tff(544,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(545,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[544])).
% 5.16/5.34 tff(546,plain,
% 5.16/5.34 (^[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))))),
% 5.16/5.34 inference(bind,[status(th)],[])).
% 5.16/5.34 tff(547,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(quant_intro,[status(thm)],[546])).
% 5.16/5.34 tff(548,plain,
% 5.16/5.34 (![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)))),
% 5.16/5.34 inference(transitivity,[status(thm)],[547, 545])).
% 5.16/5.34 tff(549,plain,
% 5.16/5.34 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_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)))))),
% 5.16/5.35 inference(bind,[status(th)],[])).
% 5.16/5.35 tff(550,plain,
% 5.16/5.35 (![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)))),
% 5.16/5.35 inference(quant_intro,[status(thm)],[549])).
% 5.16/5.35 tff(551,plain,
% 5.16/5.35 (![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)))))),
% 5.16/5.35 inference(rewrite,[status(thm)],[])).
% 5.16/5.35 tff(552,plain,
% 5.16/5.35 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : 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)))))))),
% 5.16/5.35 inference(bind,[status(th)],[])).
% 5.16/5.35 tff(553,plain,
% 5.16/5.35 (![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)))))),
% 5.16/5.35 inference(quant_intro,[status(thm)],[552])).
% 5.16/5.35 tff(554,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')).
% 5.16/5.35 tff(555,plain,
% 5.16/5.35 (![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)))))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[554, 553])).
% 5.16/5.35 tff(556,plain,
% 5.16/5.35 (![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)))))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[555, 551])).
% 5.16/5.35 tff(557,plain,(
% 5.16/5.35 ![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)))))),
% 5.16/5.35 inference(skolemize,[status(sab)],[556])).
% 5.16/5.35 tff(558,plain,
% 5.16/5.35 (![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)))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[557, 550])).
% 5.16/5.35 tff(559,plain,
% 5.16/5.35 (![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)))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[558, 548])).
% 5.16/5.35 tff(560,plain,
% 5.16/5.35 (![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)))))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[559, 543])).
% 5.16/5.35 tff(561,plain,
% 5.16/5.35 (((~![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)))))),
% 5.16/5.35 inference(rewrite,[status(thm)],[])).
% 5.16/5.35 tff(562,plain,
% 5.16/5.35 ((~![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)))))),
% 5.16/5.35 inference(quant_inst,[status(thm)],[])).
% 5.16/5.35 tff(563,plain,
% 5.16/5.35 ((~![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))))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[562, 561])).
% 5.16/5.35 tff(564,plain,
% 5.16/5.35 (![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))))),
% 5.16/5.35 inference(unit_resolution,[status(thm)],[563, 221, 220, 26, 560])).
% 5.16/5.35 tff(565,plain,
% 5.16/5.35 (((~![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_C_27(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_C_27(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_C_27(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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 5.16/5.35 inference(rewrite,[status(thm)],[])).
% 5.16/5.35 tff(566,plain,
% 5.16/5.35 ((~![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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 5.16/5.35 inference(quant_inst,[status(thm)],[])).
% 5.16/5.35 tff(567,plain,
% 5.16/5.35 ((~![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_C_27(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_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[566, 565])).
% 5.16/5.35 tff(568,plain,
% 5.16/5.35 (r2_filter_2(A!0, tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 5.16/5.35 inference(unit_resolution,[status(thm)],[567, 564, 515])).
% 5.16/5.35 tff(569,plain,
% 5.16/5.35 (((~m1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.35 inference(tautology,[status(thm)],[])).
% 5.16/5.35 tff(570,plain,
% 5.16/5.35 (r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.35 inference(unit_resolution,[status(thm)],[569, 376])).
% 5.16/5.35 tff(571,plain,
% 5.16/5.35 (^[C: $i] : refl(((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))),
% 5.16/5.35 inference(bind,[status(th)],[])).
% 5.16/5.35 tff(572,plain,
% 5.16/5.35 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 5.16/5.35 inference(quant_intro,[status(thm)],[571])).
% 5.16/5.35 tff(573,plain,
% 5.16/5.35 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r2_hidden(B!1, C) & r2_filter_2(A!0, C)) <=> (~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))), ((~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))) <=> (~(~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))))), rewrite((~(~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))) <=> ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))), ((~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))) <=> ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))), (((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))))), rewrite(((~m2_filter_2(C, A!0)) | ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))), (((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))))),
% 5.16/5.35 inference(bind,[status(th)],[])).
% 5.16/5.35 tff(574,plain,
% 5.16/5.35 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 5.16/5.35 inference(quant_intro,[status(thm)],[573])).
% 5.16/5.35 tff(575,plain,
% 5.16/5.35 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))),
% 5.16/5.35 inference(and_elim,[status(thm)],[25])).
% 5.16/5.35 tff(576,plain,
% 5.16/5.35 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[575, 574])).
% 5.16/5.35 tff(577,plain,
% 5.16/5.35 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 5.16/5.35 inference(modus_ponens,[status(thm)],[576, 572])).
% 5.16/5.35 tff(578,plain,
% 5.16/5.35 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.35 inference(rewrite,[status(thm)],[])).
% 5.16/5.35 tff(579,plain,
% 5.16/5.35 (((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.35 inference(rewrite,[status(thm)],[])).
% 5.16/5.35 tff(580,plain,
% 5.16/5.35 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 5.16/5.35 inference(monotonicity,[status(thm)],[579])).
% 5.16/5.35 tff(581,plain,
% 5.16/5.35 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(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_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.35 inference(transitivity,[status(thm)],[580, 578])).
% 5.16/5.35 tff(582,plain,
% 5.16/5.35 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 5.16/5.35 inference(quant_inst,[status(thm)],[])).
% 5.16/5.35 tff(583,plain,
% 5.16/5.35 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.36 inference(modus_ponens,[status(thm)],[582, 581])).
% 5.16/5.36 tff(584,plain,
% 5.16/5.36 ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 5.16/5.36 inference(unit_resolution,[status(thm)],[583, 577, 570])).
% 5.16/5.36 tff(585,plain,
% 5.16/5.36 (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 5.16/5.36 inference(unit_resolution,[status(thm)],[584, 515])).
% 5.16/5.36 tff(586,plain,
% 5.16/5.36 ((~(r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 5.16/5.36 inference(tautology,[status(thm)],[])).
% 5.16/5.36 tff(587,plain,
% 5.16/5.36 (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 5.16/5.36 inference(unit_resolution,[status(thm)],[586, 585, 568])).
% 5.16/5.36 tff(588,plain,
% 5.16/5.36 ($false),
% 5.16/5.36 inference(unit_resolution,[status(thm)],[587, 541])).
% 5.16/5.36 % SZS output end Proof
% 5.16/5.39 % E exiting
%------------------------------------------------------------------------------