%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT311+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:17 AM UTC 2025
% Result : Theorem 0.60s 0.78s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT311+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:12:12 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 % SZS output start Proof
% 0.60/0.78 tff(r1_tarski_type, type, (
% 0.60/0.78 r1_tarski: ( $i * $i ) > $o)).
% 0.60/0.78 tff(k3_filter_0_type, type, (
% 0.60/0.78 k3_filter_0: ( $i * $i ) > $i)).
% 0.60/0.78 tff(tptp_fun_C_2_type, type, (
% 0.60/0.78 tptp_fun_C_2: $i)).
% 0.60/0.78 tff(g3_lattices_type, type, (
% 0.60/0.78 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.60/0.78 tff(u2_lattices_type, type, (
% 0.60/0.78 u2_lattices: $i > $i)).
% 0.60/0.78 tff(tptp_fun_A_0_type, type, (
% 0.60/0.78 tptp_fun_A_0: $i)).
% 0.60/0.78 tff(u1_lattices_type, type, (
% 0.60/0.78 u1_lattices: $i > $i)).
% 0.60/0.78 tff(u1_struct_0_type, type, (
% 0.60/0.78 u1_struct_0: $i > $i)).
% 0.60/0.78 tff(k2_filter_0_type, type, (
% 0.60/0.78 k2_filter_0: ( $i * $i ) > $i)).
% 0.60/0.78 tff(tptp_fun_B_1_type, type, (
% 0.60/0.78 tptp_fun_B_1: $i)).
% 0.60/0.78 tff(k19_filter_2_type, type, (
% 0.60/0.78 k19_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(k18_filter_2_type, type, (
% 0.60/0.78 k18_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(k3_filter_2_type, type, (
% 0.60/0.78 k3_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(k7_filter_2_type, type, (
% 0.60/0.78 k7_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(k1_lattice2_type, type, (
% 0.60/0.78 k1_lattice2: $i > $i)).
% 0.60/0.78 tff(k8_filter_2_type, type, (
% 0.60/0.78 k8_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(m1_subset_1_type, type, (
% 0.60/0.78 m1_subset_1: ( $i * $i ) > $o)).
% 0.60/0.78 tff(k1_zfmisc_1_type, type, (
% 0.60/0.78 k1_zfmisc_1: $i > $i)).
% 0.60/0.78 tff(v10_lattices_type, type, (
% 0.60/0.78 v10_lattices: $i > $o)).
% 0.60/0.78 tff(l3_lattices_type, type, (
% 0.60/0.78 l3_lattices: $i > $o)).
% 0.60/0.78 tff(v3_struct_0_type, type, (
% 0.60/0.78 v3_struct_0: $i > $o)).
% 0.60/0.78 tff(v1_xboole_0_type, type, (
% 0.60/0.78 v1_xboole_0: $i > $o)).
% 0.60/0.78 tff(r2_hidden_type, type, (
% 0.60/0.78 r2_hidden: ( $i * $i ) > $o)).
% 0.60/0.78 tff(v9_lattices_type, type, (
% 0.60/0.78 v9_lattices: $i > $o)).
% 0.60/0.78 tff(v8_lattices_type, type, (
% 0.60/0.78 v8_lattices: $i > $o)).
% 0.60/0.78 tff(v7_lattices_type, type, (
% 0.60/0.78 v7_lattices: $i > $o)).
% 0.60/0.78 tff(v6_lattices_type, type, (
% 0.60/0.78 v6_lattices: $i > $o)).
% 0.60/0.78 tff(v5_lattices_type, type, (
% 0.60/0.78 v5_lattices: $i > $o)).
% 0.60/0.78 tff(v4_lattices_type, type, (
% 0.60/0.78 v4_lattices: $i > $o)).
% 0.60/0.78 tff(v3_lattices_type, type, (
% 0.60/0.78 v3_lattices: $i > $o)).
% 0.60/0.78 tff(m1_relset_1_type, type, (
% 0.60/0.78 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.60/0.78 tff(k2_zfmisc_1_type, type, (
% 0.60/0.78 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.60/0.78 tff(m2_relset_1_type, type, (
% 0.60/0.78 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.60/0.78 tff(v1_funct_2_type, type, (
% 0.60/0.78 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.60/0.78 tff(v1_funct_1_type, type, (
% 0.60/0.78 v1_funct_1: $i > $o)).
% 0.60/0.78 tff(l1_lattices_type, type, (
% 0.60/0.78 l1_lattices: $i > $o)).
% 0.60/0.78 tff(l2_lattices_type, type, (
% 0.60/0.78 l2_lattices: $i > $o)).
% 0.60/0.78 tff(k2_filter_2_type, type, (
% 0.60/0.78 k2_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(k5_filter_2_type, type, (
% 0.60/0.78 k5_filter_2: ( $i * $i ) > $i)).
% 0.60/0.78 tff(1,plain,
% 0.60/0.78 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(2,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.78 tff(3,plain,
% 0.60/0.78 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(4,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[3])).
% 0.60/0.78 tff(5,plain,
% 0.60/0.78 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(6,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[5])).
% 0.60/0.78 tff(7,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(transitivity,[status(thm)],[6, 4])).
% 0.60/0.78 tff(8,plain,
% 0.60/0.78 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(9,plain,
% 0.60/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[8])).
% 0.60/0.78 tff(10,plain,
% 0.60/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(11,plain,
% 0.60/0.78 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(12,plain,
% 0.60/0.78 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[11])).
% 0.60/0.78 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 0.60/0.78 tff(14,plain,
% 0.60/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.60/0.78 tff(15,plain,
% 0.60/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.60/0.78 tff(16,plain,(
% 0.60/0.78 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[15])).
% 0.60/0.78 tff(17,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.60/0.78 tff(18,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.60/0.78 tff(19,plain,
% 0.60/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.60/0.78 tff(20,plain,
% 0.60/0.78 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(21,plain,
% 0.60/0.78 ((~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(22,plain,
% 0.60/0.78 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[21])).
% 0.60/0.78 tff(23,plain,
% 0.60/0.78 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))))),
% 0.60/0.78 inference(monotonicity,[status(thm)],[22])).
% 0.60/0.78 tff(24,plain,
% 0.60/0.78 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.60/0.78 inference(transitivity,[status(thm)],[23, 20])).
% 0.60/0.78 tff(25,plain,
% 0.60/0.78 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(26,plain,
% 0.60/0.78 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(27,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t40_filter_2')).
% 0.60/0.78 tff(28,plain,
% 0.60/0.78 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.60/0.78 tff(29,plain,
% 0.60/0.78 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.60/0.78 tff(30,plain,
% 0.60/0.78 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.60/0.78 tff(31,plain,
% 0.60/0.78 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k18_filter_2(A, B), k19_filter_2(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.60/0.78 tff(32,plain,
% 0.60/0.78 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.60/0.78 tff(33,plain,
% 0.60/0.78 (l3_lattices(A!0)),
% 0.60/0.78 inference(and_elim,[status(thm)],[32])).
% 0.60/0.78 tff(34,plain,
% 0.60/0.78 (v10_lattices(A!0)),
% 0.60/0.78 inference(and_elim,[status(thm)],[32])).
% 0.60/0.78 tff(35,plain,
% 0.60/0.78 (~v3_struct_0(A!0)),
% 0.60/0.78 inference(and_elim,[status(thm)],[32])).
% 0.60/0.78 tff(36,plain,
% 0.60/0.78 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(37,plain,
% 0.60/0.78 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(38,plain,
% 0.60/0.78 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.60/0.78 tff(39,plain,
% 0.60/0.78 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 19])).
% 0.60/0.78 tff(40,plain,
% 0.60/0.78 (~(r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) | (~r2_hidden(B!1, C!2)) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.60/0.78 inference(and_elim,[status(thm)],[32])).
% 0.60/0.78 tff(41,plain,
% 0.60/0.78 ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.78 inference(or_elim,[status(thm)],[40])).
% 0.60/0.78 tff(42,plain,
% 0.60/0.78 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.78 inference(and_elim,[status(thm)],[41])).
% 0.60/0.78 tff(43,plain,
% 0.60/0.78 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(44,plain,
% 0.60/0.78 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 0.60/0.78 inference(quant_inst,[status(thm)],[])).
% 0.60/0.78 tff(45,plain,
% 0.60/0.78 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.60/0.78 tff(46,plain,
% 0.60/0.78 (k7_filter_2(A!0, C!2) = C!2),
% 0.60/0.78 inference(unit_resolution,[status(thm)],[45, 42, 39])).
% 0.60/0.78 tff(47,plain,
% 0.60/0.78 (C!2 = k7_filter_2(A!0, C!2)),
% 0.60/0.78 inference(symmetry,[status(thm)],[46])).
% 0.60/0.79 tff(48,plain,
% 0.60/0.79 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[47])).
% 0.60/0.79 tff(49,plain,
% 0.60/0.79 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.79 inference(symmetry,[status(thm)],[48])).
% 0.60/0.79 tff(50,plain,
% 0.60/0.79 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(51,plain,
% 0.60/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[50])).
% 0.60/0.79 tff(52,plain,
% 0.60/0.79 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(53,plain,
% 0.60/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[52])).
% 0.60/0.79 tff(54,plain,
% 0.60/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(55,plain,
% 0.60/0.79 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(56,plain,
% 0.60/0.79 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[55])).
% 0.60/0.79 tff(57,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_filter_2')).
% 0.60/0.79 tff(58,plain,
% 0.60/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.60/0.79 tff(59,plain,
% 0.60/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.60/0.79 tff(60,plain,(
% 0.60/0.79 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.60/0.79 inference(skolemize,[status(sab)],[59])).
% 0.60/0.79 tff(61,plain,
% 0.60/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.60/0.79 tff(62,plain,
% 0.60/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.60/0.79 tff(63,plain,
% 0.60/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(64,plain,
% 0.60/0.79 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(65,plain,
% 0.60/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[64])).
% 0.60/0.79 tff(66,plain,
% 0.60/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[65, 63])).
% 0.60/0.79 tff(67,plain,
% 0.60/0.79 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(68,plain,
% 0.60/0.79 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.60/0.79 tff(69,plain,
% 0.60/0.79 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[68, 35, 34, 33, 42, 62])).
% 0.60/0.79 tff(70,plain,
% 0.60/0.79 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[69, 49])).
% 0.60/0.79 tff(71,plain,
% 0.60/0.79 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(72,plain,
% 0.60/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[71])).
% 0.60/0.79 tff(73,plain,
% 0.60/0.79 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(74,plain,
% 0.60/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[73])).
% 0.60/0.79 tff(75,plain,
% 0.60/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(transitivity,[status(thm)],[74, 72])).
% 0.60/0.79 tff(76,plain,
% 0.60/0.79 (^[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)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), rewrite(((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), rewrite(((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(77,plain,
% 0.60/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[76])).
% 0.60/0.79 tff(78,plain,
% 0.60/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(79,plain,
% 0.60/0.79 (^[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(trans(monotonicity(rewrite((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)))), (((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> (((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), rewrite((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))), (((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(80,plain,
% 0.60/0.79 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[79])).
% 0.60/0.79 tff(81,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_filter_2')).
% 0.60/0.79 tff(82,plain,
% 0.60/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[81, 80])).
% 0.60/0.79 tff(83,plain,
% 0.60/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[82, 78])).
% 0.60/0.79 tff(84,plain,(
% 0.60/0.79 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.60/0.79 inference(skolemize,[status(sab)],[83])).
% 0.60/0.79 tff(85,plain,
% 0.60/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[84, 77])).
% 0.60/0.79 tff(86,plain,
% 0.60/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[85, 75])).
% 0.60/0.79 tff(87,plain,
% 0.60/0.79 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(88,plain,
% 0.60/0.79 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(89,plain,
% 0.60/0.79 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[88, 87])).
% 0.60/0.79 tff(90,plain,
% 0.60/0.79 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[89, 35, 34, 33, 86])).
% 0.60/0.79 tff(91,plain,
% 0.60/0.79 (~v1_xboole_0(C!2)),
% 0.60/0.79 inference(and_elim,[status(thm)],[41])).
% 0.60/0.79 tff(92,plain,
% 0.60/0.79 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(93,plain,
% 0.60/0.80 ((v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))) <=> (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(94,plain,
% 0.60/0.80 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[93])).
% 0.60/0.80 tff(95,plain,
% 0.60/0.80 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[94, 92])).
% 0.60/0.80 tff(96,plain,
% 0.60/0.80 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(97,plain,
% 0.60/0.80 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.60/0.80 tff(98,plain,
% 0.60/0.80 (![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[97, 91, 42, 90])).
% 0.60/0.80 tff(99,plain,
% 0.60/0.80 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(100,plain,
% 0.60/0.80 ((v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))) <=> (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(101,plain,
% 0.60/0.80 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[100])).
% 0.60/0.80 tff(102,plain,
% 0.60/0.80 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[101, 99])).
% 0.60/0.80 tff(103,plain,
% 0.60/0.80 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(104,plain,
% 0.60/0.80 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[103, 102])).
% 0.60/0.80 tff(105,plain,
% 0.60/0.80 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[104, 91, 98])).
% 0.60/0.80 tff(106,plain,
% 0.60/0.80 (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2)))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[105, 70])).
% 0.60/0.80 tff(107,plain,
% 0.60/0.80 (((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C!2)) = k19_filter_2(k1_lattice2(A!0), C!2))) | (~(k3_filter_2(k1_lattice2(A!0), C!2) = k19_filter_2(A!0, k8_filter_2(A!0, C!2))))) | (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))),
% 0.60/0.80 inference(tautology,[status(thm)],[])).
% 0.60/0.80 tff(108,plain,
% 0.60/0.80 (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[107, 106])).
% 0.60/0.80 tff(109,plain,
% 0.60/0.80 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(110,plain,
% 0.60/0.80 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[109])).
% 0.60/0.80 tff(111,plain,
% 0.60/0.80 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(112,plain,
% 0.60/0.80 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(113,plain,
% 0.60/0.80 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[112])).
% 0.60/0.80 tff(114,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 0.60/0.80 tff(115,plain,
% 0.60/0.80 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.60/0.80 tff(116,plain,
% 0.60/0.80 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.60/0.80 tff(117,plain,(
% 0.60/0.80 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(skolemize,[status(sab)],[116])).
% 0.60/0.80 tff(118,plain,
% 0.60/0.80 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[117, 110])).
% 0.60/0.80 tff(119,plain,
% 0.60/0.80 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(120,plain,
% 0.60/0.80 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(121,plain,
% 0.60/0.80 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[120, 119])).
% 0.60/0.80 tff(122,plain,
% 0.60/0.80 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[121, 33, 118])).
% 0.60/0.80 tff(123,plain,
% 0.60/0.80 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.60/0.80 inference(symmetry,[status(thm)],[122])).
% 0.60/0.80 tff(124,plain,
% 0.60/0.80 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[123, 47])).
% 0.60/0.80 tff(125,plain,
% 0.60/0.80 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[123])).
% 0.60/0.80 tff(126,plain,
% 0.60/0.80 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[125])).
% 0.60/0.80 tff(127,plain,
% 0.60/0.80 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[47, 126])).
% 0.60/0.80 tff(128,plain,
% 0.60/0.80 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.80 inference(symmetry,[status(thm)],[127])).
% 0.60/0.80 tff(129,plain,
% 0.60/0.80 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[69, 128])).
% 0.60/0.80 tff(130,plain,
% 0.60/0.80 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[123])).
% 0.60/0.80 tff(131,plain,
% 0.60/0.80 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.80 inference(symmetry,[status(thm)],[130])).
% 0.60/0.80 tff(132,plain,
% 0.60/0.80 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(133,plain,
% 0.60/0.80 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[132])).
% 0.60/0.80 tff(134,plain,
% 0.60/0.80 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(135,plain,
% 0.60/0.80 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[134])).
% 0.60/0.80 tff(136,plain,
% 0.60/0.80 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(137,plain,
% 0.60/0.80 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(138,plain,
% 0.60/0.80 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[137])).
% 0.60/0.80 tff(139,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.60/0.80 tff(140,plain,
% 0.60/0.80 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.60/0.80 tff(141,plain,
% 0.60/0.80 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[140, 136])).
% 0.60/0.80 tff(142,plain,(
% 0.60/0.80 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.80 inference(skolemize,[status(sab)],[141])).
% 0.60/0.80 tff(143,plain,
% 0.60/0.80 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[142, 135])).
% 0.60/0.80 tff(144,plain,
% 0.60/0.80 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[143, 133])).
% 0.60/0.80 tff(145,plain,
% 0.60/0.80 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(146,plain,
% 0.60/0.81 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(147,plain,
% 0.60/0.81 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.60/0.81 tff(148,plain,
% 0.60/0.81 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[147, 35, 34, 33, 144])).
% 0.60/0.81 tff(149,plain,
% 0.60/0.81 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(150,plain,
% 0.60/0.81 (v10_lattices(k1_lattice2(A!0))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[149, 148])).
% 0.60/0.81 tff(151,plain,
% 0.60/0.81 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[150, 131])).
% 0.60/0.81 tff(152,plain,
% 0.60/0.81 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[123])).
% 0.60/0.81 tff(153,plain,
% 0.60/0.81 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.81 inference(symmetry,[status(thm)],[152])).
% 0.60/0.81 tff(154,plain,
% 0.60/0.81 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[153])).
% 0.60/0.81 tff(155,plain,
% 0.60/0.81 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(156,plain,
% 0.60/0.81 (~v3_struct_0(k1_lattice2(A!0))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[155, 148])).
% 0.60/0.81 tff(157,plain,
% 0.60/0.81 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[156, 154])).
% 0.60/0.81 tff(158,plain,
% 0.60/0.81 (^[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)))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(159,plain,
% 0.60/0.81 (![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))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[158])).
% 0.60/0.81 tff(160,plain,
% 0.60/0.81 (![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))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(161,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')).
% 0.60/0.81 tff(162,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.60/0.81 tff(163,plain,(
% 0.60/0.81 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.60/0.81 inference(skolemize,[status(sab)],[162])).
% 0.60/0.81 tff(164,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[163, 159])).
% 0.60/0.81 tff(165,plain,
% 0.60/0.81 ((~![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)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(166,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.60/0.81 tff(167,plain,
% 0.60/0.81 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(168,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[167])).
% 0.60/0.81 tff(169,plain,
% 0.60/0.81 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(170,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[169])).
% 0.60/0.81 tff(171,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(172,plain,
% 0.60/0.81 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(173,plain,
% 0.60/0.81 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[172])).
% 0.60/0.81 tff(174,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.60/0.81 tff(175,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[174, 173])).
% 0.60/0.81 tff(176,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.60/0.81 tff(177,plain,(
% 0.60/0.81 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[176])).
% 0.60/0.81 tff(178,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[177, 170])).
% 0.60/0.81 tff(179,plain,
% 0.60/0.81 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[178, 168])).
% 0.60/0.81 tff(180,plain,
% 0.60/0.81 (((~![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)))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(181,plain,
% 0.60/0.81 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(182,plain,
% 0.60/0.81 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[181, 180])).
% 0.60/0.81 tff(183,plain,
% 0.60/0.81 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[182, 33, 179])).
% 0.60/0.81 tff(184,plain,
% 0.60/0.81 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(185,plain,
% 0.60/0.81 (l1_lattices(A!0)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.60/0.81 tff(186,plain,
% 0.60/0.81 (^[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)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(187,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[186])).
% 0.60/0.81 tff(188,plain,
% 0.60/0.81 (^[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)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(189,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[188])).
% 0.60/0.81 tff(190,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(191,plain,
% 0.60/0.81 (^[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))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(192,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[191])).
% 0.60/0.81 tff(193,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')).
% 0.60/0.81 tff(194,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.60/0.81 tff(195,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.60/0.81 tff(196,plain,(
% 0.60/0.81 ![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))))),
% 0.60/0.81 inference(skolemize,[status(sab)],[195])).
% 0.60/0.81 tff(197,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.60/0.81 tff(198,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[197, 187])).
% 0.60/0.81 tff(199,plain,
% 0.60/0.81 (((~![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))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(200,plain,
% 0.60/0.81 ((~![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))))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(201,plain,
% 0.60/0.81 ((~![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)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.60/0.81 tff(202,plain,
% 0.60/0.81 ((~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)))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[201, 198])).
% 0.60/0.81 tff(203,plain,
% 0.60/0.81 (~((~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))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[202, 185])).
% 0.60/0.81 tff(204,plain,
% 0.60/0.81 (((~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))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(205,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[204, 203])).
% 0.60/0.81 tff(206,plain,
% 0.60/0.81 ((~(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))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(207,plain,
% 0.60/0.81 ((~(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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[206, 205])).
% 0.60/0.81 tff(208,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[207, 166])).
% 0.60/0.81 tff(209,plain,
% 0.60/0.81 ((~![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)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(210,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[209, 164])).
% 0.60/0.81 tff(211,plain,
% 0.60/0.81 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(212,plain,
% 0.60/0.81 (l2_lattices(A!0)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[211, 183])).
% 0.60/0.81 tff(213,plain,
% 0.60/0.81 (^[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)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(214,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[213])).
% 0.60/0.81 tff(215,plain,
% 0.60/0.81 (^[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)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(216,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[215])).
% 0.60/0.81 tff(217,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(218,plain,
% 0.60/0.81 (^[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))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(219,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[218])).
% 0.60/0.81 tff(220,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')).
% 0.60/0.81 tff(221,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.60/0.81 tff(222,plain,
% 0.60/0.81 (![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))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.60/0.81 tff(223,plain,(
% 0.60/0.81 ![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))))),
% 0.60/0.81 inference(skolemize,[status(sab)],[222])).
% 0.60/0.81 tff(224,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.60/0.81 tff(225,plain,
% 0.60/0.81 (![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))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[224, 214])).
% 0.60/0.81 tff(226,plain,
% 0.60/0.81 (((~![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))))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(227,plain,
% 0.60/0.81 ((~![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))))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(228,plain,
% 0.60/0.81 ((~![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)))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.60/0.81 tff(229,plain,
% 0.60/0.81 ((~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)))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[228, 225])).
% 0.60/0.81 tff(230,plain,
% 0.60/0.81 (~((~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))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[229, 212])).
% 0.60/0.81 tff(231,plain,
% 0.60/0.81 (((~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))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(232,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[231, 230])).
% 0.60/0.81 tff(233,plain,
% 0.60/0.81 ((~(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))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(234,plain,
% 0.60/0.81 ((~(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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.60/0.81 tff(235,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[234, 210])).
% 0.60/0.81 tff(236,plain,
% 0.60/0.81 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(237,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[236, 230])).
% 0.60/0.81 tff(238,plain,
% 0.60/0.81 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(239,plain,
% 0.60/0.81 (v1_funct_1(u2_lattices(A!0))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[238, 230])).
% 0.60/0.81 tff(240,plain,
% 0.60/0.81 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(241,plain,
% 0.60/0.81 (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))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[240, 203])).
% 0.60/0.81 tff(242,plain,
% 0.60/0.81 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 0.60/0.81 inference(tautology,[status(thm)],[])).
% 0.60/0.81 tff(243,plain,
% 0.60/0.81 (v1_funct_1(u1_lattices(A!0))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[242, 203])).
% 0.60/0.81 tff(244,plain,
% 0.60/0.81 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(245,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[244])).
% 0.60/0.81 tff(246,plain,
% 0.60/0.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(247,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[246])).
% 0.60/0.81 tff(248,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(249,plain,
% 0.60/0.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(250,plain,
% 0.60/0.81 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[249])).
% 0.60/0.81 tff(251,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 0.60/0.82 tff(252,plain,
% 0.60/0.82 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.60/0.82 tff(253,plain,
% 0.60/0.82 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[252, 248])).
% 0.60/0.82 tff(254,plain,(
% 0.60/0.82 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.60/0.82 inference(skolemize,[status(sab)],[253])).
% 0.60/0.82 tff(255,plain,
% 0.60/0.82 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[254, 247])).
% 0.60/0.82 tff(256,plain,
% 0.60/0.82 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[255, 245])).
% 0.60/0.82 tff(257,plain,
% 0.60/0.82 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(258,plain,
% 0.60/0.82 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(259,plain,
% 0.60/0.82 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(260,plain,
% 0.60/0.82 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[259])).
% 0.60/0.82 tff(261,plain,
% 0.60/0.82 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[260, 258])).
% 0.60/0.82 tff(262,plain,
% 0.60/0.82 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[261])).
% 0.60/0.82 tff(263,plain,
% 0.60/0.82 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[262, 257])).
% 0.60/0.82 tff(264,plain,
% 0.60/0.82 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(265,plain,
% 0.60/0.82 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.60/0.82 tff(266,plain,
% 0.60/0.82 ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[265, 256, 243, 241, 239, 237])).
% 0.60/0.82 tff(267,plain,
% 0.60/0.82 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[266, 235, 208])).
% 0.60/0.82 tff(268,plain,
% 0.60/0.82 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.82 inference(tautology,[status(thm)],[])).
% 0.60/0.82 tff(269,plain,
% 0.60/0.82 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[268, 267])).
% 0.60/0.82 tff(270,plain,
% 0.60/0.82 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(271,plain,
% 0.60/0.82 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[270])).
% 0.60/0.82 tff(272,plain,
% 0.60/0.82 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k3_filter_2(A, B) = k3_filter_0(A, B))))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(273,plain,
% 0.60/0.82 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[272])).
% 0.60/0.82 tff(274,plain,
% 0.60/0.82 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(275,plain,
% 0.60/0.82 (^[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))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(276,plain,
% 0.60/0.82 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[275])).
% 0.60/0.82 tff(277,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_filter_2')).
% 0.60/0.82 tff(278,plain,
% 0.60/0.82 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.60/0.82 tff(279,plain,
% 0.60/0.82 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[278, 274])).
% 0.60/0.82 tff(280,plain,(
% 0.60/0.82 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.60/0.82 inference(skolemize,[status(sab)],[279])).
% 0.60/0.82 tff(281,plain,
% 0.60/0.82 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[280, 273])).
% 0.60/0.82 tff(282,plain,
% 0.60/0.82 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[281, 271])).
% 0.60/0.82 tff(283,plain,
% 0.60/0.82 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(284,plain,
% 0.60/0.82 ((v1_xboole_0(C!2) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> (v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(285,plain,
% 0.60/0.82 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[284])).
% 0.60/0.82 tff(286,plain,
% 0.60/0.82 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[285, 283])).
% 0.60/0.82 tff(287,plain,
% 0.60/0.82 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(C!2) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(288,plain,
% 0.60/0.82 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v1_xboole_0(C!2) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[287, 286])).
% 0.60/0.82 tff(289,plain,
% 0.60/0.82 ((k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[288, 91, 282, 269, 157, 151])).
% 0.60/0.82 tff(290,plain,
% 0.60/0.82 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[289, 129])).
% 0.60/0.82 tff(291,plain,
% 0.60/0.82 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)),
% 0.60/0.82 inference(symmetry,[status(thm)],[290])).
% 0.60/0.82 tff(292,plain,
% 0.60/0.82 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2) = k19_filter_2(A!0, C!2)),
% 0.60/0.82 inference(transitivity,[status(thm)],[291, 124, 108])).
% 0.60/0.82 tff(293,plain,
% 0.60/0.82 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(294,plain,
% 0.60/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[293])).
% 0.60/0.82 tff(295,plain,
% 0.60/0.82 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(296,plain,
% 0.60/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[295])).
% 0.60/0.82 tff(297,plain,
% 0.60/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[296, 294])).
% 0.60/0.82 tff(298,plain,
% 0.60/0.82 (^[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_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(299,plain,
% 0.60/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[298])).
% 0.60/0.82 tff(300,plain,
% 0.60/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(301,plain,
% 0.60/0.82 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(302,plain,
% 0.60/0.82 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[301])).
% 0.60/0.82 tff(303,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_filter_2')).
% 0.60/0.82 tff(304,plain,
% 0.60/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.60/0.82 tff(305,plain,
% 0.60/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[304, 300])).
% 0.60/0.82 tff(306,plain,(
% 0.60/0.82 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.82 inference(skolemize,[status(sab)],[305])).
% 0.60/0.82 tff(307,plain,
% 0.60/0.82 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[306, 299])).
% 0.60/0.83 tff(308,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[307, 297])).
% 0.60/0.83 tff(309,plain,
% 0.60/0.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(310,plain,
% 0.60/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(311,plain,
% 0.60/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.60/0.83 tff(312,plain,
% 0.60/0.83 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[311, 35, 34, 33, 308])).
% 0.60/0.83 tff(313,plain,
% 0.60/0.83 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.60/0.83 inference(and_elim,[status(thm)],[32])).
% 0.60/0.83 tff(314,plain,
% 0.60/0.83 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(315,plain,
% 0.60/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(316,plain,
% 0.60/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.60/0.83 tff(317,plain,
% 0.60/0.83 (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[316, 313, 312])).
% 0.60/0.83 tff(318,plain,
% 0.60/0.83 (((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))) | (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))),
% 0.60/0.83 inference(tautology,[status(thm)],[])).
% 0.60/0.83 tff(319,plain,
% 0.60/0.83 (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[318, 317])).
% 0.60/0.83 tff(320,plain,
% 0.60/0.83 (k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k18_filter_2(A!0, B!1)),
% 0.60/0.83 inference(symmetry,[status(thm)],[319])).
% 0.60/0.83 tff(321,plain,
% 0.60/0.83 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(322,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[321])).
% 0.60/0.83 tff(323,plain,
% 0.60/0.83 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(324,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[323])).
% 0.60/0.83 tff(325,plain,
% 0.60/0.83 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(326,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[325])).
% 0.60/0.83 tff(327,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[326, 324])).
% 0.60/0.83 tff(328,plain,
% 0.60/0.83 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(329,plain,
% 0.60/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[328])).
% 0.60/0.83 tff(330,plain,
% 0.60/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(331,plain,
% 0.60/0.83 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(332,plain,
% 0.60/0.83 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[331])).
% 0.60/0.83 tff(333,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 0.60/0.83 tff(334,plain,
% 0.60/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[333, 332])).
% 0.60/0.83 tff(335,plain,
% 0.60/0.83 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[334, 330])).
% 0.60/0.83 tff(336,plain,(
% 0.60/0.83 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[335])).
% 0.60/0.83 tff(337,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[336, 329])).
% 0.60/0.83 tff(338,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[337, 327])).
% 0.60/0.83 tff(339,plain,
% 0.60/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[338, 322])).
% 0.60/0.83 tff(340,plain,
% 0.60/0.83 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(341,plain,
% 0.60/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(342,plain,
% 0.60/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.60/0.83 tff(343,plain,
% 0.60/0.83 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[342, 35, 34, 33, 339])).
% 0.60/0.83 tff(344,plain,
% 0.60/0.83 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(345,plain,
% 0.60/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(346,plain,
% 0.60/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.60/0.83 tff(347,plain,
% 0.60/0.83 (k5_filter_2(A!0, B!1) = B!1),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[346, 313, 343])).
% 0.60/0.83 tff(348,plain,
% 0.60/0.83 (B!1 = k5_filter_2(A!0, B!1)),
% 0.60/0.83 inference(symmetry,[status(thm)],[347])).
% 0.60/0.83 tff(349,plain,
% 0.60/0.83 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[123, 348])).
% 0.60/0.83 tff(350,plain,
% 0.60/0.83 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.83 inference(symmetry,[status(thm)],[125])).
% 0.60/0.83 tff(351,plain,
% 0.60/0.83 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[347, 350])).
% 0.60/0.83 tff(352,plain,
% 0.60/0.83 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(353,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[352])).
% 0.60/0.83 tff(354,plain,
% 0.60/0.83 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(355,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[354])).
% 0.60/0.83 tff(356,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(357,plain,
% 0.60/0.83 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(358,plain,
% 0.60/0.83 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[357])).
% 0.60/0.83 tff(359,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 0.60/0.83 tff(360,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[359, 358])).
% 0.60/0.83 tff(361,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[360, 356])).
% 0.60/0.83 tff(362,plain,(
% 0.60/0.83 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.60/0.83 inference(skolemize,[status(sab)],[361])).
% 0.60/0.83 tff(363,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[362, 355])).
% 0.60/0.83 tff(364,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[363, 353])).
% 0.60/0.83 tff(365,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(366,plain,
% 0.60/0.83 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(367,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[366])).
% 0.60/0.83 tff(368,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[367, 365])).
% 0.60/0.83 tff(369,plain,
% 0.60/0.83 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(370,plain,
% 0.60/0.83 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[369, 368])).
% 0.60/0.83 tff(371,plain,
% 0.60/0.83 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[370, 35, 34, 33, 313, 364])).
% 0.60/0.83 tff(372,plain,
% 0.60/0.83 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[371, 351])).
% 0.60/0.83 tff(373,plain,
% 0.60/0.83 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(374,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[373])).
% 0.60/0.83 tff(375,plain,
% 0.60/0.83 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(376,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[375])).
% 0.60/0.83 tff(377,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(378,plain,
% 0.60/0.83 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(379,plain,
% 0.60/0.83 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[378])).
% 0.60/0.83 tff(380,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 0.60/0.83 tff(381,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.60/0.83 tff(382,plain,
% 0.60/0.83 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[381, 377])).
% 0.60/0.83 tff(383,plain,(
% 0.60/0.83 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[382])).
% 0.60/0.83 tff(384,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[383, 376])).
% 0.60/0.83 tff(385,plain,
% 0.60/0.83 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[384, 374])).
% 0.60/0.83 tff(386,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(387,plain,
% 0.60/0.83 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(388,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[387])).
% 0.60/0.83 tff(389,plain,
% 0.60/0.83 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[388, 386])).
% 0.60/0.83 tff(390,plain,
% 0.60/0.83 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(391,plain,
% 0.60/0.83 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.60/0.83 tff(392,plain,
% 0.60/0.83 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[391, 385, 269, 157, 151, 372])).
% 0.60/0.83 tff(393,plain,
% 0.60/0.83 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.60/0.83 inference(symmetry,[status(thm)],[392])).
% 0.60/0.83 tff(394,plain,
% 0.60/0.83 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k18_filter_2(A!0, B!1)),
% 0.60/0.83 inference(transitivity,[status(thm)],[393, 349, 320])).
% 0.60/0.83 tff(395,plain,
% 0.60/0.83 (r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)) <=> r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[394, 292])).
% 0.60/0.83 tff(396,plain,
% 0.60/0.83 (r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2)) <=> r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2))),
% 0.60/0.83 inference(symmetry,[status(thm)],[395])).
% 0.60/0.83 tff(397,plain,
% 0.60/0.83 ((~r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2))) <=> (~r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[396])).
% 0.60/0.83 tff(398,plain,
% 0.60/0.83 (~r1_tarski(k18_filter_2(A!0, B!1), k19_filter_2(A!0, C!2))),
% 0.60/0.83 inference(or_elim,[status(thm)],[40])).
% 0.60/0.83 tff(399,plain,
% 0.60/0.83 (~r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[398, 397])).
% 0.60/0.84 tff(400,plain,
% 0.60/0.84 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(401,plain,
% 0.60/0.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[400])).
% 0.60/0.84 tff(402,plain,
% 0.60/0.84 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(403,plain,
% 0.60/0.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[402])).
% 0.60/0.84 tff(404,plain,
% 0.60/0.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[403, 401])).
% 0.60/0.84 tff(405,plain,
% 0.60/0.84 (^[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_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(406,plain,
% 0.60/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[405])).
% 0.60/0.84 tff(407,plain,
% 0.60/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(408,plain,
% 0.60/0.84 (^[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((r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C))) <=> ((~r2_hidden(B, C)) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((~r2_hidden(B, C)) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((~r2_hidden(B, C)) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))) <=> (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))) <=> (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))) <=> ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(409,plain,
% 0.60/0.84 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[408])).
% 0.60/0.84 tff(410,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r2_hidden(B, C) => r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t29_filter_0')).
% 0.60/0.84 tff(411,plain,
% 0.60/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[410, 409])).
% 0.60/0.84 tff(412,plain,
% 0.60/0.84 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[411, 407])).
% 0.60/0.84 tff(413,plain,(
% 0.60/0.84 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.60/0.84 inference(skolemize,[status(sab)],[412])).
% 0.60/0.84 tff(414,plain,
% 0.60/0.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[413, 406])).
% 0.60/0.84 tff(415,plain,
% 0.60/0.84 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[414, 404])).
% 0.60/0.84 tff(416,plain,
% 0.60/0.84 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(417,plain,
% 0.60/0.84 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(418,plain,
% 0.60/0.84 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[417])).
% 0.60/0.84 tff(419,plain,
% 0.60/0.84 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[418, 416])).
% 0.60/0.84 tff(420,plain,
% 0.60/0.84 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(421,plain,
% 0.60/0.84 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (v1_xboole_0(C) | r1_tarski(k2_filter_0(A, B), k3_filter_0(A, C)) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.60/0.84 tff(422,plain,
% 0.60/0.84 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[421, 415, 269, 157, 151])).
% 0.60/0.84 tff(423,plain,
% 0.60/0.84 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(424,plain,
% 0.60/0.84 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(425,plain,
% 0.60/0.84 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[424, 423])).
% 0.60/0.84 tff(426,plain,
% 0.60/0.84 (![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[425, 422, 372])).
% 0.60/0.84 tff(427,plain,
% 0.60/0.84 (r2_hidden(B!1, C!2)),
% 0.60/0.84 inference(or_elim,[status(thm)],[40])).
% 0.60/0.84 tff(428,plain,
% 0.60/0.85 (((~![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))) | (v1_xboole_0(C!2) | (~r2_hidden(B!1, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))) | v1_xboole_0(C!2) | (~r2_hidden(B!1, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(429,plain,
% 0.60/0.85 ((~![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))) | (v1_xboole_0(C!2) | (~r2_hidden(B!1, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(430,plain,
% 0.60/0.85 ((~![C: $i] : (v1_xboole_0(C) | (~r2_hidden(B!1, C)) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C)))) | v1_xboole_0(C!2) | (~r2_hidden(B!1, C!2)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[429, 428])).
% 0.60/0.85 tff(431,plain,
% 0.60/0.85 (r1_tarski(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1), k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), C!2))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[430, 427, 91, 129, 426])).
% 0.60/0.85 tff(432,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[431, 399])).
% 0.60/0.85 % SZS output end Proof
% 0.60/0.85 % E exiting
%------------------------------------------------------------------------------