%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT326+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:22 AM UTC 2025
% Result : Theorem 1.22s 1.44s
% Output : Proof 1.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : LAT326+1 : TPTP v9.0.0. Released v3.4.0.
% 0.11/0.11 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n010.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Thu Jun 19 20:22:11 EDT 2025
% 0.12/0.32 % CPUTime :
% 1.22/1.44 % SZS status Theorem
% 1.22/1.44 % SZS output start Proof
% 1.22/1.44 tff(v2_binop_1_type, type, (
% 1.22/1.44 v2_binop_1: ( $i * $i ) > $o)).
% 1.22/1.44 tff(tptp_fun_B_1_type, type, (
% 1.22/1.44 tptp_fun_B_1: $i)).
% 1.22/1.44 tff(k1_realset1_type, type, (
% 1.22/1.44 k1_realset1: ( $i * $i ) > $i)).
% 1.22/1.44 tff(u2_lattices_type, type, (
% 1.22/1.44 u2_lattices: $i > $i)).
% 1.22/1.44 tff(tptp_fun_A_0_type, type, (
% 1.22/1.44 tptp_fun_A_0: $i)).
% 1.22/1.44 tff(u1_struct_0_type, type, (
% 1.22/1.44 u1_struct_0: $i > $i)).
% 1.22/1.44 tff(v3_binop_1_type, type, (
% 1.22/1.44 v3_binop_1: ( $i * $i ) > $o)).
% 1.22/1.44 tff(v1_binop_1_type, type, (
% 1.22/1.44 v1_binop_1: ( $i * $i ) > $o)).
% 1.22/1.44 tff(v1_funct_2_type, type, (
% 1.22/1.44 v1_funct_2: ( $i * $i * $i ) > $o)).
% 1.22/1.44 tff(k2_zfmisc_1_type, type, (
% 1.22/1.44 k2_zfmisc_1: ( $i * $i ) > $i)).
% 1.22/1.44 tff(v1_funct_1_type, type, (
% 1.22/1.44 v1_funct_1: $i > $o)).
% 1.22/1.44 tff(m2_relset_1_type, type, (
% 1.22/1.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 1.22/1.44 tff(m1_subset_1_type, type, (
% 1.22/1.44 m1_subset_1: ( $i * $i ) > $o)).
% 1.22/1.44 tff(k1_zfmisc_1_type, type, (
% 1.22/1.44 k1_zfmisc_1: $i > $i)).
% 1.22/1.44 tff(m2_lattice4_type, type, (
% 1.22/1.44 m2_lattice4: ( $i * $i ) > $o)).
% 1.22/1.44 tff(v10_lattices_type, type, (
% 1.22/1.44 v10_lattices: $i > $o)).
% 1.22/1.44 tff(l3_lattices_type, type, (
% 1.22/1.44 l3_lattices: $i > $o)).
% 1.22/1.44 tff(v3_struct_0_type, type, (
% 1.22/1.44 v3_struct_0: $i > $o)).
% 1.22/1.44 tff(v1_xboole_0_type, type, (
% 1.22/1.44 v1_xboole_0: $i > $o)).
% 1.22/1.44 tff(u1_lattices_type, type, (
% 1.22/1.44 u1_lattices: $i > $i)).
% 1.22/1.44 tff(r1_lattice2_type, type, (
% 1.22/1.44 r1_lattice2: ( $i * $i * $i ) > $o)).
% 1.22/1.44 tff(l1_struct_0_type, type, (
% 1.22/1.44 l1_struct_0: $i > $o)).
% 1.22/1.44 tff(l2_lattices_type, type, (
% 1.22/1.44 l2_lattices: $i > $o)).
% 1.22/1.44 tff(l1_lattices_type, type, (
% 1.22/1.44 l1_lattices: $i > $o)).
% 1.22/1.44 tff(v1_partfun1_type, type, (
% 1.22/1.44 v1_partfun1: ( $i * $i * $i ) > $o)).
% 1.22/1.44 tff(v1_relat_1_type, type, (
% 1.22/1.44 v1_relat_1: $i > $o)).
% 1.22/1.44 tff(v5_lattices_type, type, (
% 1.22/1.44 v5_lattices: $i > $o)).
% 1.22/1.44 tff(v9_lattices_type, type, (
% 1.22/1.44 v9_lattices: $i > $o)).
% 1.22/1.44 tff(v8_lattices_type, type, (
% 1.22/1.44 v8_lattices: $i > $o)).
% 1.22/1.44 tff(v7_lattices_type, type, (
% 1.22/1.44 v7_lattices: $i > $o)).
% 1.22/1.44 tff(v6_lattices_type, type, (
% 1.22/1.44 v6_lattices: $i > $o)).
% 1.22/1.44 tff(v4_lattices_type, type, (
% 1.22/1.44 v4_lattices: $i > $o)).
% 1.22/1.44 tff(1,plain,
% 1.22/1.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 1.22/1.44 inference(bind,[status(th)],[])).
% 1.22/1.44 tff(2,plain,
% 1.22/1.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.44 inference(quant_intro,[status(thm)],[1])).
% 1.22/1.44 tff(3,plain,
% 1.22/1.44 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 1.22/1.44 inference(bind,[status(th)],[])).
% 1.22/1.44 tff(4,plain,
% 1.22/1.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.44 inference(quant_intro,[status(thm)],[3])).
% 1.22/1.44 tff(5,plain,
% 1.22/1.44 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 1.22/1.44 inference(bind,[status(th)],[])).
% 1.22/1.44 tff(6,plain,
% 1.22/1.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.44 inference(quant_intro,[status(thm)],[5])).
% 1.22/1.44 tff(7,plain,
% 1.22/1.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.44 inference(transitivity,[status(thm)],[6, 4])).
% 1.22/1.44 tff(8,plain,
% 1.22/1.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 1.22/1.44 inference(bind,[status(th)],[])).
% 1.22/1.44 tff(9,plain,
% 1.22/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.44 inference(quant_intro,[status(thm)],[8])).
% 1.22/1.44 tff(10,plain,
% 1.22/1.44 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.44 inference(rewrite,[status(thm)],[])).
% 1.22/1.44 tff(11,plain,
% 1.22/1.44 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(12,plain,
% 1.22/1.45 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[11])).
% 1.22/1.45 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 1.22/1.45 tff(14,plain,
% 1.22/1.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[13, 12])).
% 1.22/1.45 tff(15,plain,
% 1.22/1.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[14, 10])).
% 1.22/1.45 tff(16,plain,(
% 1.22/1.45 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.45 inference(skolemize,[status(sab)],[15])).
% 1.22/1.45 tff(17,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[16, 9])).
% 1.22/1.45 tff(18,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[17, 7])).
% 1.22/1.45 tff(19,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[18, 2])).
% 1.22/1.45 tff(20,plain,
% 1.22/1.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(21,plain,
% 1.22/1.45 ((~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))) <=> (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(22,plain,
% 1.22/1.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[21])).
% 1.22/1.45 tff(23,plain,
% 1.22/1.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[22, 20])).
% 1.22/1.45 tff(24,plain,
% 1.22/1.45 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(25,plain,
% 1.22/1.45 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(B, B), B)) & m2_relset_1(C, k2_zfmisc_1(B, B), B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => (((C = k1_realset1(u2_lattices(A), B)) & (D = k1_realset1(u1_lattices(A), B))) => (((((v1_binop_1(C, B) & v2_binop_1(C, B)) & v1_binop_1(D, B)) & v2_binop_1(D, B)) & r1_lattice2(B, C, D)) & r1_lattice2(B, D, C)))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(26,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(B, B), B)) & m2_relset_1(C, k2_zfmisc_1(B, B), B)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => (((C = k1_realset1(u2_lattices(A), B)) & (D = k1_realset1(u1_lattices(A), B))) => (((((v1_binop_1(C, B) & v2_binop_1(C, B)) & v1_binop_1(D, B)) & v2_binop_1(D, B)) & r1_lattice2(B, C, D)) & r1_lattice2(B, D, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t62_filter_2')).
% 1.22/1.45 tff(27,plain,
% 1.22/1.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[26, 25])).
% 1.22/1.45 tff(28,plain,
% 1.22/1.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[27, 24])).
% 1.22/1.45 tff(29,plain,
% 1.22/1.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[28, 24])).
% 1.22/1.45 tff(30,plain,
% 1.22/1.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (v1_binop_1(k1_realset1(u2_lattices(A), B), B) & v2_binop_1(k1_realset1(u2_lattices(A), B), B) & v1_binop_1(k1_realset1(u1_lattices(A), B), B) & v2_binop_1(k1_realset1(u1_lattices(A), B), B) & r1_lattice2(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_lattices(A), B)) & r1_lattice2(B, k1_realset1(u1_lattices(A), B), k1_realset1(u2_lattices(A), B))) | (~v1_funct_1(k1_realset1(u1_lattices(A), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~((~v1_xboole_0(B)) & m2_lattice4(B, A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[29, 24])).
% 1.22/1.45 tff(31,plain,
% 1.22/1.45 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[30, 23])).
% 1.22/1.45 tff(32,plain,
% 1.22/1.45 (l3_lattices(A!0)),
% 1.22/1.45 inference(and_elim,[status(thm)],[31])).
% 1.22/1.45 tff(33,plain,
% 1.22/1.45 (v10_lattices(A!0)),
% 1.22/1.45 inference(and_elim,[status(thm)],[31])).
% 1.22/1.45 tff(34,plain,
% 1.22/1.45 (~v3_struct_0(A!0)),
% 1.22/1.45 inference(and_elim,[status(thm)],[31])).
% 1.22/1.45 tff(35,plain,
% 1.22/1.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(36,plain,
% 1.22/1.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(37,plain,
% 1.22/1.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[36, 35])).
% 1.22/1.45 tff(38,plain,
% 1.22/1.45 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[37, 34, 33, 32, 19])).
% 1.22/1.45 tff(39,plain,
% 1.22/1.45 (~((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0))))),
% 1.22/1.45 inference(and_elim,[status(thm)],[31])).
% 1.22/1.45 tff(40,plain,
% 1.22/1.45 ((~v1_xboole_0(B!1)) & m2_lattice4(B!1, A!0)),
% 1.22/1.45 inference(or_elim,[status(thm)],[39])).
% 1.22/1.45 tff(41,plain,
% 1.22/1.45 (m2_lattice4(B!1, A!0)),
% 1.22/1.45 inference(and_elim,[status(thm)],[40])).
% 1.22/1.45 tff(42,plain,
% 1.22/1.45 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(43,plain,
% 1.22/1.45 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(44,plain,
% 1.22/1.45 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[43, 42])).
% 1.22/1.45 tff(45,plain,
% 1.22/1.45 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[44, 41, 38])).
% 1.22/1.45 tff(46,plain,
% 1.22/1.45 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(47,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[46])).
% 1.22/1.45 tff(48,plain,
% 1.22/1.45 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(49,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[48])).
% 1.22/1.45 tff(50,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(51,plain,
% 1.22/1.45 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(52,plain,
% 1.22/1.45 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[51])).
% 1.22/1.45 tff(53,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 1.22/1.45 tff(54,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[53, 52])).
% 1.22/1.45 tff(55,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[54, 50])).
% 1.22/1.45 tff(56,plain,(
% 1.22/1.45 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 1.22/1.45 inference(skolemize,[status(sab)],[55])).
% 1.22/1.45 tff(57,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[56, 49])).
% 1.22/1.45 tff(58,plain,
% 1.22/1.45 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[57, 47])).
% 1.22/1.45 tff(59,plain,
% 1.22/1.45 (((~![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)))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(60,plain,
% 1.22/1.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(61,plain,
% 1.22/1.45 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[60, 59])).
% 1.22/1.45 tff(62,plain,
% 1.22/1.45 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[61, 32, 58])).
% 1.22/1.45 tff(63,plain,
% 1.22/1.45 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 1.22/1.45 inference(tautology,[status(thm)],[])).
% 1.22/1.45 tff(64,plain,
% 1.22/1.45 (l2_lattices(A!0)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[63, 62])).
% 1.22/1.45 tff(65,plain,
% 1.22/1.45 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(66,plain,
% 1.22/1.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[65])).
% 1.22/1.45 tff(67,plain,
% 1.22/1.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(68,plain,
% 1.22/1.45 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(69,plain,
% 1.22/1.45 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[68])).
% 1.22/1.45 tff(70,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 1.22/1.45 tff(71,plain,
% 1.22/1.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[70, 69])).
% 1.22/1.45 tff(72,plain,
% 1.22/1.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[71, 67])).
% 1.22/1.45 tff(73,plain,(
% 1.22/1.45 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(skolemize,[status(sab)],[72])).
% 1.22/1.45 tff(74,plain,
% 1.22/1.45 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[73, 66])).
% 1.22/1.45 tff(75,plain,
% 1.22/1.45 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(76,plain,
% 1.22/1.45 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(77,plain,
% 1.22/1.45 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[76, 75])).
% 1.22/1.45 tff(78,plain,
% 1.22/1.45 (l1_struct_0(A!0)),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[77, 74, 64])).
% 1.22/1.45 tff(79,plain,
% 1.22/1.45 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(80,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[79])).
% 1.22/1.45 tff(81,plain,
% 1.22/1.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(82,plain,
% 1.22/1.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[81])).
% 1.22/1.45 tff(83,plain,
% 1.22/1.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(84,plain,
% 1.22/1.45 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(85,plain,
% 1.22/1.45 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[84])).
% 1.22/1.45 tff(86,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 1.22/1.45 tff(87,plain,
% 1.22/1.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[86, 85])).
% 1.22/1.45 tff(88,plain,
% 1.22/1.45 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[87, 83])).
% 1.22/1.45 tff(89,plain,(
% 1.22/1.45 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 1.22/1.45 inference(skolemize,[status(sab)],[88])).
% 1.22/1.45 tff(90,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[89, 82])).
% 1.22/1.45 tff(91,plain,
% 1.22/1.45 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[90, 80])).
% 1.22/1.45 tff(92,plain,
% 1.22/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(93,plain,
% 1.22/1.45 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.22/1.45 inference(rewrite,[status(thm)],[])).
% 1.22/1.45 tff(94,plain,
% 1.22/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 1.22/1.45 inference(monotonicity,[status(thm)],[93])).
% 1.22/1.45 tff(95,plain,
% 1.22/1.45 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[94, 92])).
% 1.22/1.45 tff(96,plain,
% 1.22/1.45 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 1.22/1.45 inference(quant_inst,[status(thm)],[])).
% 1.22/1.45 tff(97,plain,
% 1.22/1.45 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.22/1.45 inference(modus_ponens,[status(thm)],[96, 95])).
% 1.22/1.45 tff(98,plain,
% 1.22/1.45 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[97, 34, 91])).
% 1.22/1.45 tff(99,plain,
% 1.22/1.45 (~v1_xboole_0(u1_struct_0(A!0))),
% 1.22/1.45 inference(unit_resolution,[status(thm)],[98, 78])).
% 1.22/1.45 tff(100,plain,
% 1.22/1.45 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(101,plain,
% 1.22/1.45 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[100])).
% 1.22/1.45 tff(102,plain,
% 1.22/1.45 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(103,plain,
% 1.22/1.45 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.45 inference(quant_intro,[status(thm)],[102])).
% 1.22/1.45 tff(104,plain,
% 1.22/1.45 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.45 inference(transitivity,[status(thm)],[103, 101])).
% 1.22/1.45 tff(105,plain,
% 1.22/1.45 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A))))))),
% 1.22/1.45 inference(bind,[status(th)],[])).
% 1.22/1.45 tff(106,plain,
% 1.22/1.45 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.46 inference(quant_intro,[status(thm)],[105])).
% 1.22/1.46 tff(107,plain,
% 1.22/1.46 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(108,plain,
% 1.22/1.46 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))), trans(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) <=> (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B))), trans(monotonicity(trans(monotonicity(rewrite(((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) <=> (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)))), rewrite((v2_binop_1(C, A) => v2_binop_1(D, B)) <=> ((~v2_binop_1(C, A)) | v2_binop_1(D, B))), ((((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B))) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))))), rewrite(((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B))) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) <=> (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B)))), ((((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))) <=> (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))))), (((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))) <=> ((D = k1_realset1(C, B)) => (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B)))))), rewrite(((D = k1_realset1(C, B)) => (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B)))) <=> ((~(D = k1_realset1(C, B))) | (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))))), (((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))) <=> ((~(D = k1_realset1(C, B))) | (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B)))))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))) <=> ((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((~(D = k1_realset1(C, B))) | (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((~(D = k1_realset1(C, B))) | (((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B))))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))) <=> ![D: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)))))), trans(trans(der(![D: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)))) <=> ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), elim_unused(![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), (![D: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), rewrite(((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), (![D: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(D, B)) & ((~v3_binop_1(C, A)) | v3_binop_1(D, B)) & ((~v2_binop_1(C, A)) | v2_binop_1(D, B))) | (~(D = k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B) & m2_relset_1(D, k2_zfmisc_1(B, B), B)))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))) <=> ((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))) <=> ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))) <=> ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))))),
% 1.22/1.46 inference(bind,[status(th)],[])).
% 1.22/1.46 tff(109,plain,
% 1.22/1.46 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B)))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))),
% 1.22/1.46 inference(quant_intro,[status(thm)],[108])).
% 1.22/1.46 tff(110,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(B, B), B)) & m2_relset_1(D, k2_zfmisc_1(B, B), B)) => ((D = k1_realset1(C, B)) => (((v1_binop_1(C, A) => v1_binop_1(D, B)) & (v3_binop_1(C, A) => v3_binop_1(D, B))) & (v2_binop_1(C, A) => v2_binop_1(D, B))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t1_filter_2')).
% 1.22/1.46 tff(111,plain,
% 1.22/1.46 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[110, 109])).
% 1.22/1.46 tff(112,plain,
% 1.22/1.46 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[111, 107])).
% 1.22/1.46 tff(113,plain,(
% 1.22/1.46 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B)) & ((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B)) & ((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))))),
% 1.22/1.46 inference(skolemize,[status(sab)],[112])).
% 1.22/1.46 tff(114,plain,
% 1.22/1.46 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[113, 106])).
% 1.22/1.46 tff(115,plain,
% 1.22/1.46 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[114, 104])).
% 1.22/1.46 tff(116,plain,
% 1.22/1.46 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(117,plain,
% 1.22/1.46 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(118,plain,
% 1.22/1.46 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, A)) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, A)) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, A)) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 1.22/1.46 inference(modus_ponens,[status(thm)],[117, 116])).
% 1.22/1.46 tff(119,plain,
% 1.22/1.46 (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[118, 115])).
% 1.22/1.46 tff(120,plain,
% 1.22/1.46 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 1.22/1.46 inference(unit_resolution,[status(thm)],[119, 99])).
% 1.22/1.46 tff(121,plain,
% 1.22/1.46 (~v1_xboole_0(B!1)),
% 1.22/1.46 inference(and_elim,[status(thm)],[40])).
% 1.22/1.46 tff(122,plain,
% 1.22/1.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1)))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1)))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(123,plain,
% 1.22/1.46 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1)))))))),
% 1.22/1.46 inference(rewrite,[status(thm)],[])).
% 1.22/1.46 tff(124,plain,
% 1.22/1.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))))),
% 1.22/1.46 inference(monotonicity,[status(thm)],[123])).
% 1.22/1.46 tff(125,plain,
% 1.22/1.46 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1)))))))),
% 1.22/1.46 inference(transitivity,[status(thm)],[124, 122])).
% 1.22/1.46 tff(126,plain,
% 1.22/1.46 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 1.22/1.46 inference(quant_inst,[status(thm)],[])).
% 1.22/1.46 tff(127,plain,
% 1.22/1.46 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B), B))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B), B))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B), B))))) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[126, 125])).
% 1.30/1.46 tff(128,plain,
% 1.30/1.46 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))),
% 1.30/1.46 inference(unit_resolution,[status(thm)],[127, 121, 120, 45])).
% 1.30/1.46 tff(129,plain,
% 1.30/1.46 (^[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)))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(130,plain,
% 1.30/1.46 (![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))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[129])).
% 1.30/1.46 tff(131,plain,
% 1.30/1.46 (^[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)))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(132,plain,
% 1.30/1.46 (![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))))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[131])).
% 1.30/1.46 tff(133,plain,
% 1.30/1.46 (![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))))),
% 1.30/1.46 inference(rewrite,[status(thm)],[])).
% 1.30/1.46 tff(134,plain,
% 1.30/1.46 (^[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))))))),
% 1.30/1.46 inference(bind,[status(th)],[])).
% 1.30/1.46 tff(135,plain,
% 1.30/1.46 (![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))))),
% 1.30/1.46 inference(quant_intro,[status(thm)],[134])).
% 1.30/1.46 tff(136,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')).
% 1.30/1.46 tff(137,plain,
% 1.30/1.46 (![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))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[136, 135])).
% 1.30/1.46 tff(138,plain,
% 1.30/1.46 (![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))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[137, 133])).
% 1.30/1.46 tff(139,plain,(
% 1.30/1.46 ![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))))),
% 1.30/1.46 inference(skolemize,[status(sab)],[138])).
% 1.30/1.46 tff(140,plain,
% 1.30/1.46 (![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))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[139, 132])).
% 1.30/1.46 tff(141,plain,
% 1.30/1.46 (![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))))))),
% 1.30/1.46 inference(modus_ponens,[status(thm)],[140, 130])).
% 1.30/1.46 tff(142,plain,
% 1.30/1.46 (((~![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))))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(143,plain,
% 1.30/1.47 ((~![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))))))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(144,plain,
% 1.30/1.47 ((~![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)))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[143, 142])).
% 1.30/1.47 tff(145,plain,
% 1.30/1.47 ((~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)))))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[144, 141])).
% 1.30/1.47 tff(146,plain,
% 1.30/1.47 (~((~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))))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[145, 64])).
% 1.30/1.47 tff(147,plain,
% 1.30/1.47 (((~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))),
% 1.30/1.47 inference(tautology,[status(thm)],[])).
% 1.30/1.47 tff(148,plain,
% 1.30/1.47 (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))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[147, 146])).
% 1.30/1.47 tff(149,plain,
% 1.30/1.47 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(150,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[149])).
% 1.30/1.47 tff(151,plain,
% 1.30/1.47 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))))), rewrite(((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(152,plain,
% 1.30/1.47 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[151])).
% 1.30/1.47 tff(153,plain,
% 1.30/1.47 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(154,plain,
% 1.30/1.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(155,plain,
% 1.30/1.47 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[154])).
% 1.30/1.47 tff(156,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 1.30/1.47 tff(157,plain,
% 1.30/1.47 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[156, 155])).
% 1.30/1.47 tff(158,plain,
% 1.30/1.47 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[157, 153])).
% 1.30/1.47 tff(159,plain,(
% 1.30/1.47 ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 1.30/1.47 inference(skolemize,[status(sab)],[158])).
% 1.30/1.47 tff(160,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[159, 152])).
% 1.30/1.47 tff(161,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[160, 150])).
% 1.30/1.47 tff(162,plain,
% 1.30/1.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(163,plain,
% 1.30/1.47 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(164,plain,
% 1.30/1.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[163])).
% 1.30/1.47 tff(165,plain,
% 1.30/1.47 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 1.30/1.47 inference(transitivity,[status(thm)],[164, 162])).
% 1.30/1.47 tff(166,plain,
% 1.30/1.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(167,plain,
% 1.30/1.47 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[166, 165])).
% 1.30/1.47 tff(168,plain,
% 1.30/1.47 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[167, 34, 33, 32, 161])).
% 1.30/1.47 tff(169,plain,
% 1.30/1.47 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v5_lattices(A!0)),
% 1.30/1.47 inference(tautology,[status(thm)],[])).
% 1.30/1.47 tff(170,plain,
% 1.30/1.47 (v5_lattices(A!0)),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[169, 168])).
% 1.30/1.47 tff(171,plain,
% 1.30/1.47 (^[A: $i] : refl((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(172,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[171])).
% 1.30/1.47 tff(173,plain,
% 1.30/1.47 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))), ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)))), ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))), rewrite((v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(174,plain,
% 1.30/1.47 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[173])).
% 1.30/1.47 tff(175,plain,
% 1.30/1.47 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(176,plain,
% 1.30/1.47 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u2_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))) <=> (v1_relat_1(u2_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)))), ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.30/1.47 inference(bind,[status(th)],[])).
% 1.30/1.47 tff(177,plain,
% 1.30/1.47 (![A: $i] : ((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.30/1.47 inference(quant_intro,[status(thm)],[176])).
% 1.30/1.47 tff(178,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(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','fc3_lattice2')).
% 1.30/1.47 tff(179,plain,
% 1.30/1.47 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[178, 177])).
% 1.30/1.47 tff(180,plain,
% 1.30/1.47 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[179, 175])).
% 1.30/1.47 tff(181,plain,(
% 1.30/1.47 ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.30/1.47 inference(skolemize,[status(sab)],[180])).
% 1.30/1.47 tff(182,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[181, 174])).
% 1.30/1.47 tff(183,plain,
% 1.30/1.47 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[182, 172])).
% 1.30/1.47 tff(184,plain,
% 1.30/1.47 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(185,plain,
% 1.30/1.47 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 1.30/1.47 inference(quant_inst,[status(thm)],[])).
% 1.30/1.47 tff(186,plain,
% 1.30/1.47 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 1.30/1.47 inference(modus_ponens,[status(thm)],[185, 184])).
% 1.30/1.47 tff(187,plain,
% 1.30/1.47 ((~l2_lattices(A!0)) | (~v5_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[186, 34, 183])).
% 1.30/1.47 tff(188,plain,
% 1.30/1.47 (~((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[187, 64, 170])).
% 1.30/1.47 tff(189,plain,
% 1.30/1.47 (((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(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))),
% 1.30/1.47 inference(tautology,[status(thm)],[])).
% 1.30/1.47 tff(190,plain,
% 1.30/1.47 (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))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[189, 188])).
% 1.30/1.47 tff(191,plain,
% 1.30/1.47 (((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 1.30/1.47 inference(tautology,[status(thm)],[])).
% 1.30/1.47 tff(192,plain,
% 1.30/1.47 (v1_funct_1(u2_lattices(A!0))),
% 1.30/1.47 inference(unit_resolution,[status(thm)],[191, 188])).
% 1.30/1.47 tff(193,plain,
% 1.30/1.47 (v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 1.30/1.47 inference(or_elim,[status(thm)],[39])).
% 1.30/1.47 tff(194,plain,
% 1.30/1.47 (v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))),
% 1.30/1.47 inference(or_elim,[status(thm)],[39])).
% 1.30/1.47 tff(195,plain,
% 1.30/1.47 (m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 1.30/1.47 inference(or_elim,[status(thm)],[39])).
% 1.30/1.47 tff(196,plain,
% 1.30/1.47 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(197,plain,
% 1.30/1.47 (((~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)))))) <=> ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))),
% 1.30/1.47 inference(rewrite,[status(thm)],[])).
% 1.30/1.47 tff(198,plain,
% 1.30/1.47 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)))))))),
% 1.30/1.47 inference(monotonicity,[status(thm)],[197])).
% 1.30/1.47 tff(199,plain,
% 1.30/1.47 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))),
% 1.30/1.48 inference(transitivity,[status(thm)],[198, 196])).
% 1.30/1.48 tff(200,plain,
% 1.30/1.48 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))))),
% 1.30/1.48 inference(quant_inst,[status(thm)],[])).
% 1.30/1.48 tff(201,plain,
% 1.30/1.48 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)))))),
% 1.30/1.48 inference(modus_ponens,[status(thm)],[200, 199])).
% 1.30/1.48 tff(202,plain,
% 1.30/1.48 (~((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))))),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[201, 195, 194, 193, 192, 190, 148, 128])).
% 1.30/1.48 tff(203,plain,
% 1.30/1.48 (((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)))) | ((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))),
% 1.30/1.48 inference(tautology,[status(thm)],[])).
% 1.30/1.48 tff(204,plain,
% 1.30/1.48 ((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[203, 202])).
% 1.30/1.48 tff(205,plain,
% 1.30/1.48 (((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))) | v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))),
% 1.30/1.48 inference(tautology,[status(thm)],[])).
% 1.30/1.48 tff(206,plain,
% 1.30/1.48 (v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[205, 188])).
% 1.30/1.48 tff(207,plain,
% 1.30/1.48 ((~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.30/1.48 inference(tautology,[status(thm)],[])).
% 1.30/1.48 tff(208,plain,
% 1.30/1.48 ((~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[207, 206])).
% 1.30/1.48 tff(209,plain,
% 1.30/1.48 (v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[208, 204])).
% 1.30/1.48 tff(210,plain,
% 1.30/1.48 (((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)))) | ((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))),
% 1.30/1.48 inference(tautology,[status(thm)],[])).
% 1.30/1.48 tff(211,plain,
% 1.30/1.48 ((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.30/1.48 inference(unit_resolution,[status(thm)],[210, 202])).
% 1.30/1.48 tff(212,plain,
% 1.30/1.48 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v4_lattices(A!0)),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(213,plain,
% 1.32/1.48 (v4_lattices(A!0)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[212, 168])).
% 1.32/1.48 tff(214,plain,
% 1.32/1.48 (^[A: $i] : refl((v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(215,plain,
% 1.32/1.48 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[214])).
% 1.32/1.48 tff(216,plain,
% 1.32/1.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A)) | (~v4_lattices(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v4_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v4_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_lattices(A)))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_lattices(A))))), rewrite((v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(217,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[216])).
% 1.32/1.48 tff(218,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(219,plain,
% 1.32/1.48 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u2_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))) <=> (v1_relat_1(u2_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)))), ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(220,plain,
% 1.32/1.48 (![A: $i] : ((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[219])).
% 1.32/1.48 tff(221,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_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))) & v1_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(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','fc2_lattice2')).
% 1.32/1.48 tff(222,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[221, 220])).
% 1.32/1.48 tff(223,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[222, 218])).
% 1.32/1.48 tff(224,plain,(
% 1.32/1.48 ![A: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_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)) & v1_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(skolemize,[status(sab)],[223])).
% 1.32/1.48 tff(225,plain,
% 1.32/1.48 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[224, 217])).
% 1.32/1.48 tff(226,plain,
% 1.32/1.48 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[225, 215])).
% 1.32/1.48 tff(227,plain,
% 1.32/1.48 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(228,plain,
% 1.32/1.48 ((v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(229,plain,
% 1.32/1.48 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))))),
% 1.32/1.48 inference(monotonicity,[status(thm)],[228])).
% 1.32/1.48 tff(230,plain,
% 1.32/1.48 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.48 inference(transitivity,[status(thm)],[229, 227])).
% 1.32/1.48 tff(231,plain,
% 1.32/1.48 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(232,plain,
% 1.32/1.48 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A))) | (~v1_binop_1(u2_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[231, 230])).
% 1.32/1.48 tff(233,plain,
% 1.32/1.48 ((~l2_lattices(A!0)) | (~v4_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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[232, 34, 226])).
% 1.32/1.48 tff(234,plain,
% 1.32/1.48 (~((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[233, 64, 213])).
% 1.32/1.48 tff(235,plain,
% 1.32/1.48 (((~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))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))) | v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(236,plain,
% 1.32/1.48 (v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[235, 234])).
% 1.32/1.48 tff(237,plain,
% 1.32/1.48 ((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | (~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(238,plain,
% 1.32/1.48 ((~((~v1_binop_1(u2_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1))) | v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[237, 236])).
% 1.32/1.48 tff(239,plain,
% 1.32/1.48 (v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[238, 211])).
% 1.32/1.48 tff(240,plain,
% 1.32/1.48 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(241,plain,
% 1.32/1.48 (l1_lattices(A!0)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[240, 62])).
% 1.32/1.48 tff(242,plain,
% 1.32/1.48 (^[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)))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(243,plain,
% 1.32/1.48 (![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))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[242])).
% 1.32/1.48 tff(244,plain,
% 1.32/1.48 (^[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)))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(245,plain,
% 1.32/1.48 (![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))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[244])).
% 1.32/1.48 tff(246,plain,
% 1.32/1.48 (![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))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(247,plain,
% 1.32/1.48 (^[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))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(248,plain,
% 1.32/1.48 (![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))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[247])).
% 1.32/1.48 tff(249,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')).
% 1.32/1.48 tff(250,plain,
% 1.32/1.48 (![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))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[249, 248])).
% 1.32/1.48 tff(251,plain,
% 1.32/1.48 (![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))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[250, 246])).
% 1.32/1.48 tff(252,plain,(
% 1.32/1.48 ![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))))),
% 1.32/1.48 inference(skolemize,[status(sab)],[251])).
% 1.32/1.48 tff(253,plain,
% 1.32/1.48 (![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))))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[252, 245])).
% 1.32/1.48 tff(254,plain,
% 1.32/1.48 (![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))))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[253, 243])).
% 1.32/1.48 tff(255,plain,
% 1.32/1.48 (((~![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))))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(256,plain,
% 1.32/1.48 ((~![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))))))),
% 1.32/1.48 inference(quant_inst,[status(thm)],[])).
% 1.32/1.48 tff(257,plain,
% 1.32/1.48 ((~![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)))))),
% 1.32/1.48 inference(modus_ponens,[status(thm)],[256, 255])).
% 1.32/1.48 tff(258,plain,
% 1.32/1.48 ((~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)))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[257, 254])).
% 1.32/1.48 tff(259,plain,
% 1.32/1.48 (~((~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))))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[258, 241])).
% 1.32/1.48 tff(260,plain,
% 1.32/1.48 (((~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))),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(261,plain,
% 1.32/1.48 (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))),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[260, 259])).
% 1.32/1.48 tff(262,plain,
% 1.32/1.48 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v7_lattices(A!0)),
% 1.32/1.48 inference(tautology,[status(thm)],[])).
% 1.32/1.48 tff(263,plain,
% 1.32/1.48 (v7_lattices(A!0)),
% 1.32/1.48 inference(unit_resolution,[status(thm)],[262, 168])).
% 1.32/1.48 tff(264,plain,
% 1.32/1.48 (^[A: $i] : refl((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(265,plain,
% 1.32/1.48 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[264])).
% 1.32/1.48 tff(266,plain,
% 1.32/1.48 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A)))), ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_lattices(A))))), rewrite((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))))),
% 1.32/1.48 inference(bind,[status(th)],[])).
% 1.32/1.48 tff(267,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 1.32/1.48 inference(quant_intro,[status(thm)],[266])).
% 1.32/1.48 tff(268,plain,
% 1.32/1.48 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.48 inference(rewrite,[status(thm)],[])).
% 1.32/1.48 tff(269,plain,
% 1.32/1.48 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u1_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))) <=> (v1_relat_1(u1_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)))), ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(270,plain,
% 1.32/1.49 (![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[269])).
% 1.32/1.49 tff(271,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v7_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v2_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(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','fc5_lattice2')).
% 1.32/1.49 tff(272,plain,
% 1.32/1.49 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[271, 270])).
% 1.32/1.49 tff(273,plain,
% 1.32/1.49 (![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[272, 268])).
% 1.32/1.49 tff(274,plain,(
% 1.32/1.49 ![A: $i] : ((~((~v3_struct_0(A)) & v7_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v2_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.49 inference(skolemize,[status(sab)],[273])).
% 1.32/1.49 tff(275,plain,
% 1.32/1.49 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[274, 267])).
% 1.32/1.49 tff(276,plain,
% 1.32/1.49 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[275, 265])).
% 1.32/1.49 tff(277,plain,
% 1.32/1.49 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(278,plain,
% 1.32/1.49 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(279,plain,
% 1.32/1.49 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v7_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u1_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[278, 277])).
% 1.32/1.49 tff(280,plain,
% 1.32/1.49 ((~l1_lattices(A!0)) | (~v7_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[279, 34, 276])).
% 1.32/1.49 tff(281,plain,
% 1.32/1.49 (~((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[280, 241, 263])).
% 1.32/1.49 tff(282,plain,
% 1.32/1.49 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(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))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(283,plain,
% 1.32/1.49 (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))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[282, 281])).
% 1.32/1.49 tff(284,plain,
% 1.32/1.49 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(285,plain,
% 1.32/1.49 (v1_funct_1(u1_lattices(A!0))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[284, 281])).
% 1.32/1.49 tff(286,plain,
% 1.32/1.49 (v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 1.32/1.49 inference(or_elim,[status(thm)],[39])).
% 1.32/1.49 tff(287,plain,
% 1.32/1.49 (v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))),
% 1.32/1.49 inference(or_elim,[status(thm)],[39])).
% 1.32/1.49 tff(288,plain,
% 1.32/1.49 (m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)),
% 1.32/1.49 inference(or_elim,[status(thm)],[39])).
% 1.32/1.49 tff(289,plain,
% 1.32/1.49 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(290,plain,
% 1.32/1.49 (((~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)))))) <=> ((~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(291,plain,
% 1.32/1.49 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)))))))),
% 1.32/1.49 inference(monotonicity,[status(thm)],[290])).
% 1.32/1.49 tff(292,plain,
% 1.32/1.49 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))),
% 1.32/1.49 inference(transitivity,[status(thm)],[291, 289])).
% 1.32/1.49 tff(293,plain,
% 1.32/1.49 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | ((~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))))),
% 1.32/1.49 inference(quant_inst,[status(thm)],[])).
% 1.32/1.49 tff(294,plain,
% 1.32/1.49 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~((~((~v1_binop_1(C, u1_struct_0(A!0))) | v1_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v2_binop_1(C, u1_struct_0(A!0))) | v2_binop_1(k1_realset1(C, B!1), B!1))) | (~((~v3_binop_1(C, u1_struct_0(A!0))) | v3_binop_1(k1_realset1(C, B!1), B!1))))))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)))))),
% 1.32/1.49 inference(modus_ponens,[status(thm)],[293, 292])).
% 1.32/1.49 tff(295,plain,
% 1.32/1.49 (~((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[294, 288, 287, 286, 285, 283, 261, 128])).
% 1.32/1.49 tff(296,plain,
% 1.32/1.49 (((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)))) | ((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(297,plain,
% 1.32/1.49 ((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[296, 295])).
% 1.32/1.49 tff(298,plain,
% 1.32/1.49 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(299,plain,
% 1.32/1.49 (v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[298, 281])).
% 1.32/1.49 tff(300,plain,
% 1.32/1.49 ((~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(301,plain,
% 1.32/1.49 ((~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[300, 299])).
% 1.32/1.49 tff(302,plain,
% 1.32/1.49 (v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[301, 297])).
% 1.32/1.49 tff(303,plain,
% 1.32/1.49 (((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v2_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~((~v3_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v3_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)))) | ((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(304,plain,
% 1.32/1.49 ((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[303, 295])).
% 1.32/1.49 tff(305,plain,
% 1.32/1.49 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 1.32/1.49 inference(tautology,[status(thm)],[])).
% 1.32/1.49 tff(306,plain,
% 1.32/1.49 (v6_lattices(A!0)),
% 1.32/1.49 inference(unit_resolution,[status(thm)],[305, 168])).
% 1.32/1.49 tff(307,plain,
% 1.32/1.49 (^[A: $i] : refl((v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(308,plain,
% 1.32/1.49 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[307])).
% 1.32/1.49 tff(309,plain,
% 1.32/1.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A)) | (~v6_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v6_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A)) | (~v6_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_lattices(A))))), rewrite((v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))))),
% 1.32/1.49 inference(bind,[status(th)],[])).
% 1.32/1.49 tff(310,plain,
% 1.32/1.49 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.49 inference(quant_intro,[status(thm)],[309])).
% 1.32/1.49 tff(311,plain,
% 1.32/1.49 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.49 inference(rewrite,[status(thm)],[])).
% 1.32/1.49 tff(312,plain,
% 1.32/1.49 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u1_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))) <=> (v1_relat_1(u1_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)))), ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) => (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(313,plain,
% 1.32/1.50 (![A: $i] : ((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[312])).
% 1.32/1.50 tff(314,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) => ((((v1_relat_1(u1_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))) & v1_binop_1(u1_lattices(A), u1_struct_0(A))) & v1_partfun1(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','fc4_lattice2')).
% 1.32/1.50 tff(315,plain,
% 1.32/1.50 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[314, 313])).
% 1.32/1.50 tff(316,plain,
% 1.32/1.50 (![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[315, 311])).
% 1.32/1.50 tff(317,plain,(
% 1.32/1.50 ![A: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))) | (v1_relat_1(u1_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)) & v1_binop_1(u1_lattices(A), u1_struct_0(A)) & v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 1.32/1.50 inference(skolemize,[status(sab)],[316])).
% 1.32/1.50 tff(318,plain,
% 1.32/1.50 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[317, 310])).
% 1.32/1.50 tff(319,plain,
% 1.32/1.50 (![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[318, 308])).
% 1.32/1.50 tff(320,plain,
% 1.32/1.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(321,plain,
% 1.32/1.50 ((v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(322,plain,
% 1.32/1.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))))),
% 1.32/1.50 inference(monotonicity,[status(thm)],[321])).
% 1.32/1.50 tff(323,plain,
% 1.32/1.50 (((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[322, 320])).
% 1.32/1.50 tff(324,plain,
% 1.32/1.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 1.32/1.50 inference(quant_inst,[status(thm)],[])).
% 1.32/1.50 tff(325,plain,
% 1.32/1.50 ((~![A: $i] : (v3_struct_0(A) | (~l1_lattices(A)) | (~v6_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))) | (~v1_relat_1(u1_lattices(A))) | (~v1_binop_1(u1_lattices(A), u1_struct_0(A))) | (~v1_partfun1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[324, 323])).
% 1.32/1.50 tff(326,plain,
% 1.32/1.50 ((~l1_lattices(A!0)) | (~v6_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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[325, 34, 319])).
% 1.32/1.50 tff(327,plain,
% 1.32/1.50 (~((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[326, 241, 306])).
% 1.32/1.50 tff(328,plain,
% 1.32/1.50 (((~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_relat_1(u1_lattices(A!0))) | (~v1_partfun1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0)))) | v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.50 inference(tautology,[status(thm)],[])).
% 1.32/1.50 tff(329,plain,
% 1.32/1.50 (v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[328, 327])).
% 1.32/1.50 tff(330,plain,
% 1.32/1.50 ((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | (~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.50 inference(tautology,[status(thm)],[])).
% 1.32/1.50 tff(331,plain,
% 1.32/1.50 ((~((~v1_binop_1(u1_lattices(A!0), u1_struct_0(A!0))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1))) | v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[330, 329])).
% 1.32/1.50 tff(332,plain,
% 1.32/1.50 (v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)),
% 1.32/1.50 inference(unit_resolution,[status(thm)],[331, 304])).
% 1.32/1.50 tff(333,plain,
% 1.32/1.50 (^[A: $i] : refl((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(334,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[333])).
% 1.32/1.50 tff(335,plain,
% 1.32/1.50 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(336,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[335])).
% 1.32/1.50 tff(337,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(transitivity,[status(thm)],[336, 334])).
% 1.32/1.50 tff(338,plain,
% 1.32/1.50 (^[A: $i] : rewrite((v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(339,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[338])).
% 1.32/1.50 tff(340,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(341,plain,
% 1.32/1.50 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))), trans(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(rewrite(((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) <=> (v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))), trans(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(rewrite(((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) <=> (v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))), trans(monotonicity(rewrite((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) <=> ((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))), (((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)) <=> (((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))), rewrite((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)) <=> ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | r1_lattice2(B, E, F))), (((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)) <=> ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | r1_lattice2(B, E, F)))), ((((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))) <=> ((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | r1_lattice2(B, E, F))))), rewrite(((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | r1_lattice2(B, E, F))) <=> (r1_lattice2(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))) <=> (r1_lattice2(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B))))))), (![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))) <=> ![F: $i] : (r1_lattice2(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))))), trans(der(![F: $i] : (r1_lattice2(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))) <=> ![F: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))))), elim_unused(![F: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B)))) <=> ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))))), (![F: $i] : (r1_lattice2(B, E, F) | (~((E = k1_realset1(C, B)) & (F = k1_realset1(D, B)) & r1_lattice2(A, C, D))) | (~(v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B) & m2_relset_1(F, k2_zfmisc_1(B, B), B)))) <=> ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B)))))), (![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))) <=> ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B)))))), ((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))) <=> ((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))))))), rewrite(((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))))) <=> ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))) <=> ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B))))))), (![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))) <=> ![E: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)))))), trans(trans(der(![E: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)))) <=> ![E: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), elim_unused(![E: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)))), (![E: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))))), rewrite(((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))), (![E: $i] : ((~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, E, k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~(E = k1_realset1(C, B))) | (~(v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B) & m2_relset_1(E, k2_zfmisc_1(B, B), B)))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))), (![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))) <=> ((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))), rewrite(((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))), ((((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))) <=> ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))), (![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))) <=> ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))) <=> ((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))), rewrite(((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))), ((((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))) <=> ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))), (![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))) <=> ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))))) <=> ((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))))), rewrite(((~v1_xboole_0(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))), (((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))))) <=> (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))))),
% 1.32/1.50 inference(bind,[status(th)],[])).
% 1.32/1.50 tff(342,plain,
% 1.32/1.50 (![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F)))))))) <=> ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(quant_intro,[status(thm)],[341])).
% 1.32/1.50 tff(343,axiom,(![A: $i] : ((~v1_xboole_0(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A))) => ![C: $i] : (((v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m2_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i] : (((v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A)) & m2_relset_1(D, k2_zfmisc_1(A, A), A)) => ![E: $i] : (((v1_funct_1(E) & v1_funct_2(E, k2_zfmisc_1(B, B), B)) & m2_relset_1(E, k2_zfmisc_1(B, B), B)) => ![F: $i] : (((v1_funct_1(F) & v1_funct_2(F, k2_zfmisc_1(B, B), B)) & m2_relset_1(F, k2_zfmisc_1(B, B), B)) => ((((E = k1_realset1(C, B)) & (F = k1_realset1(D, B))) & r1_lattice2(A, C, D)) => r1_lattice2(B, E, F))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t5_filter_2')).
% 1.32/1.50 tff(344,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[343, 342])).
% 1.32/1.50 tff(345,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[344, 340])).
% 1.32/1.50 tff(346,plain,(
% 1.32/1.50 ![A: $i] : (v1_xboole_0(A) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(A)))) | ![C: $i] : ((~(v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m2_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i] : ((~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~(v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, A), A) & m2_relset_1(D, k2_zfmisc_1(A, A), A))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(skolemize,[status(sab)],[345])).
% 1.32/1.50 tff(347,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[346, 339])).
% 1.32/1.50 tff(348,plain,
% 1.32/1.50 (![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.50 inference(modus_ponens,[status(thm)],[347, 337])).
% 1.32/1.50 tff(349,plain,
% 1.32/1.50 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D))))))),
% 1.32/1.50 inference(rewrite,[status(thm)],[])).
% 1.32/1.50 tff(350,plain,
% 1.32/1.51 ((v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D))))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(351,plain,
% 1.32/1.51 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))))),
% 1.32/1.51 inference(monotonicity,[status(thm)],[350])).
% 1.32/1.51 tff(352,plain,
% 1.32/1.51 (((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) <=> ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D))))))),
% 1.32/1.51 inference(transitivity,[status(thm)],[351, 349])).
% 1.32/1.51 tff(353,plain,
% 1.32/1.51 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))),
% 1.32/1.51 inference(quant_inst,[status(thm)],[])).
% 1.32/1.51 tff(354,plain,
% 1.32/1.51 ((~![A: $i] : (v1_xboole_0(A) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(A))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~v1_funct_2(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(D, k2_zfmisc_1(A, A), A)) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~r1_lattice2(A, C, D)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B))))))) | v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))),
% 1.32/1.51 inference(modus_ponens,[status(thm)],[353, 352])).
% 1.32/1.51 tff(355,plain,
% 1.32/1.51 (v1_xboole_0(u1_struct_0(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[354, 348])).
% 1.32/1.51 tff(356,plain,
% 1.32/1.51 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))),
% 1.32/1.51 inference(unit_resolution,[status(thm)],[355, 99])).
% 1.32/1.51 tff(357,plain,
% 1.32/1.51 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(358,plain,
% 1.32/1.51 ((v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D))))) <=> (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)))))),
% 1.32/1.51 inference(rewrite,[status(thm)],[])).
% 1.32/1.51 tff(359,plain,
% 1.32/1.51 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))))),
% 1.35/1.51 inference(monotonicity,[status(thm)],[358])).
% 1.35/1.51 tff(360,plain,
% 1.35/1.51 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)))))),
% 1.35/1.51 inference(transitivity,[status(thm)],[359, 357])).
% 1.35/1.51 tff(361,plain,
% 1.35/1.51 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | (v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))),
% 1.35/1.51 inference(quant_inst,[status(thm)],[])).
% 1.35/1.51 tff(362,plain,
% 1.35/1.51 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(k1_realset1(C, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_1(k1_realset1(C, B))) | (~m2_relset_1(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | r1_lattice2(B, k1_realset1(C, B), k1_realset1(D, B)) | (~v1_funct_1(k1_realset1(D, B))) | (~v1_funct_2(k1_realset1(D, B), k2_zfmisc_1(B, B), B)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)))))) | v1_xboole_0(B!1) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))),
% 1.35/1.51 inference(modus_ponens,[status(thm)],[361, 360])).
% 1.35/1.51 tff(363,plain,
% 1.35/1.51 (![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))),
% 1.35/1.51 inference(unit_resolution,[status(thm)],[362, 121, 356, 45])).
% 1.35/1.51 tff(364,plain,
% 1.35/1.51 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(365,plain,
% 1.35/1.52 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(366,plain,
% 1.35/1.52 (^[D: $i] : rewrite(((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))) <=> ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(bind,[status(th)],[])).
% 1.35/1.52 tff(367,plain,
% 1.35/1.52 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.35/1.52 inference(quant_intro,[status(thm)],[366])).
% 1.35/1.52 tff(368,plain,
% 1.35/1.52 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[367])).
% 1.35/1.52 tff(369,plain,
% 1.35/1.52 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[368, 365])).
% 1.35/1.52 tff(370,plain,
% 1.35/1.52 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))))),
% 1.35/1.52 inference(monotonicity,[status(thm)],[369])).
% 1.35/1.52 tff(371,plain,
% 1.35/1.52 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(transitivity,[status(thm)],[370, 364])).
% 1.35/1.52 tff(372,plain,
% 1.35/1.52 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(373,plain,
% 1.35/1.52 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[372, 371])).
% 1.35/1.52 tff(374,plain,
% 1.35/1.52 (![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[373, 285, 283, 261, 363])).
% 1.35/1.52 tff(375,plain,
% 1.35/1.52 (^[A: $i] : refl((v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 1.35/1.52 inference(bind,[status(th)],[])).
% 1.35/1.52 tff(376,plain,
% 1.35/1.52 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.35/1.52 inference(quant_intro,[status(thm)],[375])).
% 1.35/1.52 tff(377,plain,
% 1.35/1.52 (^[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))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 1.35/1.52 inference(bind,[status(th)],[])).
% 1.35/1.52 tff(378,plain,
% 1.35/1.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.35/1.52 inference(quant_intro,[status(thm)],[377])).
% 1.35/1.52 tff(379,plain,
% 1.35/1.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(380,plain,
% 1.35/1.52 (^[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)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 1.35/1.52 inference(bind,[status(th)],[])).
% 1.35/1.52 tff(381,plain,
% 1.35/1.52 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))),
% 1.35/1.52 inference(quant_intro,[status(thm)],[380])).
% 1.35/1.52 tff(382,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t41_lattice2')).
% 1.35/1.52 tff(383,plain,
% 1.35/1.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[382, 381])).
% 1.35/1.52 tff(384,plain,
% 1.35/1.52 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[383, 379])).
% 1.35/1.52 tff(385,plain,(
% 1.35/1.52 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))),
% 1.35/1.52 inference(skolemize,[status(sab)],[384])).
% 1.35/1.52 tff(386,plain,
% 1.35/1.52 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[385, 378])).
% 1.35/1.52 tff(387,plain,
% 1.35/1.52 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[386, 376])).
% 1.35/1.52 tff(388,plain,
% 1.35/1.52 (((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 1.35/1.52 inference(rewrite,[status(thm)],[])).
% 1.35/1.52 tff(389,plain,
% 1.35/1.52 ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 1.35/1.52 inference(quant_inst,[status(thm)],[])).
% 1.35/1.52 tff(390,plain,
% 1.35/1.52 ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u1_lattices(A), u2_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))),
% 1.35/1.52 inference(modus_ponens,[status(thm)],[389, 388])).
% 1.35/1.52 tff(391,plain,
% 1.35/1.52 (r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 1.35/1.52 inference(unit_resolution,[status(thm)],[390, 34, 33, 32, 387])).
% 1.35/1.52 tff(392,plain,
% 1.35/1.52 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(393,plain,
% 1.35/1.53 (((~v1_funct_1(u2_lattices(A!0))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) <=> ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 1.35/1.53 inference(rewrite,[status(thm)],[])).
% 1.35/1.53 tff(394,plain,
% 1.35/1.53 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[393])).
% 1.37/1.53 tff(395,plain,
% 1.37/1.53 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 1.37/1.53 inference(transitivity,[status(thm)],[394, 392])).
% 1.37/1.53 tff(396,plain,
% 1.37/1.53 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))),
% 1.37/1.53 inference(quant_inst,[status(thm)],[])).
% 1.37/1.53 tff(397,plain,
% 1.37/1.53 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 1.37/1.53 inference(modus_ponens,[status(thm)],[396, 395])).
% 1.37/1.53 tff(398,plain,
% 1.37/1.53 (r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))),
% 1.37/1.53 inference(unit_resolution,[status(thm)],[397, 195, 288, 287, 286, 194, 193, 391, 192, 190, 148, 374])).
% 1.37/1.53 tff(399,plain,
% 1.37/1.53 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(400,plain,
% 1.37/1.53 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.53 inference(rewrite,[status(thm)],[])).
% 1.37/1.53 tff(401,plain,
% 1.37/1.53 (^[D: $i] : rewrite(((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))) <=> ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.53 inference(bind,[status(th)],[])).
% 1.37/1.53 tff(402,plain,
% 1.37/1.53 (![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))) <=> ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.37/1.53 inference(quant_intro,[status(thm)],[401])).
% 1.37/1.53 tff(403,plain,
% 1.37/1.53 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.53 inference(monotonicity,[status(thm)],[402])).
% 1.37/1.53 tff(404,plain,
% 1.37/1.53 (((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) <=> ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.54 inference(transitivity,[status(thm)],[403, 400])).
% 1.37/1.54 tff(405,plain,
% 1.37/1.54 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[404])).
% 1.37/1.54 tff(406,plain,
% 1.37/1.54 (((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))) <=> ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.54 inference(transitivity,[status(thm)],[405, 399])).
% 1.37/1.54 tff(407,plain,
% 1.37/1.54 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | ((~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1))))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(408,plain,
% 1.37/1.54 ((~![C: $i] : ((~v1_funct_1(C)) | (~v1_funct_2(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(C, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~r1_lattice2(u1_struct_0(A!0), C, D)) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(k1_realset1(C, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(C, B!1))) | r1_lattice2(B!1, k1_realset1(C, B!1), k1_realset1(D, B!1))))) | (~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))) | ![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[407, 406])).
% 1.37/1.54 tff(409,plain,
% 1.37/1.54 (![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[408, 192, 190, 148, 363])).
% 1.37/1.54 tff(410,plain,
% 1.37/1.54 (^[A: $i] : refl((v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(411,plain,
% 1.37/1.54 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[410])).
% 1.37/1.54 tff(412,plain,
% 1.37/1.54 (^[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))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(413,plain,
% 1.37/1.54 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[412])).
% 1.37/1.54 tff(414,plain,
% 1.37/1.54 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(415,plain,
% 1.37/1.54 (^[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)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))),
% 1.37/1.54 inference(bind,[status(th)],[])).
% 1.37/1.54 tff(416,plain,
% 1.37/1.54 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))),
% 1.37/1.54 inference(quant_intro,[status(thm)],[415])).
% 1.37/1.54 tff(417,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_lattice2')).
% 1.37/1.54 tff(418,plain,
% 1.37/1.54 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[417, 416])).
% 1.37/1.54 tff(419,plain,
% 1.37/1.54 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[418, 414])).
% 1.37/1.54 tff(420,plain,(
% 1.37/1.54 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))),
% 1.37/1.54 inference(skolemize,[status(sab)],[419])).
% 1.37/1.54 tff(421,plain,
% 1.37/1.54 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[420, 413])).
% 1.37/1.54 tff(422,plain,
% 1.37/1.54 (![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[421, 411])).
% 1.37/1.54 tff(423,plain,
% 1.37/1.54 (((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(424,plain,
% 1.37/1.54 ((v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(425,plain,
% 1.37/1.54 (((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[424])).
% 1.37/1.54 tff(426,plain,
% 1.37/1.54 (((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 1.37/1.54 inference(transitivity,[status(thm)],[425, 423])).
% 1.37/1.54 tff(427,plain,
% 1.37/1.54 ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 1.37/1.54 inference(quant_inst,[status(thm)],[])).
% 1.37/1.54 tff(428,plain,
% 1.37/1.54 ((~![A: $i] : (v3_struct_0(A) | r1_lattice2(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 1.37/1.54 inference(modus_ponens,[status(thm)],[427, 426])).
% 1.37/1.54 tff(429,plain,
% 1.37/1.54 (r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 1.37/1.54 inference(unit_resolution,[status(thm)],[428, 34, 33, 32, 422])).
% 1.37/1.54 tff(430,plain,
% 1.37/1.54 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(431,plain,
% 1.37/1.54 (((~v1_funct_1(u1_lattices(A!0))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) <=> ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 1.37/1.54 inference(rewrite,[status(thm)],[])).
% 1.37/1.54 tff(432,plain,
% 1.37/1.54 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))))),
% 1.37/1.54 inference(monotonicity,[status(thm)],[431])).
% 1.37/1.54 tff(433,plain,
% 1.37/1.54 (((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)))) <=> ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 1.37/1.55 inference(transitivity,[status(thm)],[432, 430])).
% 1.37/1.55 tff(434,plain,
% 1.37/1.55 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | ((~v1_funct_1(u1_lattices(A!0))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)))),
% 1.37/1.55 inference(quant_inst,[status(thm)],[])).
% 1.37/1.55 tff(435,plain,
% 1.37/1.55 ((~![D: $i] : ((~v1_funct_1(D)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_2(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(D, k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(D, B!1))) | (~v1_funct_2(k1_realset1(D, B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), D)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(D, B!1)))) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~v1_funct_1(k1_realset1(u2_lattices(A!0), B!1))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B!1), k2_zfmisc_1(B!1, B!1), B!1)) | (~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))) | (~r1_lattice2(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[434, 433])).
% 1.37/1.55 tff(436,plain,
% 1.37/1.55 (r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[435, 195, 288, 287, 286, 194, 193, 429, 285, 283, 261, 409])).
% 1.37/1.55 tff(437,plain,
% 1.37/1.55 ((~(~((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))))) <=> ((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(438,plain,
% 1.37/1.55 ((v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))) <=> (~((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))))),
% 1.37/1.55 inference(rewrite,[status(thm)],[])).
% 1.37/1.55 tff(439,plain,
% 1.37/1.55 ((~(v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))) <=> (~(~((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))))))),
% 1.37/1.55 inference(monotonicity,[status(thm)],[438])).
% 1.37/1.55 tff(440,plain,
% 1.37/1.55 ((~(v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))) <=> ((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1))))),
% 1.37/1.55 inference(transitivity,[status(thm)],[439, 437])).
% 1.37/1.55 tff(441,plain,
% 1.37/1.55 (~(v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1) & v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1) & r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1)) & r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))),
% 1.37/1.55 inference(or_elim,[status(thm)],[39])).
% 1.37/1.55 tff(442,plain,
% 1.37/1.55 ((~v1_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u2_lattices(A!0), B!1), B!1)) | (~v1_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~v2_binop_1(k1_realset1(u1_lattices(A!0), B!1), B!1)) | (~r1_lattice2(B!1, k1_realset1(u2_lattices(A!0), B!1), k1_realset1(u1_lattices(A!0), B!1))) | (~r1_lattice2(B!1, k1_realset1(u1_lattices(A!0), B!1), k1_realset1(u2_lattices(A!0), B!1)))),
% 1.37/1.55 inference(modus_ponens,[status(thm)],[441, 440])).
% 1.37/1.55 tff(443,plain,
% 1.37/1.55 ($false),
% 1.37/1.55 inference(unit_resolution,[status(thm)],[442, 436, 398, 332, 302, 239, 209])).
% 1.37/1.55 % SZS output end Proof
% 1.37/1.55 % E exiting
%------------------------------------------------------------------------------