%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT332+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:14:23 AM UTC 2025
% Result : Theorem 10.67s 10.85s
% Output : Proof 10.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.15 % Problem : LAT332+1 : TPTP v9.0.0. Released v3.4.0.
% 0.04/0.15 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n016.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu Jun 19 20:22:32 EDT 2025
% 0.14/0.36 % CPUTime :
% 10.67/10.85 % SZS status Theorem
% 10.67/10.85 % SZS output start Proof
% 10.67/10.85 tff(g3_lattices_type, type, (
% 10.67/10.85 g3_lattices: ( $i * $i * $i ) > $i)).
% 10.67/10.85 tff(u1_lattices_type, type, (
% 10.67/10.85 u1_lattices: $i > $i)).
% 10.67/10.85 tff(tptp_fun_A_0_type, type, (
% 10.67/10.85 tptp_fun_A_0: $i)).
% 10.67/10.85 tff(u2_lattices_type, type, (
% 10.67/10.85 u2_lattices: $i > $i)).
% 10.67/10.85 tff(u1_struct_0_type, type, (
% 10.67/10.85 u1_struct_0: $i > $i)).
% 10.67/10.85 tff(k23_filter_2_type, type, (
% 10.67/10.85 k23_filter_2: ( $i * $i ) > $i)).
% 10.67/10.85 tff(k17_filter_2_type, type, (
% 10.67/10.85 k17_filter_2: $i > $i)).
% 10.67/10.85 tff(k1_filter_2_type, type, (
% 10.67/10.85 k1_filter_2: $i > $i)).
% 10.67/10.85 tff(v10_lattices_type, type, (
% 10.67/10.85 v10_lattices: $i > $o)).
% 10.67/10.85 tff(l3_lattices_type, type, (
% 10.67/10.85 l3_lattices: $i > $o)).
% 10.67/10.85 tff(v3_struct_0_type, type, (
% 10.67/10.85 v3_struct_0: $i > $o)).
% 10.67/10.85 tff(k1_filter_0_type, type, (
% 10.67/10.85 k1_filter_0: $i > $i)).
% 10.67/10.85 tff(k1_realset1_type, type, (
% 10.67/10.85 k1_realset1: ( $i * $i ) > $i)).
% 10.67/10.85 tff(k7_relat_1_type, type, (
% 10.67/10.85 k7_relat_1: ( $i * $i ) > $i)).
% 10.67/10.85 tff(k2_zfmisc_1_type, type, (
% 10.67/10.85 k2_zfmisc_1: ( $i * $i ) > $i)).
% 10.67/10.85 tff(v1_relat_1_type, type, (
% 10.67/10.85 v1_relat_1: $i > $o)).
% 10.67/10.85 tff(v1_binop_1_type, type, (
% 10.67/10.85 v1_binop_1: ( $i * $i ) > $o)).
% 10.67/10.85 tff(v1_partfun1_type, type, (
% 10.67/10.85 v1_partfun1: ( $i * $i * $i ) > $o)).
% 10.67/10.85 tff(v1_funct_2_type, type, (
% 10.67/10.85 v1_funct_2: ( $i * $i * $i ) > $o)).
% 10.67/10.85 tff(v1_funct_1_type, type, (
% 10.67/10.85 v1_funct_1: $i > $o)).
% 10.67/10.85 tff(l1_lattices_type, type, (
% 10.67/10.85 l1_lattices: $i > $o)).
% 10.67/10.85 tff(l2_lattices_type, type, (
% 10.67/10.85 l2_lattices: $i > $o)).
% 10.67/10.85 tff(v6_lattices_type, type, (
% 10.67/10.85 v6_lattices: $i > $o)).
% 10.67/10.85 tff(v9_lattices_type, type, (
% 10.67/10.85 v9_lattices: $i > $o)).
% 10.67/10.85 tff(v8_lattices_type, type, (
% 10.67/10.85 v8_lattices: $i > $o)).
% 10.67/10.85 tff(v7_lattices_type, type, (
% 10.67/10.85 v7_lattices: $i > $o)).
% 10.67/10.85 tff(v5_lattices_type, type, (
% 10.67/10.85 v5_lattices: $i > $o)).
% 10.67/10.85 tff(v4_lattices_type, type, (
% 10.67/10.85 v4_lattices: $i > $o)).
% 10.67/10.85 tff(r1_tarski_type, type, (
% 10.67/10.85 r1_tarski: ( $i * $i ) > $o)).
% 10.67/10.85 tff(k1_relat_1_type, type, (
% 10.67/10.85 k1_relat_1: $i > $i)).
% 10.67/10.85 tff(m1_subset_1_type, type, (
% 10.67/10.85 m1_subset_1: ( $i * $i ) > $o)).
% 10.67/10.85 tff(k1_zfmisc_1_type, type, (
% 10.67/10.85 k1_zfmisc_1: $i > $i)).
% 10.67/10.85 tff(k4_relset_1_type, type, (
% 10.67/10.85 k4_relset_1: ( $i * $i * $i ) > $i)).
% 10.67/10.85 tff(m1_relset_1_type, type, (
% 10.67/10.85 m1_relset_1: ( $i * $i * $i ) > $o)).
% 10.67/10.85 tff(m2_relset_1_type, type, (
% 10.67/10.85 m2_relset_1: ( $i * $i * $i ) > $o)).
% 10.67/10.85 tff(m2_nat_lat_type, type, (
% 10.67/10.85 m2_nat_lat: ( $i * $i ) > $o)).
% 10.67/10.85 tff(m2_lattice4_type, type, (
% 10.67/10.85 m2_lattice4: ( $i * $i ) > $o)).
% 10.67/10.85 tff(v1_xboole_0_type, type, (
% 10.67/10.85 v1_xboole_0: $i > $o)).
% 10.67/10.85 tff(m1_filter_2_type, type, (
% 10.67/10.85 m1_filter_2: ( $i * $i ) > $o)).
% 10.67/10.85 tff(l1_struct_0_type, type, (
% 10.67/10.85 l1_struct_0: $i > $o)).
% 10.67/10.85 tff(1,plain,
% 10.67/10.85 (^[A: $i] : refl((v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(2,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[1])).
% 10.67/10.85 tff(3,plain,
% 10.67/10.85 (^[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))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(4,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[3])).
% 10.67/10.85 tff(5,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(6,plain,
% 10.67/10.85 (^[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)) => (k17_filter_2(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(7,plain,
% 10.67/10.85 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[6])).
% 10.67/10.85 tff(8,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_filter_2')).
% 10.67/10.85 tff(9,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[8, 7])).
% 10.67/10.85 tff(10,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[9, 5])).
% 10.67/10.85 tff(11,plain,(
% 10.67/10.85 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(skolemize,[status(sab)],[10])).
% 10.67/10.85 tff(12,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[11, 4])).
% 10.67/10.85 tff(13,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[12, 2])).
% 10.67/10.85 tff(14,plain,
% 10.67/10.85 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(15,plain,
% 10.67/10.85 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(16,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t72_filter_2')).
% 10.67/10.85 tff(17,plain,
% 10.67/10.85 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[16, 15])).
% 10.67/10.85 tff(18,plain,
% 10.67/10.85 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[17, 14])).
% 10.67/10.85 tff(19,plain,
% 10.67/10.85 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[18, 14])).
% 10.67/10.85 tff(20,plain,
% 10.67/10.85 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((k23_filter_2(A, k17_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) & (k23_filter_2(A, k1_filter_2(A)) = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[19, 14])).
% 10.67/10.85 tff(21,plain,(
% 10.67/10.85 ~((~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))) | ((k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) & (k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))))),
% 10.67/10.85 inference(skolemize,[status(sab)],[20])).
% 10.67/10.85 tff(22,plain,
% 10.67/10.85 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 10.67/10.85 inference(or_elim,[status(thm)],[21])).
% 10.67/10.85 tff(23,plain,
% 10.67/10.85 (l3_lattices(A!0)),
% 10.67/10.85 inference(and_elim,[status(thm)],[22])).
% 10.67/10.85 tff(24,plain,
% 10.67/10.85 (v10_lattices(A!0)),
% 10.67/10.85 inference(and_elim,[status(thm)],[22])).
% 10.67/10.85 tff(25,plain,
% 10.67/10.85 (~v3_struct_0(A!0)),
% 10.67/10.85 inference(and_elim,[status(thm)],[22])).
% 10.67/10.85 tff(26,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(27,plain,
% 10.67/10.85 ((v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(28,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))))),
% 10.67/10.85 inference(monotonicity,[status(thm)],[27])).
% 10.67/10.85 tff(29,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(transitivity,[status(thm)],[28, 26])).
% 10.67/10.85 tff(30,plain,
% 10.67/10.85 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 10.67/10.85 inference(quant_inst,[status(thm)],[])).
% 10.67/10.85 tff(31,plain,
% 10.67/10.85 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[30, 29])).
% 10.67/10.85 tff(32,plain,
% 10.67/10.85 (k17_filter_2(A!0) = u1_struct_0(A!0)),
% 10.67/10.85 inference(unit_resolution,[status(thm)],[31, 25, 24, 23, 13])).
% 10.67/10.85 tff(33,plain,
% 10.67/10.85 (u1_struct_0(A!0) = k17_filter_2(A!0)),
% 10.67/10.85 inference(symmetry,[status(thm)],[32])).
% 10.67/10.85 tff(34,plain,
% 10.67/10.85 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(35,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[34])).
% 10.67/10.85 tff(36,plain,
% 10.67/10.85 (^[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))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(37,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[36])).
% 10.67/10.85 tff(38,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(39,plain,
% 10.67/10.85 (^[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)) => (k1_filter_0(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(40,plain,
% 10.67/10.85 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[39])).
% 10.67/10.85 tff(41,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_filter_0')).
% 10.67/10.85 tff(42,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[41, 40])).
% 10.67/10.85 tff(43,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[42, 38])).
% 10.67/10.85 tff(44,plain,(
% 10.67/10.85 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 10.67/10.85 inference(skolemize,[status(sab)],[43])).
% 10.67/10.85 tff(45,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[44, 37])).
% 10.67/10.85 tff(46,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[45, 35])).
% 10.67/10.85 tff(47,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(48,plain,
% 10.67/10.85 ((v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(49,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))))),
% 10.67/10.85 inference(monotonicity,[status(thm)],[48])).
% 10.67/10.85 tff(50,plain,
% 10.67/10.85 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 10.67/10.85 inference(transitivity,[status(thm)],[49, 47])).
% 10.67/10.85 tff(51,plain,
% 10.67/10.85 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 10.67/10.85 inference(quant_inst,[status(thm)],[])).
% 10.67/10.85 tff(52,plain,
% 10.67/10.85 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[51, 50])).
% 10.67/10.85 tff(53,plain,
% 10.67/10.85 (k1_filter_0(A!0) = u1_struct_0(A!0)),
% 10.67/10.85 inference(unit_resolution,[status(thm)],[52, 25, 24, 23, 46])).
% 10.67/10.85 tff(54,plain,
% 10.67/10.85 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(55,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[54])).
% 10.67/10.85 tff(56,plain,
% 10.67/10.85 (^[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))) | (k1_filter_2(A) = k1_filter_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A))) <=> (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A))) <=> (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(57,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[56])).
% 10.67/10.85 tff(58,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))),
% 10.67/10.85 inference(rewrite,[status(thm)],[])).
% 10.67/10.85 tff(59,plain,
% 10.67/10.85 (^[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)) => (k1_filter_2(A) = k1_filter_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_2(A) = k1_filter_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_2(A) = k1_filter_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_2(A) = k1_filter_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))))),
% 10.67/10.85 inference(bind,[status(th)],[])).
% 10.67/10.85 tff(60,plain,
% 10.67/10.85 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_2(A) = k1_filter_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))),
% 10.67/10.85 inference(quant_intro,[status(thm)],[59])).
% 10.67/10.85 tff(61,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_2(A) = k1_filter_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k1_filter_2')).
% 10.67/10.85 tff(62,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[61, 60])).
% 10.67/10.85 tff(63,plain,
% 10.67/10.85 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))),
% 10.67/10.85 inference(modus_ponens,[status(thm)],[62, 58])).
% 10.67/10.85 tff(64,plain,(
% 10.67/10.85 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_2(A) = k1_filter_0(A)))),
% 10.67/10.85 inference(skolemize,[status(sab)],[63])).
% 10.67/10.85 tff(65,plain,
% 10.67/10.85 (![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[64, 57])).
% 10.67/10.86 tff(66,plain,
% 10.67/10.86 (![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[65, 55])).
% 10.67/10.86 tff(67,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0)))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(68,plain,
% 10.67/10.86 ((v3_struct_0(A!0) | (k1_filter_2(A!0) = k1_filter_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0)))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(69,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_2(A!0) = k1_filter_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0))))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[68])).
% 10.67/10.86 tff(70,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_2(A!0) = k1_filter_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0)))),
% 10.67/10.86 inference(transitivity,[status(thm)],[69, 67])).
% 10.67/10.86 tff(71,plain,
% 10.67/10.86 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_2(A!0) = k1_filter_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(72,plain,
% 10.67/10.86 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_2(A) = k1_filter_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k1_filter_2(A!0) = k1_filter_0(A!0))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[71, 70])).
% 10.67/10.86 tff(73,plain,
% 10.67/10.86 (k1_filter_2(A!0) = k1_filter_0(A!0)),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[72, 25, 24, 23, 66])).
% 10.67/10.86 tff(74,plain,
% 10.67/10.86 (k1_filter_2(A!0) = k17_filter_2(A!0)),
% 10.67/10.86 inference(transitivity,[status(thm)],[73, 53, 33])).
% 10.67/10.86 tff(75,plain,
% 10.67/10.86 (k23_filter_2(A!0, k1_filter_2(A!0)) = k23_filter_2(A!0, k17_filter_2(A!0))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[74])).
% 10.67/10.86 tff(76,plain,
% 10.67/10.86 ((k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[75])).
% 10.67/10.86 tff(77,plain,
% 10.67/10.86 ((~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) <=> (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[76])).
% 10.67/10.86 tff(78,plain,
% 10.67/10.86 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(79,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[78])).
% 10.67/10.86 tff(80,plain,
% 10.67/10.86 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(81,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[80])).
% 10.67/10.86 tff(82,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(83,plain,
% 10.67/10.86 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(84,plain,
% 10.67/10.86 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[83])).
% 10.67/10.86 tff(85,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 10.67/10.86 tff(86,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[85, 84])).
% 10.67/10.86 tff(87,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[86, 82])).
% 10.67/10.86 tff(88,plain,(
% 10.67/10.86 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 10.67/10.86 inference(skolemize,[status(sab)],[87])).
% 10.67/10.86 tff(89,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[88, 81])).
% 10.67/10.86 tff(90,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[89, 79])).
% 10.67/10.86 tff(91,plain,
% 10.67/10.86 (((~![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)))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(92,plain,
% 10.67/10.86 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(93,plain,
% 10.67/10.86 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[92, 91])).
% 10.67/10.86 tff(94,plain,
% 10.67/10.86 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[93, 23, 90])).
% 10.67/10.86 tff(95,plain,
% 10.67/10.86 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 10.67/10.86 inference(tautology,[status(thm)],[])).
% 10.67/10.86 tff(96,plain,
% 10.67/10.86 (l1_lattices(A!0)),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[95, 94])).
% 10.67/10.86 tff(97,plain,
% 10.67/10.86 (^[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))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(98,plain,
% 10.67/10.86 (![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)))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[97])).
% 10.67/10.86 tff(99,plain,
% 10.67/10.86 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(100,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[99])).
% 10.67/10.86 tff(101,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(102,plain,
% 10.67/10.86 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(103,plain,
% 10.67/10.86 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[102])).
% 10.67/10.86 tff(104,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')).
% 10.67/10.86 tff(105,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[104, 103])).
% 10.67/10.86 tff(106,plain,
% 10.67/10.86 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[105, 101])).
% 10.67/10.86 tff(107,plain,(
% 10.67/10.86 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 10.67/10.86 inference(skolemize,[status(sab)],[106])).
% 10.67/10.86 tff(108,plain,
% 10.67/10.86 (![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)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[107, 100])).
% 10.67/10.86 tff(109,plain,
% 10.67/10.86 (![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)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[108, 98])).
% 10.67/10.86 tff(110,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(111,plain,
% 10.67/10.86 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(112,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[111])).
% 10.67/10.86 tff(113,plain,
% 10.67/10.86 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 10.67/10.86 inference(transitivity,[status(thm)],[112, 110])).
% 10.67/10.86 tff(114,plain,
% 10.67/10.86 ((~![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)))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(115,plain,
% 10.67/10.86 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[114, 113])).
% 10.67/10.86 tff(116,plain,
% 10.67/10.86 (~(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)))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[115, 25, 24, 23, 109])).
% 10.67/10.86 tff(117,plain,
% 10.67/10.86 ((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)),
% 10.67/10.86 inference(tautology,[status(thm)],[])).
% 10.67/10.86 tff(118,plain,
% 10.67/10.86 (v6_lattices(A!0)),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[117, 116])).
% 10.67/10.86 tff(119,plain,
% 10.67/10.86 (^[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)))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(120,plain,
% 10.67/10.86 (![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))))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[119])).
% 10.67/10.86 tff(121,plain,
% 10.67/10.86 (^[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))))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(122,plain,
% 10.67/10.86 (![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))))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[121])).
% 10.67/10.86 tff(123,plain,
% 10.67/10.86 (![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))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(124,plain,
% 10.67/10.86 (^[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))))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(125,plain,
% 10.67/10.86 (![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))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[124])).
% 10.67/10.86 tff(126,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')).
% 10.67/10.86 tff(127,plain,
% 10.67/10.86 (![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))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[126, 125])).
% 10.67/10.86 tff(128,plain,
% 10.67/10.86 (![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))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[127, 123])).
% 10.67/10.86 tff(129,plain,(
% 10.67/10.86 ![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))))),
% 10.67/10.86 inference(skolemize,[status(sab)],[128])).
% 10.67/10.86 tff(130,plain,
% 10.67/10.86 (![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))))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[129, 122])).
% 10.67/10.86 tff(131,plain,
% 10.67/10.86 (![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))))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[130, 120])).
% 10.67/10.86 tff(132,plain,
% 10.67/10.86 (((~![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))))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(133,plain,
% 10.67/10.86 ((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))))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(134,plain,
% 10.67/10.86 (((~![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)))))))),
% 10.67/10.86 inference(monotonicity,[status(thm)],[133])).
% 10.67/10.86 tff(135,plain,
% 10.67/10.86 (((~![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))))))),
% 10.67/10.86 inference(transitivity,[status(thm)],[134, 132])).
% 10.67/10.86 tff(136,plain,
% 10.67/10.86 ((~![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))))))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(137,plain,
% 10.67/10.86 ((~![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)))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[136, 135])).
% 10.67/10.86 tff(138,plain,
% 10.67/10.86 ((~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)))))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[137, 25, 131])).
% 10.67/10.86 tff(139,plain,
% 10.67/10.86 (~((~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))))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[138, 118, 96])).
% 10.67/10.86 tff(140,plain,
% 10.67/10.86 (((~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_relat_1(u1_lattices(A!0))),
% 10.67/10.86 inference(tautology,[status(thm)],[])).
% 10.67/10.86 tff(141,plain,
% 10.67/10.86 (v1_relat_1(u1_lattices(A!0))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[140, 139])).
% 10.67/10.86 tff(142,plain,
% 10.67/10.86 (^[A: $i] : refl(((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(143,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[142])).
% 10.67/10.86 tff(144,plain,
% 10.67/10.86 (^[A: $i] : rewrite(((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(145,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[144])).
% 10.67/10.86 tff(146,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(transitivity,[status(thm)],[145, 143])).
% 10.67/10.86 tff(147,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(148,plain,
% 10.67/10.86 (^[A: $i] : rewrite((v1_relat_1(A) => ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(149,plain,
% 10.67/10.86 (![A: $i] : (v1_relat_1(A) => ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B)))) <=> ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[148])).
% 10.67/10.86 tff(150,axiom,(![A: $i] : (v1_relat_1(A) => ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d3_realset1')).
% 10.67/10.86 tff(151,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[150, 149])).
% 10.67/10.86 tff(152,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[151, 147])).
% 10.67/10.86 tff(153,plain,(
% 10.67/10.86 ![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(skolemize,[status(sab)],[152])).
% 10.67/10.86 tff(154,plain,
% 10.67/10.86 (![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[153, 146])).
% 10.67/10.86 tff(155,plain,
% 10.67/10.86 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | ((~v1_relat_1(u1_lattices(A!0))) | ![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | (~v1_relat_1(u1_lattices(A!0))) | ![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(156,plain,
% 10.67/10.86 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | ((~v1_relat_1(u1_lattices(A!0))) | ![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B))))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(157,plain,
% 10.67/10.86 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | (~v1_relat_1(u1_lattices(A!0))) | ![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B)))),
% 10.67/10.86 inference(modus_ponens,[status(thm)],[156, 155])).
% 10.67/10.86 tff(158,plain,
% 10.67/10.86 (![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B)))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[157, 154, 141])).
% 10.67/10.86 tff(159,plain,
% 10.67/10.86 ((~![B: $i] : (k1_realset1(u1_lattices(A!0), B) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(B, B)))) | (k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.86 inference(quant_inst,[status(thm)],[])).
% 10.67/10.86 tff(160,plain,
% 10.67/10.86 (k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.86 inference(unit_resolution,[status(thm)],[159, 158])).
% 10.67/10.86 tff(161,plain,
% 10.67/10.86 (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))),
% 10.67/10.86 inference(symmetry,[status(thm)],[160])).
% 10.67/10.86 tff(162,plain,
% 10.67/10.86 (^[A: $i, B: $i] : refl((m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)))),
% 10.67/10.86 inference(bind,[status(th)],[])).
% 10.67/10.86 tff(163,plain,
% 10.67/10.86 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 10.67/10.86 inference(quant_intro,[status(thm)],[162])).
% 10.67/10.86 tff(164,plain,
% 10.67/10.86 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B)) <=> ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 10.67/10.86 inference(rewrite,[status(thm)],[])).
% 10.67/10.86 tff(165,axiom,(![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t3_subset')).
% 10.67/10.87 tff(166,plain,
% 10.67/10.87 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[165, 164])).
% 10.67/10.87 tff(167,plain,(
% 10.67/10.87 ![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 10.67/10.87 inference(skolemize,[status(sab)],[166])).
% 10.67/10.87 tff(168,plain,
% 10.67/10.87 (![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[167, 163])).
% 10.67/10.87 tff(169,plain,
% 10.67/10.87 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(170,plain,
% 10.67/10.87 (m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[169, 168])).
% 10.67/10.87 tff(171,plain,
% 10.67/10.87 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(172,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[171])).
% 10.67/10.87 tff(173,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(174,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 10.67/10.87 tff(175,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[174, 173])).
% 10.67/10.87 tff(176,plain,(
% 10.67/10.87 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 10.67/10.87 inference(skolemize,[status(sab)],[175])).
% 10.67/10.87 tff(177,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[176, 172])).
% 10.67/10.87 tff(178,plain,
% 10.67/10.87 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(179,plain,
% 10.67/10.87 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[178, 177])).
% 10.67/10.87 tff(180,plain,
% 10.67/10.87 (^[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)))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(181,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[180])).
% 10.67/10.87 tff(182,plain,
% 10.67/10.87 (^[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)))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(183,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[182])).
% 10.67/10.87 tff(184,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(185,plain,
% 10.67/10.87 (^[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))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(186,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[185])).
% 10.67/10.87 tff(187,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')).
% 10.67/10.87 tff(188,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[187, 186])).
% 10.67/10.87 tff(189,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[188, 184])).
% 10.67/10.87 tff(190,plain,(
% 10.67/10.87 ![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))))),
% 10.67/10.87 inference(skolemize,[status(sab)],[189])).
% 10.67/10.87 tff(191,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[190, 183])).
% 10.67/10.87 tff(192,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[191, 181])).
% 10.67/10.87 tff(193,plain,
% 10.67/10.87 (((~![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))))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(194,plain,
% 10.67/10.87 ((~![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))))))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(195,plain,
% 10.67/10.87 ((~![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)))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[194, 193])).
% 10.67/10.87 tff(196,plain,
% 10.67/10.87 (~((~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))))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[195, 192, 96])).
% 10.67/10.87 tff(197,plain,
% 10.67/10.87 (((~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))),
% 10.67/10.87 inference(tautology,[status(thm)],[])).
% 10.67/10.87 tff(198,plain,
% 10.67/10.87 (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))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[197, 196])).
% 10.67/10.87 tff(199,plain,
% 10.67/10.87 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.87 inference(tautology,[status(thm)],[])).
% 10.67/10.87 tff(200,plain,
% 10.67/10.87 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[199, 198])).
% 10.67/10.87 tff(201,plain,
% 10.67/10.87 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[200, 179])).
% 10.67/10.87 tff(202,plain,
% 10.67/10.87 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(203,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[202])).
% 10.67/10.87 tff(204,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(205,plain,
% 10.67/10.87 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(206,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[205])).
% 10.67/10.87 tff(207,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => (k4_relset_1(A, B, C) = k1_relat_1(C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_relset_1')).
% 10.67/10.87 tff(208,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[207, 206])).
% 10.67/10.87 tff(209,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[208, 204])).
% 10.67/10.87 tff(210,plain,(
% 10.67/10.87 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(skolemize,[status(sab)],[209])).
% 10.67/10.87 tff(211,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[210, 203])).
% 10.67/10.87 tff(212,plain,
% 10.67/10.87 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)) = k1_relat_1(u1_lattices(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)) = k1_relat_1(u1_lattices(A!0))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(213,plain,
% 10.67/10.87 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)) = k1_relat_1(u1_lattices(A!0))))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(214,plain,
% 10.67/10.87 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)) = k1_relat_1(u1_lattices(A!0)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[213, 212])).
% 10.67/10.87 tff(215,plain,
% 10.67/10.87 (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)) = k1_relat_1(u1_lattices(A!0))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[214, 211, 201])).
% 10.67/10.87 tff(216,plain,
% 10.67/10.87 (k1_relat_1(u1_lattices(A!0)) = k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0))),
% 10.67/10.87 inference(symmetry,[status(thm)],[215])).
% 10.67/10.87 tff(217,plain,
% 10.67/10.87 (m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(monotonicity,[status(thm)],[216])).
% 10.67/10.87 tff(218,plain,
% 10.67/10.87 (m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(symmetry,[status(thm)],[217])).
% 10.67/10.87 tff(219,plain,
% 10.67/10.87 (^[A: $i, B: $i, C: $i] : refl(((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(220,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[219])).
% 10.67/10.87 tff(221,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(222,plain,
% 10.67/10.87 (^[A: $i, B: $i, C: $i] : rewrite((m1_relset_1(C, A, B) => m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(223,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[222])).
% 10.67/10.87 tff(224,axiom,(![A: $i, B: $i, C: $i] : (m1_relset_1(C, A, B) => m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k4_relset_1')).
% 10.67/10.87 tff(225,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[224, 223])).
% 10.67/10.87 tff(226,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[225, 221])).
% 10.67/10.87 tff(227,plain,(
% 10.67/10.87 ![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(skolemize,[status(sab)],[226])).
% 10.67/10.87 tff(228,plain,
% 10.67/10.87 (![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[227, 220])).
% 10.67/10.87 tff(229,plain,
% 10.67/10.87 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(230,plain,
% 10.67/10.87 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(231,plain,
% 10.67/10.87 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[230, 229])).
% 10.67/10.87 tff(232,plain,
% 10.67/10.87 (m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[231, 228, 201])).
% 10.67/10.87 tff(233,plain,
% 10.67/10.87 (m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[232, 218])).
% 10.67/10.87 tff(234,plain,
% 10.67/10.87 ((~(m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) | (~m1_subset_1(k1_relat_1(u1_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) | r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.87 inference(tautology,[status(thm)],[])).
% 10.67/10.87 tff(235,plain,
% 10.67/10.87 (r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[234, 233, 170])).
% 10.67/10.87 tff(236,plain,
% 10.67/10.87 (^[A: $i, B: $i] : refl(((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A))) <=> ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(237,plain,
% 10.67/10.87 (![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A))) <=> ![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[236])).
% 10.67/10.87 tff(238,plain,
% 10.67/10.87 (![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A))) <=> ![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(239,plain,
% 10.67/10.87 (^[A: $i, B: $i] : trans(monotonicity(rewrite((r1_tarski(k1_relat_1(B), A) => (k7_relat_1(B, A) = B)) <=> ((~r1_tarski(k1_relat_1(B), A)) | (k7_relat_1(B, A) = B))), ((v1_relat_1(B) => (r1_tarski(k1_relat_1(B), A) => (k7_relat_1(B, A) = B))) <=> (v1_relat_1(B) => ((~r1_tarski(k1_relat_1(B), A)) | (k7_relat_1(B, A) = B))))), rewrite((v1_relat_1(B) => ((~r1_tarski(k1_relat_1(B), A)) | (k7_relat_1(B, A) = B))) <=> ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))), ((v1_relat_1(B) => (r1_tarski(k1_relat_1(B), A) => (k7_relat_1(B, A) = B))) <=> ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(240,plain,
% 10.67/10.87 (![A: $i, B: $i] : (v1_relat_1(B) => (r1_tarski(k1_relat_1(B), A) => (k7_relat_1(B, A) = B))) <=> ![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[239])).
% 10.67/10.87 tff(241,axiom,(![A: $i, B: $i] : (v1_relat_1(B) => (r1_tarski(k1_relat_1(B), A) => (k7_relat_1(B, A) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t97_relat_1')).
% 10.67/10.87 tff(242,plain,
% 10.67/10.87 (![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[241, 240])).
% 10.67/10.87 tff(243,plain,
% 10.67/10.87 (![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[242, 238])).
% 10.67/10.87 tff(244,plain,(
% 10.67/10.87 ![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(skolemize,[status(sab)],[243])).
% 10.67/10.87 tff(245,plain,
% 10.67/10.87 (![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[244, 237])).
% 10.67/10.87 tff(246,plain,
% 10.67/10.87 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(247,plain,
% 10.67/10.87 (((k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~v1_relat_1(u1_lattices(A!0))) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(248,plain,
% 10.67/10.87 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~v1_relat_1(u1_lattices(A!0))) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 10.67/10.87 inference(monotonicity,[status(thm)],[247])).
% 10.67/10.87 tff(249,plain,
% 10.67/10.87 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~v1_relat_1(u1_lattices(A!0))) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(transitivity,[status(thm)],[248, 246])).
% 10.67/10.87 tff(250,plain,
% 10.67/10.87 ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~v1_relat_1(u1_lattices(A!0))) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.87 inference(quant_inst,[status(thm)],[])).
% 10.67/10.87 tff(251,plain,
% 10.67/10.87 ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u1_lattices(A!0))) | (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[250, 249])).
% 10.67/10.87 tff(252,plain,
% 10.67/10.87 ((k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)) | (~r1_tarski(k1_relat_1(u1_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[251, 245, 141])).
% 10.67/10.87 tff(253,plain,
% 10.67/10.87 (k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u1_lattices(A!0)),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[252, 235])).
% 10.67/10.87 tff(254,plain,
% 10.67/10.87 (u1_lattices(A!0) = k7_relat_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.87 inference(symmetry,[status(thm)],[253])).
% 10.67/10.87 tff(255,plain,
% 10.67/10.87 (u1_lattices(A!0) = k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))),
% 10.67/10.87 inference(transitivity,[status(thm)],[254, 161])).
% 10.67/10.87 tff(256,plain,
% 10.67/10.87 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 10.67/10.87 inference(tautology,[status(thm)],[])).
% 10.67/10.87 tff(257,plain,
% 10.67/10.87 (l2_lattices(A!0)),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[256, 94])).
% 10.67/10.87 tff(258,plain,
% 10.67/10.87 ((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)),
% 10.67/10.87 inference(tautology,[status(thm)],[])).
% 10.67/10.87 tff(259,plain,
% 10.67/10.87 (v4_lattices(A!0)),
% 10.67/10.87 inference(unit_resolution,[status(thm)],[258, 116])).
% 10.67/10.87 tff(260,plain,
% 10.67/10.87 (^[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)))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(261,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[260])).
% 10.67/10.87 tff(262,plain,
% 10.67/10.87 (^[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))))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(263,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[262])).
% 10.67/10.87 tff(264,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(265,plain,
% 10.67/10.87 (^[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))))))),
% 10.67/10.87 inference(bind,[status(th)],[])).
% 10.67/10.87 tff(266,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(quant_intro,[status(thm)],[265])).
% 10.67/10.87 tff(267,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')).
% 10.67/10.87 tff(268,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[267, 266])).
% 10.67/10.87 tff(269,plain,
% 10.67/10.87 (![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))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[268, 264])).
% 10.67/10.87 tff(270,plain,(
% 10.67/10.87 ![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))))),
% 10.67/10.87 inference(skolemize,[status(sab)],[269])).
% 10.67/10.87 tff(271,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[270, 263])).
% 10.67/10.87 tff(272,plain,
% 10.67/10.87 (![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))))))),
% 10.67/10.87 inference(modus_ponens,[status(thm)],[271, 261])).
% 10.67/10.87 tff(273,plain,
% 10.67/10.87 (((~![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))))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(274,plain,
% 10.67/10.87 ((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))))))),
% 10.67/10.87 inference(rewrite,[status(thm)],[])).
% 10.67/10.87 tff(275,plain,
% 10.67/10.87 (((~![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)))))))),
% 10.67/10.87 inference(monotonicity,[status(thm)],[274])).
% 10.67/10.87 tff(276,plain,
% 10.67/10.87 (((~![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))))))),
% 10.67/10.87 inference(transitivity,[status(thm)],[275, 273])).
% 10.67/10.87 tff(277,plain,
% 10.67/10.87 ((~![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))))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(278,plain,
% 10.67/10.88 ((~![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)))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[277, 276])).
% 10.67/10.88 tff(279,plain,
% 10.67/10.88 ((~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)))))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[278, 25, 272])).
% 10.67/10.88 tff(280,plain,
% 10.67/10.88 (~((~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))))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[279, 259, 257])).
% 10.67/10.88 tff(281,plain,
% 10.67/10.88 (((~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_relat_1(u2_lattices(A!0))),
% 10.67/10.88 inference(tautology,[status(thm)],[])).
% 10.67/10.88 tff(282,plain,
% 10.67/10.88 (v1_relat_1(u2_lattices(A!0))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[281, 280])).
% 10.67/10.88 tff(283,plain,
% 10.67/10.88 (((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | ((~v1_relat_1(u2_lattices(A!0))) | ![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B))))) <=> ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | (~v1_relat_1(u2_lattices(A!0))) | ![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(284,plain,
% 10.67/10.88 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | ((~v1_relat_1(u2_lattices(A!0))) | ![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(285,plain,
% 10.67/10.88 ((~![A: $i] : ((~v1_relat_1(A)) | ![B: $i] : (k1_realset1(A, B) = k7_relat_1(A, k2_zfmisc_1(B, B))))) | (~v1_relat_1(u2_lattices(A!0))) | ![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B)))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[284, 283])).
% 10.67/10.88 tff(286,plain,
% 10.67/10.88 (![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B)))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[285, 154, 282])).
% 10.67/10.88 tff(287,plain,
% 10.67/10.88 ((~![B: $i] : (k1_realset1(u2_lattices(A!0), B) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(B, B)))) | (k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(288,plain,
% 10.67/10.88 (k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[287, 286])).
% 10.67/10.88 tff(289,plain,
% 10.67/10.88 (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = k1_realset1(u2_lattices(A!0), u1_struct_0(A!0))),
% 10.67/10.88 inference(symmetry,[status(thm)],[288])).
% 10.67/10.88 tff(290,plain,
% 10.67/10.88 ((~![A: $i, B: $i] : (m1_subset_1(A, k1_zfmisc_1(B)) <=> r1_tarski(A, B))) | (m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(291,plain,
% 10.67/10.88 (m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[290, 168])).
% 10.67/10.88 tff(292,plain,
% 10.67/10.88 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(293,plain,
% 10.67/10.88 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[292, 177])).
% 10.67/10.88 tff(294,plain,
% 10.67/10.88 (^[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)))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(295,plain,
% 10.67/10.88 (![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))))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[294])).
% 10.67/10.88 tff(296,plain,
% 10.67/10.88 (^[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)))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(297,plain,
% 10.67/10.88 (![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))))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[296])).
% 10.67/10.88 tff(298,plain,
% 10.67/10.88 (![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))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(299,plain,
% 10.67/10.88 (^[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))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(300,plain,
% 10.67/10.88 (![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))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[299])).
% 10.67/10.88 tff(301,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')).
% 10.67/10.88 tff(302,plain,
% 10.67/10.88 (![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))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[301, 300])).
% 10.67/10.88 tff(303,plain,
% 10.67/10.88 (![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))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[302, 298])).
% 10.67/10.88 tff(304,plain,(
% 10.67/10.88 ![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))))),
% 10.67/10.88 inference(skolemize,[status(sab)],[303])).
% 10.67/10.88 tff(305,plain,
% 10.67/10.88 (![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))))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[304, 297])).
% 10.67/10.88 tff(306,plain,
% 10.67/10.88 (![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))))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[305, 295])).
% 10.67/10.88 tff(307,plain,
% 10.67/10.88 (((~![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))))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(308,plain,
% 10.67/10.88 ((~![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))))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(309,plain,
% 10.67/10.88 ((~![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)))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[308, 307])).
% 10.67/10.88 tff(310,plain,
% 10.67/10.88 (~((~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))))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[309, 306, 257])).
% 10.67/10.88 tff(311,plain,
% 10.67/10.88 (((~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))),
% 10.67/10.88 inference(tautology,[status(thm)],[])).
% 10.67/10.88 tff(312,plain,
% 10.67/10.88 (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))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[311, 310])).
% 10.67/10.88 tff(313,plain,
% 10.67/10.88 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.88 inference(tautology,[status(thm)],[])).
% 10.67/10.88 tff(314,plain,
% 10.67/10.88 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[313, 312])).
% 10.67/10.88 tff(315,plain,
% 10.67/10.88 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[314, 293])).
% 10.67/10.88 tff(316,plain,
% 10.67/10.88 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)) = k1_relat_1(u2_lattices(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)) = k1_relat_1(u2_lattices(A!0))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(317,plain,
% 10.67/10.88 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)) = k1_relat_1(u2_lattices(A!0))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(318,plain,
% 10.67/10.88 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | (k4_relset_1(A, B, C) = k1_relat_1(C)))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)) = k1_relat_1(u2_lattices(A!0)))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[317, 316])).
% 10.67/10.88 tff(319,plain,
% 10.67/10.88 (k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)) = k1_relat_1(u2_lattices(A!0))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[318, 211, 315])).
% 10.67/10.88 tff(320,plain,
% 10.67/10.88 (k1_relat_1(u2_lattices(A!0)) = k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0))),
% 10.67/10.88 inference(symmetry,[status(thm)],[319])).
% 10.67/10.88 tff(321,plain,
% 10.67/10.88 (m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(monotonicity,[status(thm)],[320])).
% 10.67/10.88 tff(322,plain,
% 10.67/10.88 (m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(symmetry,[status(thm)],[321])).
% 10.67/10.88 tff(323,plain,
% 10.67/10.88 (((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(324,plain,
% 10.67/10.88 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(325,plain,
% 10.67/10.88 ((~![A: $i, B: $i, C: $i] : ((~m1_relset_1(C, A, B)) | m1_subset_1(k4_relset_1(A, B, C), k1_zfmisc_1(A)))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[324, 323])).
% 10.67/10.88 tff(326,plain,
% 10.67/10.88 (m1_subset_1(k4_relset_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0), u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[325, 228, 315])).
% 10.67/10.88 tff(327,plain,
% 10.67/10.88 (m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[326, 322])).
% 10.67/10.88 tff(328,plain,
% 10.67/10.88 ((~(m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))) <=> r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) | (~m1_subset_1(k1_relat_1(u2_lattices(A!0)), k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) | r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(tautology,[status(thm)],[])).
% 10.67/10.88 tff(329,plain,
% 10.67/10.88 (r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[328, 327, 291])).
% 10.67/10.88 tff(330,plain,
% 10.67/10.88 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(331,plain,
% 10.67/10.88 (((k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~v1_relat_1(u2_lattices(A!0))) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))) <=> ((~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(332,plain,
% 10.67/10.88 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~v1_relat_1(u2_lattices(A!0))) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))))),
% 10.67/10.88 inference(monotonicity,[status(thm)],[331])).
% 10.67/10.88 tff(333,plain,
% 10.67/10.88 (((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~v1_relat_1(u2_lattices(A!0))) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(transitivity,[status(thm)],[332, 330])).
% 10.67/10.88 tff(334,plain,
% 10.67/10.88 ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | ((k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~v1_relat_1(u2_lattices(A!0))) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(335,plain,
% 10.67/10.88 ((~![A: $i, B: $i] : ((k7_relat_1(B, A) = B) | (~v1_relat_1(B)) | (~r1_tarski(k1_relat_1(B), A)))) | (~v1_relat_1(u2_lattices(A!0))) | (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[334, 333])).
% 10.67/10.88 tff(336,plain,
% 10.67/10.88 ((k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)) | (~r1_tarski(k1_relat_1(u2_lattices(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))))),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[335, 245, 282])).
% 10.67/10.88 tff(337,plain,
% 10.67/10.88 (k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0))) = u2_lattices(A!0)),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[336, 329])).
% 10.67/10.88 tff(338,plain,
% 10.67/10.88 (u2_lattices(A!0) = k7_relat_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(symmetry,[status(thm)],[337])).
% 10.67/10.88 tff(339,plain,
% 10.67/10.88 (u2_lattices(A!0) = k1_realset1(u2_lattices(A!0), u1_struct_0(A!0))),
% 10.67/10.88 inference(transitivity,[status(thm)],[338, 289])).
% 10.67/10.88 tff(340,plain,
% 10.67/10.88 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))),
% 10.67/10.88 inference(monotonicity,[status(thm)],[339, 255])).
% 10.67/10.88 tff(341,plain,
% 10.67/10.88 (g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 10.67/10.88 inference(symmetry,[status(thm)],[340])).
% 10.67/10.88 tff(342,plain,
% 10.67/10.88 (k23_filter_2(A!0, u1_struct_0(A!0)) = k23_filter_2(A!0, k17_filter_2(A!0))),
% 10.67/10.88 inference(monotonicity,[status(thm)],[33])).
% 10.67/10.88 tff(343,plain,
% 10.67/10.88 (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))),
% 10.67/10.88 inference(symmetry,[status(thm)],[342])).
% 10.67/10.88 tff(344,plain,
% 10.67/10.88 (m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0) <=> m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0)),
% 10.67/10.88 inference(monotonicity,[status(thm)],[343])).
% 10.67/10.88 tff(345,plain,
% 10.67/10.88 (m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0) <=> m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)),
% 10.67/10.88 inference(symmetry,[status(thm)],[344])).
% 10.67/10.88 tff(346,plain,
% 10.67/10.88 (k1_filter_0(A!0) = k1_filter_2(A!0)),
% 10.67/10.88 inference(symmetry,[status(thm)],[73])).
% 10.67/10.88 tff(347,plain,
% 10.67/10.88 (u1_struct_0(A!0) = k1_filter_0(A!0)),
% 10.67/10.88 inference(symmetry,[status(thm)],[53])).
% 10.67/10.88 tff(348,plain,
% 10.67/10.88 (u1_struct_0(A!0) = k1_filter_2(A!0)),
% 10.67/10.88 inference(transitivity,[status(thm)],[347, 346])).
% 10.67/10.88 tff(349,plain,
% 10.67/10.88 (m1_filter_2(u1_struct_0(A!0), A!0) <=> m1_filter_2(k1_filter_2(A!0), A!0)),
% 10.67/10.88 inference(monotonicity,[status(thm)],[348])).
% 10.67/10.88 tff(350,plain,
% 10.67/10.88 (m1_filter_2(k1_filter_2(A!0), A!0) <=> m1_filter_2(u1_struct_0(A!0), A!0)),
% 10.67/10.88 inference(symmetry,[status(thm)],[349])).
% 10.67/10.88 tff(351,plain,
% 10.67/10.88 (^[A: $i] : refl((v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(352,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[351])).
% 10.67/10.88 tff(353,plain,
% 10.67/10.88 (^[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))) | m1_filter_2(k1_filter_2(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_2(k1_filter_2(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_2(k1_filter_2(A), A)) <=> (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A)) <=> (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(354,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A)) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[353])).
% 10.67/10.88 tff(355,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(356,plain,
% 10.67/10.88 (^[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)) => m1_filter_2(k1_filter_2(A), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_2(k1_filter_2(A), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_2(k1_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_2(k1_filter_2(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(357,plain,
% 10.67/10.88 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_2(k1_filter_2(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[356])).
% 10.67/10.88 tff(358,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_2(k1_filter_2(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_filter_2')).
% 10.67/10.88 tff(359,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[358, 357])).
% 10.67/10.88 tff(360,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[359, 355])).
% 10.67/10.88 tff(361,plain,(
% 10.67/10.88 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_2(k1_filter_2(A), A))),
% 10.67/10.88 inference(skolemize,[status(sab)],[360])).
% 10.67/10.88 tff(362,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[361, 354])).
% 10.67/10.88 tff(363,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[362, 352])).
% 10.67/10.88 tff(364,plain,
% 10.67/10.88 (((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(365,plain,
% 10.67/10.88 ((v3_struct_0(A!0) | m1_filter_2(k1_filter_2(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(366,plain,
% 10.67/10.88 (((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k1_filter_2(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0)))),
% 10.67/10.88 inference(monotonicity,[status(thm)],[365])).
% 10.67/10.88 tff(367,plain,
% 10.67/10.88 (((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k1_filter_2(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0))),
% 10.67/10.88 inference(transitivity,[status(thm)],[366, 364])).
% 10.67/10.88 tff(368,plain,
% 10.67/10.88 ((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k1_filter_2(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.88 tff(369,plain,
% 10.67/10.88 ((~![A: $i] : (v3_struct_0(A) | m1_filter_2(k1_filter_2(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k1_filter_2(A!0), A!0)),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[368, 367])).
% 10.67/10.88 tff(370,plain,
% 10.67/10.88 (m1_filter_2(k1_filter_2(A!0), A!0)),
% 10.67/10.88 inference(unit_resolution,[status(thm)],[369, 25, 24, 23, 363])).
% 10.67/10.88 tff(371,plain,
% 10.67/10.88 (m1_filter_2(u1_struct_0(A!0), A!0)),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[370, 350])).
% 10.67/10.88 tff(372,plain,
% 10.67/10.88 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(373,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[372])).
% 10.67/10.88 tff(374,plain,
% 10.67/10.88 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(375,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[374])).
% 10.67/10.88 tff(376,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(transitivity,[status(thm)],[375, 373])).
% 10.67/10.88 tff(377,plain,
% 10.67/10.88 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(378,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[377])).
% 10.67/10.88 tff(379,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(380,plain,
% 10.67/10.88 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 10.67/10.88 inference(bind,[status(th)],[])).
% 10.67/10.88 tff(381,plain,
% 10.67/10.88 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 10.67/10.88 inference(quant_intro,[status(thm)],[380])).
% 10.67/10.88 tff(382,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_2')).
% 10.67/10.88 tff(383,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[382, 381])).
% 10.67/10.88 tff(384,plain,
% 10.67/10.88 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[383, 379])).
% 10.67/10.88 tff(385,plain,(
% 10.67/10.88 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 10.67/10.88 inference(skolemize,[status(sab)],[384])).
% 10.67/10.88 tff(386,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[385, 378])).
% 10.67/10.88 tff(387,plain,
% 10.67/10.88 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 10.67/10.88 inference(modus_ponens,[status(thm)],[386, 376])).
% 10.67/10.88 tff(388,plain,
% 10.67/10.88 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 10.67/10.88 inference(rewrite,[status(thm)],[])).
% 10.67/10.88 tff(389,plain,
% 10.67/10.88 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 10.67/10.88 inference(quant_inst,[status(thm)],[])).
% 10.67/10.89 tff(390,plain,
% 10.67/10.89 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[389, 388])).
% 10.67/10.89 tff(391,plain,
% 10.67/10.89 (![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[390, 25, 24, 23, 387])).
% 10.67/10.89 tff(392,plain,
% 10.67/10.89 (((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))) <=> ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(393,plain,
% 10.67/10.89 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))))),
% 10.67/10.89 inference(quant_inst,[status(thm)],[])).
% 10.67/10.89 tff(394,plain,
% 10.67/10.89 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[393, 392])).
% 10.67/10.89 tff(395,plain,
% 10.67/10.89 (~(v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)))),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[394, 391, 371])).
% 10.67/10.89 tff(396,plain,
% 10.67/10.89 ((v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0))) | m2_lattice4(u1_struct_0(A!0), A!0)),
% 10.67/10.89 inference(tautology,[status(thm)],[])).
% 10.67/10.89 tff(397,plain,
% 10.67/10.89 (m2_lattice4(u1_struct_0(A!0), A!0)),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[396, 395])).
% 10.67/10.89 tff(398,plain,
% 10.67/10.89 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(399,plain,
% 10.67/10.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[398])).
% 10.67/10.89 tff(400,plain,
% 10.67/10.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(401,plain,
% 10.67/10.89 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(402,plain,
% 10.67/10.89 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[401])).
% 10.67/10.89 tff(403,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 10.67/10.89 tff(404,plain,
% 10.67/10.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[403, 402])).
% 10.67/10.89 tff(405,plain,
% 10.67/10.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[404, 400])).
% 10.67/10.89 tff(406,plain,(
% 10.67/10.89 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(skolemize,[status(sab)],[405])).
% 10.67/10.89 tff(407,plain,
% 10.67/10.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[406, 399])).
% 10.67/10.89 tff(408,plain,
% 10.67/10.89 (((~![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)))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(409,plain,
% 10.67/10.89 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 10.67/10.89 inference(quant_inst,[status(thm)],[])).
% 10.67/10.89 tff(410,plain,
% 10.67/10.89 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[409, 408])).
% 10.67/10.89 tff(411,plain,
% 10.67/10.89 (l1_struct_0(A!0)),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[410, 407, 257])).
% 10.67/10.89 tff(412,plain,
% 10.67/10.89 (^[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))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(413,plain,
% 10.67/10.89 (![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)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[412])).
% 10.67/10.89 tff(414,plain,
% 10.67/10.89 (^[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)))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(415,plain,
% 10.67/10.89 (![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)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[414])).
% 10.67/10.89 tff(416,plain,
% 10.67/10.89 (![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))))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(417,plain,
% 10.67/10.89 (^[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)))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(418,plain,
% 10.67/10.89 (![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))))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[417])).
% 10.67/10.89 tff(419,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')).
% 10.67/10.89 tff(420,plain,
% 10.67/10.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[419, 418])).
% 10.67/10.89 tff(421,plain,
% 10.67/10.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[420, 416])).
% 10.67/10.89 tff(422,plain,(
% 10.67/10.89 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 10.67/10.89 inference(skolemize,[status(sab)],[421])).
% 10.67/10.89 tff(423,plain,
% 10.67/10.89 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[422, 415])).
% 10.67/10.89 tff(424,plain,
% 10.67/10.89 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[423, 413])).
% 10.67/10.89 tff(425,plain,
% 10.67/10.89 (((~![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))))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(426,plain,
% 10.67/10.89 ((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))))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(427,plain,
% 10.67/10.89 (((~![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)))))),
% 10.67/10.89 inference(monotonicity,[status(thm)],[426])).
% 10.67/10.89 tff(428,plain,
% 10.67/10.89 (((~![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))))),
% 10.67/10.89 inference(transitivity,[status(thm)],[427, 425])).
% 10.67/10.89 tff(429,plain,
% 10.67/10.89 ((~![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)))),
% 10.67/10.89 inference(quant_inst,[status(thm)],[])).
% 10.67/10.89 tff(430,plain,
% 10.67/10.89 ((~![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)))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[429, 428])).
% 10.67/10.89 tff(431,plain,
% 10.67/10.89 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[430, 25, 424])).
% 10.67/10.89 tff(432,plain,
% 10.67/10.89 (~v1_xboole_0(u1_struct_0(A!0))),
% 10.67/10.89 inference(unit_resolution,[status(thm)],[431, 411])).
% 10.67/10.89 tff(433,plain,
% 10.67/10.89 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(434,plain,
% 10.67/10.89 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[433])).
% 10.67/10.89 tff(435,plain,
% 10.67/10.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_nat_lat(k23_filter_2(A, B), A)))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(436,plain,
% 10.67/10.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[435])).
% 10.67/10.89 tff(437,plain,
% 10.67/10.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 10.67/10.89 inference(rewrite,[status(thm)],[])).
% 10.67/10.89 tff(438,plain,
% 10.67/10.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))))),
% 10.67/10.89 inference(bind,[status(th)],[])).
% 10.67/10.89 tff(439,plain,
% 10.67/10.89 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 10.67/10.89 inference(quant_intro,[status(thm)],[438])).
% 10.67/10.89 tff(440,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m2_lattice4(B, A)) => m2_nat_lat(k23_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k23_filter_2')).
% 10.67/10.89 tff(441,plain,
% 10.67/10.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[440, 439])).
% 10.67/10.89 tff(442,plain,
% 10.67/10.89 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 10.67/10.89 inference(modus_ponens,[status(thm)],[441, 437])).
% 10.67/10.89 tff(443,plain,(
% 10.67/10.89 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m2_lattice4(B, A))) | m2_nat_lat(k23_filter_2(A, B), A))),
% 10.74/10.89 inference(skolemize,[status(sab)],[442])).
% 10.74/10.89 tff(444,plain,
% 10.74/10.89 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[443, 436])).
% 10.74/10.89 tff(445,plain,
% 10.74/10.89 (![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[444, 434])).
% 10.74/10.89 tff(446,plain,
% 10.74/10.89 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0))),
% 10.74/10.89 inference(rewrite,[status(thm)],[])).
% 10.74/10.89 tff(447,plain,
% 10.74/10.89 ((v1_xboole_0(u1_struct_0(A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0) | v3_struct_0(A!0) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0))),
% 10.74/10.89 inference(rewrite,[status(thm)],[])).
% 10.74/10.89 tff(448,plain,
% 10.74/10.89 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(u1_struct_0(A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0) | v3_struct_0(A!0) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0)))),
% 10.74/10.89 inference(monotonicity,[status(thm)],[447])).
% 10.74/10.89 tff(449,plain,
% 10.74/10.89 (((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(u1_struct_0(A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0) | v3_struct_0(A!0) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0))),
% 10.74/10.89 inference(transitivity,[status(thm)],[448, 446])).
% 10.74/10.89 tff(450,plain,
% 10.74/10.89 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(u1_struct_0(A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0) | v3_struct_0(A!0) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 10.74/10.89 inference(quant_inst,[status(thm)],[])).
% 10.74/10.89 tff(451,plain,
% 10.74/10.89 ((~![A: $i, B: $i] : (v1_xboole_0(B) | m2_nat_lat(k23_filter_2(A, B), A) | v3_struct_0(A) | (~m2_lattice4(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0)),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[450, 449])).
% 10.74/10.89 tff(452,plain,
% 10.74/10.89 (m2_nat_lat(k23_filter_2(A!0, u1_struct_0(A!0)), A!0)),
% 10.74/10.89 inference(unit_resolution,[status(thm)],[451, 25, 24, 23, 445, 432, 397])).
% 10.74/10.89 tff(453,plain,
% 10.74/10.89 (m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[452, 345])).
% 10.74/10.89 tff(454,plain,
% 10.74/10.89 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))))),
% 10.74/10.89 inference(bind,[status(th)],[])).
% 10.74/10.89 tff(455,plain,
% 10.74/10.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(quant_intro,[status(thm)],[454])).
% 10.74/10.89 tff(456,plain,
% 10.74/10.89 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))))),
% 10.74/10.89 inference(bind,[status(th)],[])).
% 10.74/10.89 tff(457,plain,
% 10.74/10.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(quant_intro,[status(thm)],[456])).
% 10.74/10.89 tff(458,plain,
% 10.74/10.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(transitivity,[status(thm)],[457, 455])).
% 10.74/10.89 tff(459,plain,
% 10.74/10.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m2_lattice4(B, A)) <=> (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), rewrite((~(~(v1_xboole_0(B) | (~m2_lattice4(B, A))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)))), ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A))))), quant_intro(proof_bind(^[C: $i] : rewrite(((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))) <=> ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))), (![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))) <=> ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))), rewrite(((v1_xboole_0(B) | (~m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))), (((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))))),
% 10.74/10.89 inference(bind,[status(th)],[])).
% 10.74/10.89 tff(460,plain,
% 10.74/10.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(quant_intro,[status(thm)],[459])).
% 10.74/10.89 tff(461,plain,
% 10.74/10.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 10.74/10.89 inference(rewrite,[status(thm)],[])).
% 10.74/10.89 tff(462,plain,
% 10.74/10.89 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))) <=> ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))), ((m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), rewrite((m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))) <=> ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))), ((m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))) <=> ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), rewrite((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))), ((((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))))), (![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))))),
% 10.74/10.89 inference(bind,[status(th)],[])).
% 10.74/10.89 tff(463,plain,
% 10.74/10.89 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m2_lattice4(B, A)) => ![C: $i] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 10.74/10.89 inference(quant_intro,[status(thm)],[462])).
% 10.74/10.89 tff(464,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] : (m2_nat_lat(C, A) => ((C = k23_filter_2(A, 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)) & ?[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)) & (D = k1_realset1(u2_lattices(A), B))) & (E = k1_realset1(u1_lattices(A), B))) & (C = g3_lattices(B, D, E))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d16_filter_2')).
% 10.74/10.89 tff(465,plain,
% 10.74/10.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[464, 463])).
% 10.74/10.89 tff(466,plain,
% 10.74/10.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[465, 461])).
% 10.74/10.89 tff(467,plain,(
% 10.74/10.89 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m2_lattice4(B, A))) | ![C: $i] : ((~m2_nat_lat(C, A)) | ((C = k23_filter_2(A, 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) & m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B) & (C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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) & m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))))))),
% 10.74/10.89 inference(skolemize,[status(sab)],[466])).
% 10.74/10.89 tff(468,plain,
% 10.74/10.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[467, 460])).
% 10.74/10.89 tff(469,plain,
% 10.74/10.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))),
% 10.74/10.89 inference(modus_ponens,[status(thm)],[468, 458])).
% 10.74/10.89 tff(470,plain,
% 10.74/10.89 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B)))))))),
% 10.74/10.90 inference(rewrite,[status(thm)],[])).
% 10.74/10.90 tff(471,plain,
% 10.74/10.90 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B)))))))),
% 10.74/10.90 inference(quant_inst,[status(thm)],[])).
% 10.74/10.90 tff(472,plain,
% 10.74/10.90 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A)) | ![C: $i] : ((~m2_nat_lat(C, A)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A), B), k1_realset1(u1_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)) | (~m2_relset_1(k1_realset1(u1_lattices(A), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))),
% 10.74/10.90 inference(modus_ponens,[status(thm)],[471, 470])).
% 10.74/10.90 tff(473,plain,
% 10.74/10.90 (![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))),
% 10.74/10.90 inference(unit_resolution,[status(thm)],[472, 25, 24, 23, 469])).
% 10.74/10.90 tff(474,plain,
% 10.74/10.90 (((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0)))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0)))))))),
% 10.74/10.90 inference(rewrite,[status(thm)],[])).
% 10.74/10.90 tff(475,plain,
% 10.74/10.90 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0)))))))),
% 10.74/10.90 inference(quant_inst,[status(thm)],[])).
% 10.74/10.90 tff(476,plain,
% 10.74/10.90 ((~![B: $i] : (v1_xboole_0(B) | (~m2_lattice4(B, A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u2_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~(C = g3_lattices(B, k1_realset1(u2_lattices(A!0), B), k1_realset1(u1_lattices(A!0), B)))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), B))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B)) | (~m2_relset_1(k1_realset1(u1_lattices(A!0), B), k2_zfmisc_1(B, B), B))) <=> (C = k23_filter_2(A!0, B))))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(modus_ponens,[status(thm)],[475, 474])).
% 10.74/10.90 tff(477,plain,
% 10.74/10.90 (v1_xboole_0(u1_struct_0(A!0)) | (~m2_lattice4(u1_struct_0(A!0), A!0)) | ![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(unit_resolution,[status(thm)],[476, 473])).
% 10.74/10.90 tff(478,plain,
% 10.74/10.90 (![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(unit_resolution,[status(thm)],[477, 397, 432])).
% 10.74/10.90 tff(479,plain,
% 10.74/10.90 (((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | (~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(rewrite,[status(thm)],[])).
% 10.74/10.90 tff(480,plain,
% 10.74/10.90 (((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))))) <=> ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(rewrite,[status(thm)],[])).
% 10.74/10.90 tff(481,plain,
% 10.74/10.90 (((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))))))),
% 10.74/10.90 inference(monotonicity,[status(thm)],[480])).
% 10.74/10.90 tff(482,plain,
% 10.74/10.90 (((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))) <=> ((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | (~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(transitivity,[status(thm)],[481, 479])).
% 10.74/10.90 tff(483,plain,
% 10.74/10.90 ((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))))),
% 10.74/10.90 inference(quant_inst,[status(thm)],[])).
% 10.74/10.90 tff(484,plain,
% 10.74/10.90 ((~![C: $i] : ((~m2_nat_lat(C, A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(C = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) <=> (C = k23_filter_2(A!0, u1_struct_0(A!0))))))) | (~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))))),
% 10.74/10.90 inference(modus_ponens,[status(thm)],[483, 482])).
% 10.74/10.90 tff(485,plain,
% 10.74/10.90 ((~m2_nat_lat(k23_filter_2(A!0, k17_filter_2(A!0)), A!0)) | (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))))),
% 10.74/10.90 inference(unit_resolution,[status(thm)],[484, 478])).
% 10.74/10.90 tff(486,plain,
% 10.74/10.90 (~(((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))),
% 10.74/10.91 inference(unit_resolution,[status(thm)],[485, 453])).
% 10.74/10.91 tff(487,plain,
% 10.74/10.91 ((((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0))))),
% 10.74/10.91 inference(tautology,[status(thm)],[])).
% 10.74/10.91 tff(488,plain,
% 10.74/10.91 ((((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) <=> (k23_filter_2(A!0, k17_filter_2(A!0)) = k23_filter_2(A!0, u1_struct_0(A!0)))) | (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))))),
% 10.74/10.91 inference(unit_resolution,[status(thm)],[487, 343])).
% 10.74/10.91 tff(489,plain,
% 10.74/10.91 (~((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))))),
% 10.74/10.91 inference(unit_resolution,[status(thm)],[488, 486])).
% 10.74/10.91 tff(490,plain,
% 10.74/10.91 (((~v1_funct_1(k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u2_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))) | (~v1_funct_2(k1_realset1(u1_lattices(A!0), u1_struct_0(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), u1_struct_0(A!0)), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))))) | (k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0))))),
% 10.74/10.91 inference(tautology,[status(thm)],[])).
% 10.74/10.91 tff(491,plain,
% 10.74/10.91 (k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), k1_realset1(u2_lattices(A!0), u1_struct_0(A!0)), k1_realset1(u1_lattices(A!0), u1_struct_0(A!0)))),
% 10.74/10.91 inference(unit_resolution,[status(thm)],[490, 489])).
% 10.74/10.91 tff(492,plain,
% 10.74/10.91 (k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 10.74/10.91 inference(transitivity,[status(thm)],[491, 341])).
% 10.74/10.91 tff(493,plain,
% 10.74/10.91 ((~(~((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))))) <=> ((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))))),
% 10.74/10.91 inference(rewrite,[status(thm)],[])).
% 10.74/10.91 tff(494,plain,
% 10.74/10.91 (((k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) & (k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) <=> (~((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))))),
% 10.74/10.91 inference(rewrite,[status(thm)],[])).
% 10.74/10.91 tff(495,plain,
% 10.74/10.91 ((~((k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) & (k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))) <=> (~(~((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))))))),
% 10.74/10.91 inference(monotonicity,[status(thm)],[494])).
% 10.74/10.93 tff(496,plain,
% 10.74/10.93 ((~((k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) & (k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))) <=> ((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))))),
% 10.74/10.93 inference(transitivity,[status(thm)],[495, 493])).
% 10.74/10.93 tff(497,plain,
% 10.74/10.93 (~((k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))) & (k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 10.74/10.93 inference(or_elim,[status(thm)],[21])).
% 10.74/10.93 tff(498,plain,
% 10.74/10.93 ((~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))))),
% 10.74/10.93 inference(modus_ponens,[status(thm)],[497, 496])).
% 10.74/10.93 tff(499,plain,
% 10.74/10.93 (~(k23_filter_2(A!0, k1_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 10.74/10.93 inference(unit_resolution,[status(thm)],[498, 492])).
% 10.74/10.93 tff(500,plain,
% 10.74/10.93 (~(k23_filter_2(A!0, k17_filter_2(A!0)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))),
% 10.74/10.93 inference(modus_ponens,[status(thm)],[499, 77])).
% 10.74/10.93 tff(501,plain,
% 10.74/10.93 ($false),
% 10.74/10.93 inference(unit_resolution,[status(thm)],[492, 500])).
% 10.74/10.93 % SZS output end Proof
% 10.74/10.97 % E exiting
%------------------------------------------------------------------------------