%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT318+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:19 AM UTC 2025
% Result : Theorem 265.79s 266.06s
% Output : Proof 267.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT318+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n016.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 20:15:17 EDT 2025
% 0.13/0.34 % CPUTime :
% 265.79/266.06 % SZS status Theorem
% 265.79/266.06 % SZS output start Proof
% 265.79/266.06 tff(m1_subset_1_type, type, (
% 265.79/266.06 m1_subset_1: ( $i * $i ) > $o)).
% 265.79/266.06 tff(k1_zfmisc_1_type, type, (
% 265.79/266.06 k1_zfmisc_1: $i > $i)).
% 265.79/266.06 tff(u1_struct_0_type, type, (
% 265.79/266.06 u1_struct_0: $i > $i)).
% 265.79/266.06 tff(tptp_fun_A_0_type, type, (
% 265.79/266.06 tptp_fun_A_0: $i)).
% 265.79/266.06 tff(k19_filter_2_type, type, (
% 265.79/266.06 k19_filter_2: ( $i * $i ) > $i)).
% 265.79/266.06 tff(k20_filter_2_type, type, (
% 265.79/266.06 k20_filter_2: ( $i * $i * $i ) > $i)).
% 265.79/266.06 tff(tptp_fun_C_2_type, type, (
% 265.79/266.06 tptp_fun_C_2: $i)).
% 265.79/266.06 tff(tptp_fun_B_1_type, type, (
% 265.79/266.06 tptp_fun_B_1: $i)).
% 265.79/266.06 tff(m2_lattice4_type, type, (
% 265.79/266.06 m2_lattice4: ( $i * $i ) > $o)).
% 265.79/266.06 tff(v1_xboole_0_type, type, (
% 265.79/266.06 v1_xboole_0: $i > $o)).
% 265.79/266.06 tff(m2_filter_2_type, type, (
% 265.79/266.06 m2_filter_2: ( $i * $i ) > $o)).
% 265.79/266.06 tff(v10_lattices_type, type, (
% 265.79/266.06 v10_lattices: $i > $o)).
% 265.79/266.06 tff(l3_lattices_type, type, (
% 265.79/266.06 l3_lattices: $i > $o)).
% 265.79/266.06 tff(v3_struct_0_type, type, (
% 265.79/266.06 v3_struct_0: $i > $o)).
% 265.79/266.06 tff(r1_filter_2_type, type, (
% 265.79/266.06 r1_filter_2: ( $i * $i * $i ) > $o)).
% 265.79/266.06 tff(k4_subset_1_type, type, (
% 265.79/266.06 k4_subset_1: ( $i * $i * $i ) > $i)).
% 265.79/266.06 tff(l1_struct_0_type, type, (
% 265.79/266.06 l1_struct_0: $i > $o)).
% 265.79/266.06 tff(l2_lattices_type, type, (
% 265.79/266.06 l2_lattices: $i > $o)).
% 265.79/266.06 tff(l1_lattices_type, type, (
% 265.79/266.06 l1_lattices: $i > $o)).
% 265.79/266.06 tff(k3_filter_2_type, type, (
% 265.79/266.06 k3_filter_2: ( $i * $i ) > $i)).
% 265.79/266.06 tff(k7_filter_2_type, type, (
% 265.79/266.06 k7_filter_2: ( $i * $i ) > $i)).
% 265.79/266.06 tff(k1_lattice2_type, type, (
% 265.79/266.06 k1_lattice2: $i > $i)).
% 265.79/266.06 tff(k8_filter_2_type, type, (
% 265.79/266.06 k8_filter_2: ( $i * $i ) > $i)).
% 265.79/266.06 tff(tptp_fun_B_11_type, type, (
% 265.79/266.06 tptp_fun_B_11: $i > $i)).
% 265.79/266.06 tff(g3_lattices_type, type, (
% 265.79/266.06 g3_lattices: ( $i * $i * $i ) > $i)).
% 265.79/266.06 tff(u2_lattices_type, type, (
% 265.79/266.06 u2_lattices: $i > $i)).
% 265.79/266.06 tff(u1_lattices_type, type, (
% 265.79/266.06 u1_lattices: $i > $i)).
% 265.79/266.06 tff(k3_filter_0_type, type, (
% 265.79/266.06 k3_filter_0: ( $i * $i ) > $i)).
% 265.79/266.06 tff(v3_lattices_type, type, (
% 265.79/266.06 v3_lattices: $i > $o)).
% 265.79/266.06 tff(m1_relset_1_type, type, (
% 265.79/266.06 m1_relset_1: ( $i * $i * $i ) > $o)).
% 265.79/266.06 tff(k2_zfmisc_1_type, type, (
% 265.79/266.06 k2_zfmisc_1: ( $i * $i ) > $i)).
% 265.79/266.06 tff(m2_relset_1_type, type, (
% 265.79/266.06 m2_relset_1: ( $i * $i * $i ) > $o)).
% 265.79/266.06 tff(v1_funct_2_type, type, (
% 265.79/266.06 v1_funct_2: ( $i * $i * $i ) > $o)).
% 265.79/266.06 tff(v1_funct_1_type, type, (
% 265.79/266.06 v1_funct_1: $i > $o)).
% 265.79/266.06 tff(v9_lattices_type, type, (
% 265.79/266.06 v9_lattices: $i > $o)).
% 265.79/266.06 tff(v8_lattices_type, type, (
% 265.79/266.06 v8_lattices: $i > $o)).
% 265.79/266.06 tff(v7_lattices_type, type, (
% 265.79/266.06 v7_lattices: $i > $o)).
% 265.79/266.06 tff(v6_lattices_type, type, (
% 265.79/266.06 v6_lattices: $i > $o)).
% 265.79/266.06 tff(v5_lattices_type, type, (
% 265.79/266.06 v5_lattices: $i > $o)).
% 265.79/266.06 tff(v4_lattices_type, type, (
% 265.79/266.06 v4_lattices: $i > $o)).
% 265.79/266.06 tff(k5_filter_0_type, type, (
% 265.79/266.06 k5_filter_0: ( $i * $i * $i ) > $i)).
% 265.79/266.06 tff(tptp_fun_B_7_type, type, (
% 265.79/266.06 tptp_fun_B_7: $i > $i)).
% 265.79/266.06 tff(tptp_fun_B_19_type, type, (
% 265.79/266.06 tptp_fun_B_19: $i > $i)).
% 265.79/266.06 tff(m1_filter_0_type, type, (
% 265.79/266.06 m1_filter_0: ( $i * $i ) > $o)).
% 265.79/266.06 tff(m1_filter_2_type, type, (
% 265.79/266.06 m1_filter_2: ( $i * $i ) > $o)).
% 265.79/266.06 tff(k15_filter_2_type, type, (
% 265.79/266.06 k15_filter_2: ( $i * $i ) > $i)).
% 265.79/266.06 tff(k2_xboole_0_type, type, (
% 265.79/266.06 k2_xboole_0: ( $i * $i ) > $i)).
% 265.79/266.06 tff(1,plain,
% 265.79/266.06 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 265.79/266.06 inference(bind,[status(th)],[])).
% 265.79/266.06 tff(2,plain,
% 265.79/266.06 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.06 inference(quant_intro,[status(thm)],[1])).
% 265.79/266.06 tff(3,plain,
% 265.79/266.06 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 265.79/266.06 inference(bind,[status(th)],[])).
% 265.79/266.06 tff(4,plain,
% 265.79/266.06 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.06 inference(quant_intro,[status(thm)],[3])).
% 265.79/266.06 tff(5,plain,
% 265.79/266.06 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.06 inference(transitivity,[status(thm)],[4, 2])).
% 265.79/266.06 tff(6,plain,
% 265.79/266.06 (^[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(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 265.79/266.06 inference(bind,[status(th)],[])).
% 265.79/266.06 tff(7,plain,
% 265.79/266.06 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.06 inference(quant_intro,[status(thm)],[6])).
% 265.79/266.06 tff(8,plain,
% 265.79/266.06 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 265.79/266.06 inference(rewrite,[status(thm)],[])).
% 265.79/266.06 tff(9,plain,
% 265.79/266.06 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(10,plain,
% 265.79/266.07 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[9])).
% 265.79/266.07 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 265.79/266.07 tff(12,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[11, 10])).
% 265.79/266.07 tff(13,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[12, 8])).
% 265.79/266.07 tff(14,plain,(
% 265.79/266.07 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 265.79/266.07 inference(skolemize,[status(sab)],[13])).
% 265.79/266.07 tff(15,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[14, 7])).
% 265.79/266.07 tff(16,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[15, 5])).
% 265.79/266.07 tff(17,plain,
% 265.79/266.07 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(18,plain,
% 265.79/266.07 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C)))))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(19,plain,
% 265.79/266.07 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ![C: $i] : (m2_filter_2(C, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C)))))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(20,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ![C: $i] : (m2_filter_2(C, A) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t52_filter_2')).
% 265.79/266.07 tff(21,plain,
% 265.79/266.07 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[20, 19])).
% 265.79/266.07 tff(22,plain,
% 265.79/266.07 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[21, 18])).
% 265.79/266.07 tff(23,plain,
% 265.79/266.07 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[22, 18])).
% 265.79/266.07 tff(24,plain,
% 265.79/266.07 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ![C: $i] : ((~m2_filter_2(C, A)) | r1_filter_2(u1_struct_0(A), k19_filter_2(A, k4_subset_1(u1_struct_0(A), B, C)), k19_filter_2(A, k20_filter_2(A, B, C))))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[23, 18])).
% 265.79/266.07 tff(25,plain,
% 265.79/266.07 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m2_filter_2(B!1, A!0) & (~((~m2_filter_2(C!2, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[24, 17])).
% 265.79/266.07 tff(26,plain,
% 265.79/266.07 (l3_lattices(A!0)),
% 265.79/266.07 inference(and_elim,[status(thm)],[25])).
% 265.79/266.07 tff(27,plain,
% 265.79/266.07 (v10_lattices(A!0)),
% 265.79/266.07 inference(and_elim,[status(thm)],[25])).
% 265.79/266.07 tff(28,plain,
% 265.79/266.07 (~v3_struct_0(A!0)),
% 265.79/266.07 inference(and_elim,[status(thm)],[25])).
% 265.79/266.07 tff(29,plain,
% 265.79/266.07 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(30,plain,
% 265.79/266.07 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(31,plain,
% 265.79/266.07 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[30, 29])).
% 265.79/266.07 tff(32,plain,
% 265.79/266.07 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[31, 28, 27, 26, 16])).
% 265.79/266.07 tff(33,plain,
% 265.79/266.07 (m2_filter_2(B!1, A!0)),
% 265.79/266.07 inference(and_elim,[status(thm)],[25])).
% 265.79/266.07 tff(34,plain,
% 265.79/266.07 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(35,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(36,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(B!1, A!0)) | (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[35, 34])).
% 265.79/266.07 tff(37,plain,
% 265.79/266.07 (~(v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0)))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[36, 33, 32])).
% 265.79/266.07 tff(38,plain,
% 265.79/266.07 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | (~v1_xboole_0(B!1))),
% 265.79/266.07 inference(tautology,[status(thm)],[])).
% 265.79/266.07 tff(39,plain,
% 265.79/266.07 (~v1_xboole_0(B!1)),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[38, 37])).
% 265.79/266.07 tff(40,plain,
% 265.79/266.07 (~((~m2_filter_2(C!2, A!0)) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 265.79/266.07 inference(and_elim,[status(thm)],[25])).
% 265.79/266.07 tff(41,plain,
% 265.79/266.07 (m2_filter_2(C!2, A!0)),
% 265.79/266.07 inference(or_elim,[status(thm)],[40])).
% 265.79/266.07 tff(42,plain,
% 265.79/266.07 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(43,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(44,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[43, 42])).
% 265.79/266.07 tff(45,plain,
% 265.79/266.07 (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[44, 41, 32])).
% 265.79/266.07 tff(46,plain,
% 265.79/266.07 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | (~v1_xboole_0(C!2))),
% 265.79/266.07 inference(tautology,[status(thm)],[])).
% 265.79/266.07 tff(47,plain,
% 265.79/266.07 (~v1_xboole_0(C!2)),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[46, 45])).
% 265.79/266.07 tff(48,plain,
% 265.79/266.07 ((v1_xboole_0(B!1) | (~m2_lattice4(B!1, A!0))) | m2_lattice4(B!1, A!0)),
% 265.79/266.07 inference(tautology,[status(thm)],[])).
% 265.79/266.07 tff(49,plain,
% 265.79/266.07 (m2_lattice4(B!1, A!0)),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[48, 37])).
% 265.79/266.07 tff(50,plain,
% 265.79/266.07 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(51,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[50])).
% 265.79/266.07 tff(52,plain,
% 265.79/266.07 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(53,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[52])).
% 265.79/266.07 tff(54,plain,
% 265.79/266.07 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(55,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[54])).
% 265.79/266.07 tff(56,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(transitivity,[status(thm)],[55, 53])).
% 265.79/266.07 tff(57,plain,
% 265.79/266.07 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(58,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[57])).
% 265.79/266.07 tff(59,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(60,plain,
% 265.79/266.07 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(61,plain,
% 265.79/266.07 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[60])).
% 265.79/266.07 tff(62,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 265.79/266.07 tff(63,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[62, 61])).
% 265.79/266.07 tff(64,plain,
% 265.79/266.07 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[63, 59])).
% 265.79/266.07 tff(65,plain,(
% 265.79/266.07 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(skolemize,[status(sab)],[64])).
% 265.79/266.07 tff(66,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[65, 58])).
% 265.79/266.07 tff(67,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[66, 56])).
% 265.79/266.07 tff(68,plain,
% 265.79/266.07 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[67, 51])).
% 265.79/266.07 tff(69,plain,
% 265.79/266.07 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(70,plain,
% 265.79/266.07 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(71,plain,
% 265.79/266.07 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[70, 69])).
% 265.79/266.07 tff(72,plain,
% 265.79/266.07 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[71, 28, 27, 26, 68])).
% 265.79/266.07 tff(73,plain,
% 265.79/266.07 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(74,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(75,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(B!1, A!0)) | m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[74, 73])).
% 265.79/266.07 tff(76,plain,
% 265.79/266.07 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[75, 72, 49])).
% 265.79/266.07 tff(77,plain,
% 265.79/266.07 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | m2_lattice4(C!2, A!0)),
% 265.79/266.07 inference(tautology,[status(thm)],[])).
% 265.79/266.07 tff(78,plain,
% 265.79/266.07 (m2_lattice4(C!2, A!0)),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[77, 45])).
% 265.79/266.07 tff(79,plain,
% 265.79/266.07 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(80,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(81,plain,
% 265.79/266.07 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[80, 79])).
% 265.79/266.07 tff(82,plain,
% 265.79/266.07 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[81, 72, 78])).
% 265.79/266.07 tff(83,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(84,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[83])).
% 265.79/266.07 tff(85,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ((v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))))), rewrite(((v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(86,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[85])).
% 265.79/266.07 tff(87,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(88,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(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)))) & (~v1_xboole_0(C))) <=> (((~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(C))))), 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(C))) <=> ((~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(C)))), (((((((~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(C))) <=> ((~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(C))))), ((((((((~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(C))) & m1_subset_1(C, 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))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), 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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), 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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), 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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), 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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), 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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(89,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[88])).
% 265.79/266.07 tff(90,axiom,(![A: $i, B: $i, C: $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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k20_filter_2')).
% 265.79/266.07 tff(91,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[90, 89])).
% 265.79/266.07 tff(92,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[91, 87])).
% 265.79/266.07 tff(93,plain,(
% 265.79/266.07 ![A: $i, B: $i, C: $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))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))))),
% 265.79/266.07 inference(skolemize,[status(sab)],[92])).
% 265.79/266.07 tff(94,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[93, 86])).
% 265.79/266.07 tff(95,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[94, 84])).
% 265.79/266.07 tff(96,plain,
% 265.79/266.07 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(97,plain,
% 265.79/266.07 ((v1_xboole_0(C!2) | v3_struct_0(A!0) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, 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, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(98,plain,
% 265.79/266.07 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1)))),
% 265.79/266.07 inference(monotonicity,[status(thm)],[97])).
% 265.79/266.07 tff(99,plain,
% 265.79/266.07 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1))),
% 265.79/266.07 inference(transitivity,[status(thm)],[98, 96])).
% 265.79/266.07 tff(100,plain,
% 265.79/266.07 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(B!1) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.07 inference(quant_inst,[status(thm)],[])).
% 265.79/266.07 tff(101,plain,
% 265.79/266.07 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | m1_subset_1(k20_filter_2(A, B, C), k1_zfmisc_1(u1_struct_0(A))) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1)),
% 265.79/266.07 inference(modus_ponens,[status(thm)],[100, 99])).
% 265.79/266.07 tff(102,plain,
% 265.79/266.07 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(C!2) | v1_xboole_0(B!1)),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[101, 28, 27, 26, 95])).
% 265.79/266.07 tff(103,plain,
% 265.79/266.07 (m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.07 inference(unit_resolution,[status(thm)],[102, 82, 76, 47, 39])).
% 265.79/266.07 tff(104,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(105,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[104])).
% 265.79/266.07 tff(106,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~v1_xboole_0(k20_filter_2(A, B, C))) | (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite(((~v1_xboole_0(k20_filter_2(A, B, C))) | (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 265.79/266.07 inference(bind,[status(th)],[])).
% 265.79/266.07 tff(107,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.07 inference(quant_intro,[status(thm)],[106])).
% 265.79/266.07 tff(108,plain,
% 265.79/266.07 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.07 inference(rewrite,[status(thm)],[])).
% 265.79/266.07 tff(109,plain,
% 265.79/266.07 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(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)))) & (~v1_xboole_0(C))) <=> (((~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(C))))), 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(C))) <=> ((~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(C)))), (((((((~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(C))) <=> ((~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(C))))), ((((((((~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(C))) & m1_subset_1(C, 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))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) & (~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) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) & (~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)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C)))) <=> (((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C)))))), 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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C)))) <=> ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, 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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C)))) <=> ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(110,plain,
% 265.79/266.08 (![A: $i, B: $i, C: $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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[109])).
% 265.79/266.08 tff(111,axiom,(![A: $i, B: $i, C: $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)))) & (~v1_xboole_0(C))) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (~v1_xboole_0(k20_filter_2(A, B, C))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc3_filter_2')).
% 265.79/266.08 tff(112,plain,
% 265.79/266.08 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[111, 110])).
% 265.79/266.08 tff(113,plain,
% 265.79/266.08 (![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[112, 108])).
% 265.79/266.08 tff(114,plain,(
% 265.79/266.08 ![A: $i, B: $i, C: $i] : ((~v1_xboole_0(k20_filter_2(A, B, C))) | (~((~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(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.79/266.08 inference(skolemize,[status(sab)],[113])).
% 265.79/266.08 tff(115,plain,
% 265.79/266.08 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[114, 107])).
% 265.79/266.08 tff(116,plain,
% 265.79/266.08 (![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[115, 105])).
% 265.79/266.08 tff(117,plain,
% 265.79/266.08 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(118,plain,
% 265.79/266.08 ((v1_xboole_0(C!2) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, 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, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(119,plain,
% 265.79/266.08 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2)))))),
% 265.79/266.08 inference(monotonicity,[status(thm)],[118])).
% 265.79/266.08 tff(120,plain,
% 265.79/266.08 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))))),
% 265.79/266.08 inference(transitivity,[status(thm)],[119, 117])).
% 265.79/266.08 tff(121,plain,
% 265.79/266.08 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v1_xboole_0(C!2) | v3_struct_0(A!0) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(122,plain,
% 265.79/266.08 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(C) | v3_struct_0(A) | v1_xboole_0(B) | (~v1_xboole_0(k20_filter_2(A, B, C))) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[121, 120])).
% 265.79/266.08 tff(123,plain,
% 265.79/266.08 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | v1_xboole_0(B!1) | (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[122, 28, 27, 26, 116])).
% 265.79/266.08 tff(124,plain,
% 265.79/266.08 (~v1_xboole_0(k20_filter_2(A!0, B!1, C!2))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[123, 82, 76, 47, 39])).
% 265.79/266.08 tff(125,plain,
% 265.79/266.08 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(126,plain,
% 265.79/266.08 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~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) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[125])).
% 265.79/266.08 tff(127,plain,
% 265.79/266.08 (^[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))))) | m2_filter_2(k19_filter_2(A, B), 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))) | m2_filter_2(k19_filter_2(A, B), 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))) | m2_filter_2(k19_filter_2(A, B), A)) <=> (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(128,plain,
% 265.79/266.08 (![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))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[127])).
% 265.79/266.08 tff(129,plain,
% 265.79/266.08 (![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))))) | m2_filter_2(k19_filter_2(A, B), A)) <=> ![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))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(130,plain,
% 265.79/266.08 (^[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)))) => m2_filter_2(k19_filter_2(A, B), 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)))) => m2_filter_2(k19_filter_2(A, B), 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)))) => m2_filter_2(k19_filter_2(A, B), 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))))) | m2_filter_2(k19_filter_2(A, B), 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)))) => m2_filter_2(k19_filter_2(A, B), 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))))) | m2_filter_2(k19_filter_2(A, B), A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(131,plain,
% 265.79/266.08 (![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)))) => m2_filter_2(k19_filter_2(A, B), A)) <=> ![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))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[130])).
% 265.79/266.08 tff(132,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)))) => m2_filter_2(k19_filter_2(A, B), A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k19_filter_2')).
% 265.79/266.08 tff(133,plain,
% 265.79/266.08 (![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))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[132, 131])).
% 265.79/266.08 tff(134,plain,
% 265.79/266.08 (![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))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[133, 129])).
% 265.79/266.08 tff(135,plain,(
% 265.79/266.08 ![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))))) | m2_filter_2(k19_filter_2(A, B), A))),
% 265.79/266.08 inference(skolemize,[status(sab)],[134])).
% 265.79/266.08 tff(136,plain,
% 265.79/266.08 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[135, 128])).
% 265.79/266.08 tff(137,plain,
% 265.79/266.08 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[136, 126])).
% 265.79/266.08 tff(138,plain,
% 265.79/266.08 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(139,plain,
% 265.79/266.08 ((v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(140,plain,
% 265.79/266.08 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 265.79/266.08 inference(monotonicity,[status(thm)],[139])).
% 265.79/266.08 tff(141,plain,
% 265.79/266.08 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.79/266.08 inference(transitivity,[status(thm)],[140, 138])).
% 265.79/266.08 tff(142,plain,
% 265.79/266.08 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(143,plain,
% 265.79/266.08 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | m2_filter_2(k19_filter_2(A, B), 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)) | v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[142, 141])).
% 265.79/266.08 tff(144,plain,
% 265.79/266.08 (v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[143, 28, 27, 26, 137])).
% 265.79/266.08 tff(145,plain,
% 265.79/266.08 (m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[144, 124, 103])).
% 265.79/266.08 tff(146,plain,
% 265.79/266.08 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(147,plain,
% 265.79/266.08 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)))))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(148,plain,
% 265.79/266.08 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[147, 146])).
% 265.79/266.08 tff(149,plain,
% 265.79/266.08 (~(v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[148, 32, 145])).
% 265.79/266.08 tff(150,plain,
% 265.79/266.08 ((v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0))) | m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)),
% 265.79/266.08 inference(tautology,[status(thm)],[])).
% 265.79/266.08 tff(151,plain,
% 265.79/266.08 (m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[150, 149])).
% 265.79/266.08 tff(152,plain,
% 265.79/266.08 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(153,plain,
% 265.79/266.08 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(154,plain,
% 265.79/266.08 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0)) | m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[153, 152])).
% 265.79/266.08 tff(155,plain,
% 265.79/266.08 (m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[154, 72, 151])).
% 265.79/266.08 tff(156,plain,
% 265.79/266.08 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(157,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[156])).
% 265.79/266.08 tff(158,plain,
% 265.79/266.08 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(159,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[158])).
% 265.79/266.08 tff(160,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(161,plain,
% 265.79/266.08 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(162,plain,
% 265.79/266.08 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[161])).
% 265.79/266.08 tff(163,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 265.79/266.08 tff(164,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[163, 162])).
% 265.79/266.08 tff(165,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[164, 160])).
% 265.79/266.08 tff(166,plain,(
% 265.79/266.08 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 265.79/266.08 inference(skolemize,[status(sab)],[165])).
% 265.79/266.08 tff(167,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[166, 159])).
% 265.79/266.08 tff(168,plain,
% 265.79/266.08 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[167, 157])).
% 265.79/266.08 tff(169,plain,
% 265.79/266.08 (((~![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)))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(170,plain,
% 265.79/266.08 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(171,plain,
% 265.79/266.08 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[170, 169])).
% 265.79/266.08 tff(172,plain,
% 265.79/266.08 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[171, 26, 168])).
% 265.79/266.08 tff(173,plain,
% 265.79/266.08 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 265.79/266.08 inference(tautology,[status(thm)],[])).
% 265.79/266.08 tff(174,plain,
% 265.79/266.08 (l2_lattices(A!0)),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[173, 172])).
% 265.79/266.08 tff(175,plain,
% 265.79/266.08 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(176,plain,
% 265.79/266.08 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[175])).
% 265.79/266.08 tff(177,plain,
% 265.79/266.08 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(178,plain,
% 265.79/266.08 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(179,plain,
% 265.79/266.08 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[178])).
% 265.79/266.08 tff(180,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 265.79/266.08 tff(181,plain,
% 265.79/266.08 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[180, 179])).
% 265.79/266.08 tff(182,plain,
% 265.79/266.08 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[181, 177])).
% 265.79/266.08 tff(183,plain,(
% 265.79/266.08 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(skolemize,[status(sab)],[182])).
% 265.79/266.08 tff(184,plain,
% 265.79/266.08 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[183, 176])).
% 265.79/266.08 tff(185,plain,
% 265.79/266.08 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(186,plain,
% 265.79/266.08 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(187,plain,
% 265.79/266.08 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[186, 185])).
% 265.79/266.08 tff(188,plain,
% 265.79/266.08 (l1_struct_0(A!0)),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[187, 184, 174])).
% 265.79/266.08 tff(189,plain,
% 265.79/266.08 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(190,plain,
% 265.79/266.08 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[189])).
% 265.79/266.08 tff(191,plain,
% 265.79/266.08 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(192,plain,
% 265.79/266.08 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[191])).
% 265.79/266.08 tff(193,plain,
% 265.79/266.08 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(194,plain,
% 265.79/266.08 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(195,plain,
% 265.79/266.08 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[194])).
% 265.79/266.08 tff(196,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 265.79/266.08 tff(197,plain,
% 265.79/266.08 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[196, 195])).
% 265.79/266.08 tff(198,plain,
% 265.79/266.08 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[197, 193])).
% 265.79/266.08 tff(199,plain,(
% 265.79/266.08 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 265.79/266.08 inference(skolemize,[status(sab)],[198])).
% 265.79/266.08 tff(200,plain,
% 265.79/266.08 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[199, 192])).
% 265.79/266.08 tff(201,plain,
% 265.79/266.08 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[200, 190])).
% 265.79/266.08 tff(202,plain,
% 265.79/266.08 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(203,plain,
% 265.79/266.08 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 265.79/266.08 inference(rewrite,[status(thm)],[])).
% 265.79/266.08 tff(204,plain,
% 265.79/266.08 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 265.79/266.08 inference(monotonicity,[status(thm)],[203])).
% 265.79/266.08 tff(205,plain,
% 265.79/266.08 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 265.79/266.08 inference(transitivity,[status(thm)],[204, 202])).
% 265.79/266.08 tff(206,plain,
% 265.79/266.08 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 265.79/266.08 inference(quant_inst,[status(thm)],[])).
% 265.79/266.08 tff(207,plain,
% 265.79/266.08 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 265.79/266.08 inference(modus_ponens,[status(thm)],[206, 205])).
% 265.79/266.08 tff(208,plain,
% 265.79/266.08 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[207, 28, 201])).
% 265.79/266.08 tff(209,plain,
% 265.79/266.08 (~v1_xboole_0(u1_struct_0(A!0))),
% 265.79/266.08 inference(unit_resolution,[status(thm)],[208, 188])).
% 265.79/266.08 tff(210,plain,
% 265.79/266.08 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A))))),
% 265.79/266.08 inference(bind,[status(th)],[])).
% 265.79/266.08 tff(211,plain,
% 265.79/266.08 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))),
% 265.79/266.08 inference(quant_intro,[status(thm)],[210])).
% 265.79/266.08 tff(212,plain,
% 265.79/266.08 (^[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))) | m2_filter_2(tptp_fun_B_11(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(tptp_fun_B_11(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m2_filter_2(tptp_fun_B_11(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(tptp_fun_B_11(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(213,plain,
% 265.79/266.09 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(tptp_fun_B_11(A), A)) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[212])).
% 265.79/266.09 tff(214,plain,
% 265.79/266.09 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(215,plain,
% 265.79/266.09 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(216,plain,
% 265.79/266.09 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[215])).
% 265.79/266.09 tff(217,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m2_filter_2(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m2_filter_2')).
% 265.79/266.09 tff(218,plain,
% 265.79/266.09 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[217, 216])).
% 265.79/266.09 tff(219,plain,
% 265.79/266.09 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m2_filter_2(B, A))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[218, 214])).
% 265.79/266.09 tff(220,plain,(
% 265.79/266.09 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m2_filter_2(tptp_fun_B_11(A), A))),
% 265.79/266.09 inference(skolemize,[status(sab)],[219])).
% 265.79/266.09 tff(221,plain,
% 265.79/266.09 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[220, 213])).
% 265.79/266.09 tff(222,plain,
% 265.79/266.09 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[221, 211])).
% 265.79/266.09 tff(223,plain,
% 265.79/266.09 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(224,plain,
% 265.79/266.09 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(225,plain,
% 265.79/266.09 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0)))),
% 265.79/266.09 inference(monotonicity,[status(thm)],[224])).
% 265.79/266.09 tff(226,plain,
% 265.79/266.09 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0))),
% 265.79/266.09 inference(transitivity,[status(thm)],[225, 223])).
% 265.79/266.09 tff(227,plain,
% 265.79/266.09 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0) | (~v10_lattices(A!0)))),
% 265.79/266.09 inference(quant_inst,[status(thm)],[])).
% 265.79/266.09 tff(228,plain,
% 265.79/266.09 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m2_filter_2(tptp_fun_B_11(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(tptp_fun_B_11(A!0), A!0)),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[227, 226])).
% 265.79/266.09 tff(229,plain,
% 265.79/266.09 (m2_filter_2(tptp_fun_B_11(A!0), A!0)),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[228, 28, 27, 26, 222])).
% 265.79/266.09 tff(230,plain,
% 265.79/266.09 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(tptp_fun_B_11(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(tptp_fun_B_11(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(231,plain,
% 265.79/266.09 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(tptp_fun_B_11(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)))))),
% 265.79/266.09 inference(quant_inst,[status(thm)],[])).
% 265.79/266.09 tff(232,plain,
% 265.79/266.09 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(tptp_fun_B_11(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[231, 230])).
% 265.79/266.09 tff(233,plain,
% 265.79/266.09 (~(v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)))),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[232, 229, 32])).
% 265.79/266.09 tff(234,plain,
% 265.79/266.09 ((v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0))) | m2_lattice4(tptp_fun_B_11(A!0), A!0)),
% 265.79/266.09 inference(tautology,[status(thm)],[])).
% 265.79/266.09 tff(235,plain,
% 265.79/266.09 (m2_lattice4(tptp_fun_B_11(A!0), A!0)),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[234, 233])).
% 265.79/266.09 tff(236,plain,
% 265.79/266.09 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_11(A!0), A!0)) | m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)) | m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(237,plain,
% 265.79/266.09 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_11(A!0), A!0)) | m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.79/266.09 inference(quant_inst,[status(thm)],[])).
% 265.79/266.09 tff(238,plain,
% 265.79/266.09 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0)) | m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[237, 236])).
% 265.79/266.09 tff(239,plain,
% 265.79/266.09 (m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[238, 72, 235])).
% 265.79/266.09 tff(240,plain,
% 265.79/266.09 ((v1_xboole_0(tptp_fun_B_11(A!0)) | (~m2_lattice4(tptp_fun_B_11(A!0), A!0))) | (~v1_xboole_0(tptp_fun_B_11(A!0)))),
% 265.79/266.09 inference(tautology,[status(thm)],[])).
% 265.79/266.09 tff(241,plain,
% 265.79/266.09 (~v1_xboole_0(tptp_fun_B_11(A!0))),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[240, 233])).
% 265.79/266.09 tff(242,plain,
% 265.79/266.09 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(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) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(243,plain,
% 265.79/266.09 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(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) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[242])).
% 265.79/266.09 tff(244,plain,
% 265.79/266.09 (^[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))))), (((~v1_xboole_0(k7_filter_2(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)))))) <=> ((~v1_xboole_0(k7_filter_2(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)))))), rewrite(((~v1_xboole_0(k7_filter_2(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)))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~v1_xboole_0(k7_filter_2(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)))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(245,plain,
% 265.79/266.09 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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)))))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[244])).
% 265.79/266.09 tff(246,plain,
% 265.79/266.09 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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)))))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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))))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(247,plain,
% 265.79/266.09 (^[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)))) => (~v1_xboole_0(k7_filter_2(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)))) => (~v1_xboole_0(k7_filter_2(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)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> ((~v1_xboole_0(k7_filter_2(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))))))), (((((((~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(k7_filter_2(A, B)))) <=> ((~v1_xboole_0(k7_filter_2(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))))))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(248,plain,
% 265.79/266.09 (![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)))) => (~v1_xboole_0(k7_filter_2(A, B)))) <=> ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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))))))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[247])).
% 265.79/266.09 tff(249,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)))) => (~v1_xboole_0(k7_filter_2(A, B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_filter_2')).
% 265.79/266.09 tff(250,plain,
% 265.79/266.09 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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))))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[249, 248])).
% 265.79/266.09 tff(251,plain,
% 265.79/266.09 (![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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))))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[250, 246])).
% 265.79/266.09 tff(252,plain,(
% 265.79/266.09 ![A: $i, B: $i] : ((~v1_xboole_0(k7_filter_2(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))))))),
% 265.79/266.09 inference(skolemize,[status(sab)],[251])).
% 265.79/266.09 tff(253,plain,
% 265.79/266.09 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[252, 245])).
% 265.79/266.09 tff(254,plain,
% 265.79/266.09 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[253, 243])).
% 265.79/266.09 tff(255,plain,
% 265.79/266.09 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(256,plain,
% 265.79/266.09 ((v1_xboole_0(tptp_fun_B_11(A!0)) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), 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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(257,plain,
% 265.79/266.09 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(tptp_fun_B_11(A!0)) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))))))),
% 265.79/266.09 inference(monotonicity,[status(thm)],[256])).
% 265.79/266.09 tff(258,plain,
% 265.79/266.09 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(tptp_fun_B_11(A!0)) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))))),
% 265.79/266.09 inference(transitivity,[status(thm)],[257, 255])).
% 265.79/266.09 tff(259,plain,
% 265.79/266.09 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(tptp_fun_B_11(A!0)) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.79/266.09 inference(quant_inst,[status(thm)],[])).
% 265.79/266.09 tff(260,plain,
% 265.79/266.09 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)) | v1_xboole_0(tptp_fun_B_11(A!0)) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[259, 258])).
% 265.79/266.09 tff(261,plain,
% 265.79/266.09 (~v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0)))),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[260, 28, 27, 26, 254, 241, 239])).
% 265.79/266.09 tff(262,plain,
% 265.79/266.09 (^[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))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(263,plain,
% 265.79/266.09 (![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)))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[262])).
% 265.79/266.09 tff(264,plain,
% 265.79/266.09 (^[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)))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(265,plain,
% 265.79/266.09 (![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)))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[264])).
% 265.79/266.09 tff(266,plain,
% 265.79/266.09 (![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)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(267,plain,
% 265.79/266.09 (^[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)))))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(268,plain,
% 265.79/266.09 (![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)))))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[267])).
% 265.79/266.09 tff(269,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/sandbox/benchmark/theBenchmark.p','dt_k7_filter_2')).
% 265.79/266.09 tff(270,plain,
% 265.79/266.09 (![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)))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[269, 268])).
% 265.79/266.09 tff(271,plain,
% 265.79/266.09 (![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)))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[270, 266])).
% 265.79/266.09 tff(272,plain,(
% 265.79/266.09 ![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)))))),
% 265.79/266.09 inference(skolemize,[status(sab)],[271])).
% 265.79/266.09 tff(273,plain,
% 265.79/266.09 (![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)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[272, 265])).
% 265.79/266.09 tff(274,plain,
% 265.79/266.09 (![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)))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[273, 263])).
% 265.79/266.09 tff(275,plain,
% 265.79/266.09 (((~![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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), 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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(276,plain,
% 265.79/266.09 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), 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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.79/266.09 inference(rewrite,[status(thm)],[])).
% 265.79/266.09 tff(277,plain,
% 265.79/266.09 (((~![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, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), 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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 265.79/266.09 inference(monotonicity,[status(thm)],[276])).
% 265.79/266.09 tff(278,plain,
% 265.79/266.09 (((~![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, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), 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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.79/266.09 inference(transitivity,[status(thm)],[277, 275])).
% 265.79/266.09 tff(279,plain,
% 265.79/266.09 ((~![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, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.79/266.09 inference(quant_inst,[status(thm)],[])).
% 265.79/266.09 tff(280,plain,
% 265.79/266.09 ((~![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(tptp_fun_B_11(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.79/266.09 inference(modus_ponens,[status(thm)],[279, 278])).
% 265.79/266.09 tff(281,plain,
% 265.79/266.09 (m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.79/266.09 inference(unit_resolution,[status(thm)],[280, 28, 27, 26, 274, 239])).
% 265.79/266.09 tff(282,plain,
% 265.79/266.09 (^[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))))))))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(283,plain,
% 265.79/266.09 (![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)))))))))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[282])).
% 265.79/266.09 tff(284,plain,
% 265.79/266.09 (^[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))))))))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(285,plain,
% 265.79/266.09 (![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)))))))))),
% 265.79/266.09 inference(quant_intro,[status(thm)],[284])).
% 265.79/266.09 tff(286,plain,
% 265.79/266.09 (![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)))))))))),
% 265.79/266.09 inference(transitivity,[status(thm)],[285, 283])).
% 265.79/266.09 tff(287,plain,
% 265.79/266.09 (^[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)))))))))))),
% 265.79/266.09 inference(bind,[status(th)],[])).
% 265.79/266.09 tff(288,plain,
% 265.79/266.09 (![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)))))))))),
% 265.79/266.10 inference(quant_intro,[status(thm)],[287])).
% 265.79/266.10 tff(289,plain,
% 265.79/266.10 (![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)))))))),
% 265.79/266.10 inference(rewrite,[status(thm)],[])).
% 265.79/266.10 tff(290,plain,
% 265.79/266.10 (^[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)))))))))),
% 265.79/266.10 inference(bind,[status(th)],[])).
% 265.79/266.10 tff(291,plain,
% 265.79/266.10 (![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)))))))),
% 265.79/266.10 inference(quant_intro,[status(thm)],[290])).
% 265.79/266.10 tff(292,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/sandbox/benchmark/theBenchmark.p','t37_filter_2')).
% 265.79/266.10 tff(293,plain,
% 265.79/266.10 (![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)))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[292, 291])).
% 265.79/266.10 tff(294,plain,
% 265.79/266.10 (![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)))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[293, 289])).
% 265.79/266.10 tff(295,plain,(
% 265.79/266.10 ![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)))))))),
% 265.79/266.10 inference(skolemize,[status(sab)],[294])).
% 265.79/266.10 tff(296,plain,
% 265.79/266.10 (![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)))))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[295, 288])).
% 265.79/266.10 tff(297,plain,
% 265.79/266.10 (![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)))))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[296, 286])).
% 265.79/266.10 tff(298,plain,
% 265.79/266.10 (((~![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)))))))))),
% 265.79/266.10 inference(rewrite,[status(thm)],[])).
% 265.79/266.10 tff(299,plain,
% 265.79/266.10 ((~![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)))))))))),
% 265.79/266.10 inference(quant_inst,[status(thm)],[])).
% 265.79/266.10 tff(300,plain,
% 265.79/266.10 ((~![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))))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[299, 298])).
% 265.79/266.10 tff(301,plain,
% 265.79/266.10 (![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))))))))),
% 265.79/266.10 inference(unit_resolution,[status(thm)],[300, 28, 27, 26, 297])).
% 265.79/266.10 tff(302,plain,
% 265.79/266.10 (((~![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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.79/266.10 inference(rewrite,[status(thm)],[])).
% 265.79/266.10 tff(303,plain,
% 265.79/266.10 ((v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.79/266.10 inference(rewrite,[status(thm)],[])).
% 265.79/266.10 tff(304,plain,
% 265.79/266.10 (((~![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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))))),
% 265.79/266.10 inference(monotonicity,[status(thm)],[303])).
% 265.79/266.10 tff(305,plain,
% 265.79/266.10 (((~![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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.79/266.10 inference(transitivity,[status(thm)],[304, 302])).
% 265.79/266.10 tff(306,plain,
% 265.79/266.10 ((~![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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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))))))))),
% 265.79/266.10 inference(quant_inst,[status(thm)],[])).
% 265.79/266.10 tff(307,plain,
% 265.79/266.10 ((~![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(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))),
% 265.79/266.10 inference(modus_ponens,[status(thm)],[306, 305])).
% 265.79/266.10 tff(308,plain,
% 265.79/266.10 (v1_xboole_0(k20_filter_2(A!0, B!1, C!2)) | (~m1_subset_1(k20_filter_2(A!0, B!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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))),
% 265.79/266.10 inference(unit_resolution,[status(thm)],[307, 301])).
% 265.79/266.10 tff(309,plain,
% 265.79/266.10 (![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[308, 124, 103])).
% 265.79/266.11 tff(310,plain,
% 265.79/266.11 (((~![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))))))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(311,plain,
% 265.79/266.11 ((v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))) <=> (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))))))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(312,plain,
% 265.79/266.11 (((~![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0))))))))))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[311])).
% 265.79/266.11 tff(313,plain,
% 265.79/266.11 (((~![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, 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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))))))),
% 265.79/266.11 inference(transitivity,[status(thm)],[312, 310])).
% 265.79/266.11 tff(314,plain,
% 265.79/266.11 ((~![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | (v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))),
% 265.79/266.11 inference(quant_inst,[status(thm)],[])).
% 265.79/266.11 tff(315,plain,
% 265.79/266.11 ((~![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, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) | v1_xboole_0(k7_filter_2(A!0, tptp_fun_B_11(A!0))) | (~m1_subset_1(k7_filter_2(A!0, tptp_fun_B_11(A!0)), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0))))))))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[314, 313])).
% 265.79/266.11 tff(316,plain,
% 265.79/266.11 (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))))))),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[315, 309, 281, 261])).
% 265.79/266.11 tff(317,plain,
% 265.79/266.11 (((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~(k3_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0)))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_11(A!0))) = k19_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, tptp_fun_B_11(A!0))))))) | (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.11 inference(tautology,[status(thm)],[])).
% 265.79/266.11 tff(318,plain,
% 265.79/266.11 (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[317, 316])).
% 265.79/266.11 tff(319,plain,
% 265.79/266.11 (^[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))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(320,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[319])).
% 265.79/266.11 tff(321,plain,
% 265.79/266.11 (^[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))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(322,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[321])).
% 265.79/266.11 tff(323,plain,
% 265.79/266.11 (^[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))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(324,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[323])).
% 265.79/266.11 tff(325,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(transitivity,[status(thm)],[324, 322])).
% 265.79/266.11 tff(326,plain,
% 265.79/266.11 (^[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)))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(327,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[326])).
% 265.79/266.11 tff(328,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(329,plain,
% 265.79/266.11 (^[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)))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(330,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[329])).
% 265.79/266.11 tff(331,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/sandbox/benchmark/theBenchmark.p','d6_filter_2')).
% 265.79/266.11 tff(332,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[331, 330])).
% 265.79/266.11 tff(333,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[332, 328])).
% 265.79/266.11 tff(334,plain,(
% 265.79/266.11 ![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)))),
% 265.79/266.11 inference(skolemize,[status(sab)],[333])).
% 265.79/266.11 tff(335,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[334, 327])).
% 265.79/266.11 tff(336,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[335, 325])).
% 265.79/266.11 tff(337,plain,
% 265.79/266.11 (![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[336, 320])).
% 265.79/266.11 tff(338,plain,
% 265.79/266.11 (((~![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)))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(339,plain,
% 265.79/266.11 ((~![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)))),
% 265.79/266.11 inference(quant_inst,[status(thm)],[])).
% 265.79/266.11 tff(340,plain,
% 265.79/266.11 ((~![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))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[339, 338])).
% 265.79/266.11 tff(341,plain,
% 265.79/266.11 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[340, 28, 27, 26, 337])).
% 265.79/266.11 tff(342,plain,
% 265.79/266.11 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k20_filter_2(A!0, B!1, 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(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(343,plain,
% 265.79/266.11 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.11 inference(quant_inst,[status(thm)],[])).
% 265.79/266.11 tff(344,plain,
% 265.79/266.11 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k20_filter_2(A!0, B!1, C!2))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[343, 342])).
% 265.79/266.11 tff(345,plain,
% 265.79/266.11 (k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)) = k20_filter_2(A!0, B!1, C!2)),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[344, 341, 103])).
% 265.79/266.11 tff(346,plain,
% 265.79/266.11 (k20_filter_2(A!0, B!1, C!2) = k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))),
% 265.79/266.11 inference(symmetry,[status(thm)],[345])).
% 265.79/266.11 tff(347,plain,
% 265.79/266.11 (k3_filter_2(k1_lattice2(A!0), k20_filter_2(A!0, B!1, C!2)) = k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[346])).
% 265.79/266.11 tff(348,plain,
% 265.79/266.11 (^[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)))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(349,plain,
% 265.79/266.11 (![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))))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[348])).
% 265.79/266.11 tff(350,plain,
% 265.79/266.11 (![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))))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(351,plain,
% 265.79/266.11 (^[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)))))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(352,plain,
% 265.79/266.11 (![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))))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[351])).
% 265.79/266.11 tff(353,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 265.79/266.11 tff(354,plain,
% 265.79/266.11 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[353, 352])).
% 265.79/266.11 tff(355,plain,
% 265.79/266.11 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[354, 350])).
% 265.79/266.11 tff(356,plain,(
% 265.79/266.11 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 265.79/266.11 inference(skolemize,[status(sab)],[355])).
% 265.79/266.11 tff(357,plain,
% 265.79/266.11 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[356, 349])).
% 265.79/266.11 tff(358,plain,
% 265.79/266.11 (((~![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))))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(359,plain,
% 265.79/266.11 ((~![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))))),
% 265.79/266.11 inference(quant_inst,[status(thm)],[])).
% 265.79/266.11 tff(360,plain,
% 265.79/266.11 ((~![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)))),
% 265.79/266.11 inference(modus_ponens,[status(thm)],[359, 358])).
% 265.79/266.11 tff(361,plain,
% 265.79/266.11 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 265.79/266.11 inference(unit_resolution,[status(thm)],[360, 26, 357])).
% 265.79/266.11 tff(362,plain,
% 265.79/266.11 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 265.79/266.11 inference(symmetry,[status(thm)],[361])).
% 265.79/266.11 tff(363,plain,
% 265.79/266.11 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_2(k1_lattice2(A!0), k20_filter_2(A!0, B!1, C!2))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[362])).
% 265.79/266.11 tff(364,plain,
% 265.79/266.11 (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))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[362])).
% 265.79/266.11 tff(365,plain,
% 265.79/266.11 (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)))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[364])).
% 265.79/266.11 tff(366,plain,
% 265.79/266.11 (m1_subset_1(k20_filter_2(A!0, B!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(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[365])).
% 265.79/266.11 tff(367,plain,
% 265.79/266.11 (m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.79/266.11 inference(symmetry,[status(thm)],[366])).
% 265.79/266.11 tff(368,plain,
% 265.79/266.11 (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)))),
% 265.79/266.11 inference(symmetry,[status(thm)],[364])).
% 265.79/266.11 tff(369,plain,
% 265.79/266.11 (g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.79/266.11 inference(monotonicity,[status(thm)],[368])).
% 265.79/266.11 tff(370,plain,
% 265.79/266.11 (g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.79/266.11 inference(symmetry,[status(thm)],[369])).
% 265.79/266.11 tff(371,plain,
% 265.79/266.11 (^[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)))),
% 265.79/266.11 inference(bind,[status(th)],[])).
% 265.79/266.11 tff(372,plain,
% 265.79/266.11 (![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))),
% 265.79/266.11 inference(quant_intro,[status(thm)],[371])).
% 265.79/266.11 tff(373,plain,
% 265.79/266.11 (![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))),
% 265.79/266.11 inference(rewrite,[status(thm)],[])).
% 265.79/266.11 tff(374,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 265.79/266.12 tff(375,plain,
% 265.79/266.12 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[374, 373])).
% 265.79/266.12 tff(376,plain,(
% 265.79/266.12 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 265.79/266.12 inference(skolemize,[status(sab)],[375])).
% 265.79/266.12 tff(377,plain,
% 265.79/266.12 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[376, 372])).
% 265.79/266.12 tff(378,plain,
% 265.79/266.12 ((~![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)))),
% 265.79/266.12 inference(quant_inst,[status(thm)],[])).
% 265.79/266.12 tff(379,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[378, 377])).
% 265.79/266.12 tff(380,plain,
% 265.79/266.12 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(381,plain,
% 265.79/266.12 (l1_lattices(A!0)),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[380, 172])).
% 265.79/266.12 tff(382,plain,
% 265.79/266.12 (^[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)))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(383,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[382])).
% 265.79/266.12 tff(384,plain,
% 265.79/266.12 (^[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)))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(385,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[384])).
% 265.79/266.12 tff(386,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(387,plain,
% 265.79/266.12 (^[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))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(388,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[387])).
% 265.79/266.12 tff(389,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/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 265.79/266.12 tff(390,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[389, 388])).
% 265.79/266.12 tff(391,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[390, 386])).
% 265.79/266.12 tff(392,plain,(
% 265.79/266.12 ![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))))),
% 265.79/266.12 inference(skolemize,[status(sab)],[391])).
% 265.79/266.12 tff(393,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[392, 385])).
% 265.79/266.12 tff(394,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[393, 383])).
% 265.79/266.12 tff(395,plain,
% 265.79/266.12 (((~![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))))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(396,plain,
% 265.79/266.12 ((~![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))))))),
% 265.79/266.12 inference(quant_inst,[status(thm)],[])).
% 265.79/266.12 tff(397,plain,
% 265.79/266.12 ((~![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)))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[396, 395])).
% 265.79/266.12 tff(398,plain,
% 265.79/266.12 ((~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)))))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[397, 394])).
% 265.79/266.12 tff(399,plain,
% 265.79/266.12 (~((~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))))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[398, 381])).
% 265.79/266.12 tff(400,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(401,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[400, 399])).
% 265.79/266.12 tff(402,plain,
% 265.79/266.12 ((~(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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(403,plain,
% 265.79/266.12 ((~(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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[402, 401])).
% 265.79/266.12 tff(404,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[403, 379])).
% 265.79/266.12 tff(405,plain,
% 265.79/266.12 ((~![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)))),
% 265.79/266.12 inference(quant_inst,[status(thm)],[])).
% 265.79/266.12 tff(406,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[405, 377])).
% 265.79/266.12 tff(407,plain,
% 265.79/266.12 (^[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)))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(408,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[407])).
% 265.79/266.12 tff(409,plain,
% 265.79/266.12 (^[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)))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(410,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[409])).
% 265.79/266.12 tff(411,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(412,plain,
% 265.79/266.12 (^[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))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(413,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[412])).
% 265.79/266.12 tff(414,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/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 265.79/266.12 tff(415,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[414, 413])).
% 265.79/266.12 tff(416,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[415, 411])).
% 265.79/266.12 tff(417,plain,(
% 265.79/266.12 ![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))))),
% 265.79/266.12 inference(skolemize,[status(sab)],[416])).
% 265.79/266.12 tff(418,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[417, 410])).
% 265.79/266.12 tff(419,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[418, 408])).
% 265.79/266.12 tff(420,plain,
% 265.79/266.12 (((~![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))))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(421,plain,
% 265.79/266.12 ((~![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))))))),
% 265.79/266.12 inference(quant_inst,[status(thm)],[])).
% 265.79/266.12 tff(422,plain,
% 265.79/266.12 ((~![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)))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[421, 420])).
% 265.79/266.12 tff(423,plain,
% 265.79/266.12 ((~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)))))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[422, 419])).
% 265.79/266.12 tff(424,plain,
% 265.79/266.12 (~((~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))))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[423, 174])).
% 265.79/266.12 tff(425,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(426,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[425, 424])).
% 265.79/266.12 tff(427,plain,
% 265.79/266.12 ((~(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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(428,plain,
% 265.79/266.12 ((~(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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[427, 426])).
% 265.79/266.12 tff(429,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[428, 406])).
% 265.79/266.12 tff(430,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(431,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[430, 424])).
% 265.79/266.12 tff(432,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(433,plain,
% 265.79/266.12 (v1_funct_1(u2_lattices(A!0))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[432, 424])).
% 265.79/266.12 tff(434,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(435,plain,
% 265.79/266.12 (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))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[434, 399])).
% 265.79/266.12 tff(436,plain,
% 265.79/266.12 (((~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))),
% 265.79/266.12 inference(tautology,[status(thm)],[])).
% 265.79/266.12 tff(437,plain,
% 265.79/266.12 (v1_funct_1(u1_lattices(A!0))),
% 265.79/266.12 inference(unit_resolution,[status(thm)],[436, 399])).
% 265.79/266.12 tff(438,plain,
% 265.79/266.12 (^[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)))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(439,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[438])).
% 265.79/266.12 tff(440,plain,
% 265.79/266.12 (^[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))))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(441,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[440])).
% 265.79/266.12 tff(442,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(443,plain,
% 265.79/266.12 (^[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))))))),
% 265.79/266.12 inference(bind,[status(th)],[])).
% 265.79/266.12 tff(444,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(quant_intro,[status(thm)],[443])).
% 265.79/266.12 tff(445,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/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 265.79/266.12 tff(446,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[445, 444])).
% 265.79/266.12 tff(447,plain,
% 265.79/266.12 (![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))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[446, 442])).
% 265.79/266.12 tff(448,plain,(
% 265.79/266.12 ![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))))),
% 265.79/266.12 inference(skolemize,[status(sab)],[447])).
% 265.79/266.12 tff(449,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[448, 441])).
% 265.79/266.12 tff(450,plain,
% 265.79/266.12 (![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))))))),
% 265.79/266.12 inference(modus_ponens,[status(thm)],[449, 439])).
% 265.79/266.12 tff(451,plain,
% 265.79/266.12 (((~![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)))))))),
% 265.79/266.12 inference(rewrite,[status(thm)],[])).
% 265.79/266.12 tff(452,plain,
% 265.79/266.12 (((~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)))))))),
% 265.79/266.13 inference(rewrite,[status(thm)],[])).
% 265.79/266.13 tff(453,plain,
% 265.79/266.13 ((~((~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))))))),
% 265.79/266.13 inference(rewrite,[status(thm)],[])).
% 265.79/266.13 tff(454,plain,
% 265.79/266.13 (((~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)))))))),
% 265.79/266.13 inference(monotonicity,[status(thm)],[453])).
% 265.79/266.13 tff(455,plain,
% 265.79/266.13 (((~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)))))))),
% 265.79/266.13 inference(transitivity,[status(thm)],[454, 452])).
% 265.79/266.13 tff(456,plain,
% 265.79/266.13 (((~![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))))))))),
% 265.79/266.13 inference(monotonicity,[status(thm)],[455])).
% 265.79/266.13 tff(457,plain,
% 265.79/266.13 (((~![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)))))))),
% 265.79/266.13 inference(transitivity,[status(thm)],[456, 451])).
% 265.79/266.13 tff(458,plain,
% 265.79/266.13 ((~![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)))))))),
% 265.79/266.13 inference(quant_inst,[status(thm)],[])).
% 265.79/266.13 tff(459,plain,
% 265.79/266.13 ((~![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))))))),
% 265.79/266.13 inference(modus_ponens,[status(thm)],[458, 457])).
% 265.79/266.13 tff(460,plain,
% 265.79/266.13 ((~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))))))),
% 265.79/266.13 inference(unit_resolution,[status(thm)],[459, 450, 437, 435, 433, 431])).
% 265.79/266.13 tff(461,plain,
% 265.79/266.13 (~((~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)))))),
% 265.79/266.13 inference(unit_resolution,[status(thm)],[460, 429, 404])).
% 265.79/266.13 tff(462,plain,
% 265.79/266.13 (((~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)))),
% 265.79/266.13 inference(tautology,[status(thm)],[])).
% 265.79/266.13 tff(463,plain,
% 265.79/266.13 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.79/266.13 inference(unit_resolution,[status(thm)],[462, 461])).
% 265.79/266.13 tff(464,plain,
% 265.79/266.13 (((~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)))),
% 265.79/266.13 inference(tautology,[status(thm)],[])).
% 265.79/266.13 tff(465,plain,
% 265.79/266.13 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.79/266.13 inference(unit_resolution,[status(thm)],[464, 461])).
% 265.79/266.13 tff(466,plain,
% 265.79/266.13 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 265.79/266.13 inference(bind,[status(th)],[])).
% 265.79/266.13 tff(467,plain,
% 265.79/266.13 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(quant_intro,[status(thm)],[466])).
% 265.79/266.13 tff(468,plain,
% 265.79/266.13 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(rewrite,[status(thm)],[])).
% 265.79/266.13 tff(469,plain,
% 265.79/266.13 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 265.79/266.13 inference(bind,[status(th)],[])).
% 265.79/266.13 tff(470,plain,
% 265.79/266.13 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(quant_intro,[status(thm)],[469])).
% 265.79/266.13 tff(471,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 265.79/266.13 tff(472,plain,
% 265.79/266.13 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(modus_ponens,[status(thm)],[471, 470])).
% 265.79/266.13 tff(473,plain,
% 265.79/266.13 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(modus_ponens,[status(thm)],[472, 468])).
% 265.79/266.13 tff(474,plain,(
% 265.79/266.13 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(skolemize,[status(sab)],[473])).
% 265.79/266.13 tff(475,plain,
% 265.79/266.13 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 265.79/266.13 inference(modus_ponens,[status(thm)],[474, 467])).
% 265.79/266.13 tff(476,plain,
% 265.79/266.13 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 265.79/266.13 inference(rewrite,[status(thm)],[])).
% 265.79/266.13 tff(477,plain,
% 265.79/266.13 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 265.79/266.13 inference(rewrite,[status(thm)],[])).
% 265.79/266.13 tff(478,plain,
% 265.79/266.13 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 265.79/266.13 inference(monotonicity,[status(thm)],[477])).
% 265.79/266.13 tff(479,plain,
% 265.79/266.13 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 265.79/266.13 inference(transitivity,[status(thm)],[478, 476])).
% 265.79/266.13 tff(480,plain,
% 265.79/266.13 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.79/266.13 inference(quant_inst,[status(thm)],[])).
% 265.79/266.13 tff(481,plain,
% 265.79/266.13 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.87/266.13 inference(modus_ponens,[status(thm)],[480, 479])).
% 265.87/266.13 tff(482,plain,
% 265.87/266.13 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.87/266.13 inference(unit_resolution,[status(thm)],[481, 475])).
% 265.87/266.13 tff(483,plain,
% 265.87/266.13 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.87/266.13 inference(unit_resolution,[status(thm)],[482, 465, 463])).
% 265.87/266.13 tff(484,plain,
% 265.87/266.13 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.87/266.13 inference(transitivity,[status(thm)],[483, 370])).
% 265.87/266.13 tff(485,plain,
% 265.87/266.13 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))))),
% 265.87/266.13 inference(bind,[status(th)],[])).
% 265.87/266.13 tff(486,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(quant_intro,[status(thm)],[485])).
% 265.87/266.13 tff(487,plain,
% 265.87/266.13 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))))),
% 265.87/266.13 inference(bind,[status(th)],[])).
% 265.87/266.13 tff(488,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(quant_intro,[status(thm)],[487])).
% 265.87/266.13 tff(489,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(transitivity,[status(thm)],[488, 486])).
% 265.87/266.13 tff(490,plain,
% 265.87/266.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))))),
% 265.87/266.13 inference(bind,[status(th)],[])).
% 265.87/266.13 tff(491,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(quant_intro,[status(thm)],[490])).
% 265.87/266.13 tff(492,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 265.87/266.13 inference(rewrite,[status(thm)],[])).
% 265.87/266.13 tff(493,plain,
% 265.87/266.13 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 265.87/266.13 inference(bind,[status(th)],[])).
% 265.87/266.13 tff(494,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 265.87/266.13 inference(quant_intro,[status(thm)],[493])).
% 265.87/266.13 tff(495,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 265.87/266.13 tff(496,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 265.87/266.13 inference(modus_ponens,[status(thm)],[495, 494])).
% 265.87/266.13 tff(497,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 265.87/266.13 inference(modus_ponens,[status(thm)],[496, 492])).
% 265.87/266.13 tff(498,plain,(
% 265.87/266.13 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 265.87/266.13 inference(skolemize,[status(sab)],[497])).
% 265.87/266.13 tff(499,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(modus_ponens,[status(thm)],[498, 491])).
% 265.87/266.13 tff(500,plain,
% 265.87/266.13 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))),
% 265.87/266.13 inference(modus_ponens,[status(thm)],[499, 489])).
% 265.87/266.13 tff(501,plain,
% 265.87/266.13 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(502,plain,
% 265.87/266.14 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(503,plain,
% 265.87/266.14 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[502])).
% 265.87/266.14 tff(504,plain,
% 265.87/266.14 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 265.87/266.14 inference(transitivity,[status(thm)],[503, 501])).
% 265.87/266.14 tff(505,plain,
% 265.87/266.14 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))))),
% 265.87/266.14 inference(quant_inst,[status(thm)],[])).
% 265.87/266.14 tff(506,plain,
% 265.87/266.14 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(B = E)) | (~(A = D)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[505, 504])).
% 265.87/266.14 tff(507,plain,
% 265.87/266.14 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[506, 500, 437, 435, 433, 431])).
% 265.87/266.14 tff(508,plain,
% 265.87/266.14 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[507, 429, 404])).
% 265.87/266.14 tff(509,plain,
% 265.87/266.14 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(510,plain,
% 265.87/266.14 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 265.87/266.14 inference(quant_inst,[status(thm)],[])).
% 265.87/266.14 tff(511,plain,
% 265.87/266.14 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_lattices(A!0) = E)) | (~(u1_struct_0(A!0) = D)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[510, 509])).
% 265.87/266.14 tff(512,plain,
% 265.87/266.14 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[511, 508])).
% 265.87/266.14 tff(513,plain,
% 265.87/266.14 (~((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[512, 484])).
% 265.87/266.14 tff(514,plain,
% 265.87/266.14 (((~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 265.87/266.14 inference(tautology,[status(thm)],[])).
% 265.87/266.14 tff(515,plain,
% 265.87/266.14 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[514, 513])).
% 265.87/266.14 tff(516,plain,
% 265.87/266.14 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[515])).
% 265.87/266.14 tff(517,plain,
% 265.87/266.14 (m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[516])).
% 265.87/266.14 tff(518,plain,
% 265.87/266.14 (m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.87/266.14 inference(transitivity,[status(thm)],[517, 367])).
% 265.87/266.14 tff(519,plain,
% 265.87/266.14 (m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[103, 518])).
% 265.87/266.14 tff(520,plain,
% 265.87/266.14 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[362])).
% 265.87/266.14 tff(521,plain,
% 265.87/266.14 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.87/266.14 inference(symmetry,[status(thm)],[520])).
% 265.87/266.14 tff(522,plain,
% 265.87/266.14 (^[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)))))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(523,plain,
% 265.87/266.14 (![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))))))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[522])).
% 265.87/266.14 tff(524,plain,
% 265.87/266.14 (^[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))))))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(525,plain,
% 265.87/266.14 (![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))))))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[524])).
% 265.87/266.14 tff(526,plain,
% 265.87/266.14 (![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))))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(527,plain,
% 265.87/266.14 (^[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))))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(528,plain,
% 265.87/266.14 (![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))))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[527])).
% 265.87/266.14 tff(529,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/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 265.87/266.14 tff(530,plain,
% 265.87/266.14 (![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))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[529, 528])).
% 265.87/266.14 tff(531,plain,
% 265.87/266.14 (![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))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[530, 526])).
% 265.87/266.14 tff(532,plain,(
% 265.87/266.14 ![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))))),
% 265.87/266.14 inference(skolemize,[status(sab)],[531])).
% 265.87/266.14 tff(533,plain,
% 265.87/266.14 (![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))))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[532, 525])).
% 265.87/266.14 tff(534,plain,
% 265.87/266.14 (![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))))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[533, 523])).
% 265.87/266.14 tff(535,plain,
% 265.87/266.14 (((~![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))))))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(536,plain,
% 265.87/266.14 ((~![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))))))),
% 265.87/266.14 inference(quant_inst,[status(thm)],[])).
% 265.87/266.14 tff(537,plain,
% 265.87/266.14 ((~![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)))))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[536, 535])).
% 265.87/266.14 tff(538,plain,
% 265.87/266.14 (~(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))))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[537, 28, 27, 26, 534])).
% 265.87/266.14 tff(539,plain,
% 265.87/266.14 ((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))),
% 265.87/266.14 inference(tautology,[status(thm)],[])).
% 265.87/266.14 tff(540,plain,
% 265.87/266.14 (v10_lattices(k1_lattice2(A!0))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[539, 538])).
% 265.87/266.14 tff(541,plain,
% 265.87/266.14 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[540, 521])).
% 265.87/266.14 tff(542,plain,
% 265.87/266.14 (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))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[362])).
% 265.87/266.14 tff(543,plain,
% 265.87/266.14 (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)))),
% 265.87/266.14 inference(symmetry,[status(thm)],[542])).
% 265.87/266.14 tff(544,plain,
% 265.87/266.14 ((~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))))),
% 265.87/266.14 inference(monotonicity,[status(thm)],[543])).
% 265.87/266.14 tff(545,plain,
% 265.87/266.14 ((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)))),
% 265.87/266.14 inference(tautology,[status(thm)],[])).
% 265.87/266.14 tff(546,plain,
% 265.87/266.14 (~v3_struct_0(k1_lattice2(A!0))),
% 265.87/266.14 inference(unit_resolution,[status(thm)],[545, 538])).
% 265.87/266.14 tff(547,plain,
% 265.87/266.14 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.87/266.14 inference(modus_ponens,[status(thm)],[546, 544])).
% 265.87/266.14 tff(548,plain,
% 265.87/266.14 (^[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))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(549,plain,
% 265.87/266.14 (![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)))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[548])).
% 265.87/266.14 tff(550,plain,
% 265.87/266.14 (^[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)))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(551,plain,
% 265.87/266.14 (![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)))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[550])).
% 265.87/266.14 tff(552,plain,
% 265.87/266.14 (![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)))),
% 265.87/266.14 inference(rewrite,[status(thm)],[])).
% 265.87/266.14 tff(553,plain,
% 265.87/266.14 (^[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)))))),
% 265.87/266.14 inference(bind,[status(th)],[])).
% 265.87/266.14 tff(554,plain,
% 265.87/266.14 (![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)))),
% 265.87/266.14 inference(quant_intro,[status(thm)],[553])).
% 265.87/266.14 tff(555,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/sandbox/benchmark/theBenchmark.p','redefinition_k3_filter_2')).
% 265.87/266.15 tff(556,plain,
% 265.87/266.15 (![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)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[555, 554])).
% 265.87/266.15 tff(557,plain,
% 265.87/266.15 (![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)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[556, 552])).
% 265.87/266.15 tff(558,plain,(
% 265.87/266.15 ![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)))),
% 265.87/266.15 inference(skolemize,[status(sab)],[557])).
% 265.87/266.15 tff(559,plain,
% 265.87/266.15 (![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)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[558, 551])).
% 265.87/266.15 tff(560,plain,
% 265.87/266.15 (![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)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[559, 549])).
% 265.87/266.15 tff(561,plain,
% 265.87/266.15 (((~![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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))))) <=> ((~![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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(562,plain,
% 265.87/266.15 ((v1_xboole_0(k20_filter_2(A!0, B!1, 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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k20_filter_2(A!0, B!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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(563,plain,
% 265.87/266.15 (((~![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(k20_filter_2(A!0, B!1, 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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k20_filter_2(A!0, B!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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2)))))),
% 265.87/266.15 inference(monotonicity,[status(thm)],[562])).
% 265.87/266.15 tff(564,plain,
% 265.87/266.15 (((~![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(k20_filter_2(A!0, B!1, 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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k20_filter_2(A!0, B!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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))))),
% 265.87/266.15 inference(transitivity,[status(thm)],[563, 561])).
% 265.87/266.15 tff(565,plain,
% 265.87/266.15 ((~![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(k20_filter_2(A!0, B!1, 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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k20_filter_2(A!0, B!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)))))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(566,plain,
% 265.87/266.15 ((~![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(k20_filter_2(A!0, B!1, 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))) | (~m1_subset_1(k20_filter_2(A!0, B!1, C!2), k1_zfmisc_1(u1_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)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[565, 564])).
% 265.87/266.15 tff(567,plain,
% 265.87/266.15 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[566, 560, 124, 465, 547, 541, 519])).
% 265.87/266.15 tff(568,plain,
% 265.87/266.15 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2)) = k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))),
% 265.87/266.15 inference(symmetry,[status(thm)],[567])).
% 265.87/266.15 tff(569,plain,
% 265.87/266.15 (((~![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))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(570,plain,
% 265.87/266.15 ((~![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))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(571,plain,
% 265.87/266.15 ((~![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)),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[570, 569])).
% 265.87/266.15 tff(572,plain,
% 265.87/266.15 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[571, 341])).
% 265.87/266.15 tff(573,plain,
% 265.87/266.15 (k7_filter_2(A!0, C!2) = C!2),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[572, 82])).
% 265.87/266.15 tff(574,plain,
% 265.87/266.15 (((~![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)))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(575,plain,
% 265.87/266.15 ((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)))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(576,plain,
% 265.87/266.15 (((~![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))))))),
% 265.87/266.15 inference(monotonicity,[status(thm)],[575])).
% 265.87/266.15 tff(577,plain,
% 265.87/266.15 (((~![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)))))),
% 265.87/266.15 inference(transitivity,[status(thm)],[576, 574])).
% 265.87/266.15 tff(578,plain,
% 265.87/266.15 ((~![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)))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(579,plain,
% 265.87/266.15 ((~![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))))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[578, 577])).
% 265.87/266.15 tff(580,plain,
% 265.87/266.15 ((~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))))),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[579, 28, 27, 26, 274])).
% 265.87/266.15 tff(581,plain,
% 265.87/266.15 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[580, 82])).
% 265.87/266.15 tff(582,plain,
% 265.87/266.15 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 265.87/266.15 inference(bind,[status(th)],[])).
% 265.87/266.15 tff(583,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(quant_intro,[status(thm)],[582])).
% 265.87/266.15 tff(584,plain,
% 265.87/266.15 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 265.87/266.15 inference(bind,[status(th)],[])).
% 265.87/266.15 tff(585,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(quant_intro,[status(thm)],[584])).
% 265.87/266.15 tff(586,plain,
% 265.87/266.15 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 265.87/266.15 inference(bind,[status(th)],[])).
% 265.87/266.15 tff(587,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(quant_intro,[status(thm)],[586])).
% 265.87/266.15 tff(588,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(transitivity,[status(thm)],[587, 585])).
% 265.87/266.15 tff(589,plain,
% 265.87/266.15 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 265.87/266.15 inference(bind,[status(th)],[])).
% 265.87/266.15 tff(590,plain,
% 265.87/266.15 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(quant_intro,[status(thm)],[589])).
% 265.87/266.15 tff(591,plain,
% 265.87/266.15 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(592,plain,
% 265.87/266.15 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 265.87/266.15 inference(bind,[status(th)],[])).
% 265.87/266.15 tff(593,plain,
% 265.87/266.15 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(quant_intro,[status(thm)],[592])).
% 265.87/266.15 tff(594,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d7_filter_2')).
% 265.87/266.15 tff(595,plain,
% 265.87/266.15 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[594, 593])).
% 265.87/266.15 tff(596,plain,
% 265.87/266.15 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[595, 591])).
% 265.87/266.15 tff(597,plain,(
% 265.87/266.15 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(skolemize,[status(sab)],[596])).
% 265.87/266.15 tff(598,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[597, 590])).
% 265.87/266.15 tff(599,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[598, 588])).
% 265.87/266.15 tff(600,plain,
% 265.87/266.15 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[599, 583])).
% 265.87/266.15 tff(601,plain,
% 265.87/266.15 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(602,plain,
% 265.87/266.15 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(603,plain,
% 265.87/266.15 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[602, 601])).
% 265.87/266.15 tff(604,plain,
% 265.87/266.15 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[603, 28, 27, 26, 600])).
% 265.87/266.15 tff(605,plain,
% 265.87/266.15 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(606,plain,
% 265.87/266.15 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(607,plain,
% 265.87/266.15 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2))),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[606, 605])).
% 265.87/266.15 tff(608,plain,
% 265.87/266.15 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = k7_filter_2(A!0, C!2)),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[607, 604, 581])).
% 265.87/266.15 tff(609,plain,
% 265.87/266.15 (k8_filter_2(A!0, k7_filter_2(A!0, C!2)) = C!2),
% 265.87/266.15 inference(transitivity,[status(thm)],[608, 573])).
% 265.87/266.15 tff(610,plain,
% 265.87/266.15 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(611,plain,
% 265.87/266.15 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1))),
% 265.87/266.15 inference(quant_inst,[status(thm)],[])).
% 265.87/266.15 tff(612,plain,
% 265.87/266.15 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 265.87/266.15 inference(modus_ponens,[status(thm)],[611, 610])).
% 265.87/266.15 tff(613,plain,
% 265.87/266.15 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B!1) = B!1)),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[612, 341])).
% 265.87/266.15 tff(614,plain,
% 265.87/266.15 (k7_filter_2(A!0, B!1) = B!1),
% 265.87/266.15 inference(unit_resolution,[status(thm)],[613, 76])).
% 265.87/266.15 tff(615,plain,
% 265.87/266.15 (((~![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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), 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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(616,plain,
% 265.87/266.15 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, 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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.87/266.15 inference(rewrite,[status(thm)],[])).
% 265.87/266.15 tff(617,plain,
% 265.87/266.15 (((~![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, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, 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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 265.87/266.15 inference(monotonicity,[status(thm)],[616])).
% 265.87/266.15 tff(618,plain,
% 265.87/266.15 (((~![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, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, 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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 265.87/266.16 inference(transitivity,[status(thm)],[617, 615])).
% 265.87/266.16 tff(619,plain,
% 265.87/266.16 ((~![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, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(620,plain,
% 265.87/266.16 ((~![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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[619, 618])).
% 265.87/266.16 tff(621,plain,
% 265.87/266.16 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[620, 28, 27, 26, 274])).
% 265.87/266.16 tff(622,plain,
% 265.87/266.16 (m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[621, 76])).
% 265.87/266.16 tff(623,plain,
% 265.87/266.16 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(624,plain,
% 265.87/266.16 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(625,plain,
% 265.87/266.16 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[624, 623])).
% 265.87/266.16 tff(626,plain,
% 265.87/266.16 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = k7_filter_2(A!0, B!1)),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[625, 604, 622])).
% 265.87/266.16 tff(627,plain,
% 265.87/266.16 (k8_filter_2(A!0, k7_filter_2(A!0, B!1)) = B!1),
% 265.87/266.16 inference(transitivity,[status(thm)],[626, 614])).
% 265.87/266.16 tff(628,plain,
% 265.87/266.16 (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k20_filter_2(A!0, B!1, C!2)),
% 265.87/266.16 inference(monotonicity,[status(thm)],[627, 609])).
% 265.87/266.16 tff(629,plain,
% 265.87/266.16 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(630,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[629])).
% 265.87/266.16 tff(631,plain,
% 265.87/266.16 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(632,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A)) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[631])).
% 265.87/266.16 tff(633,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(634,plain,
% 265.87/266.16 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(635,plain,
% 265.87/266.16 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[634])).
% 265.87/266.16 tff(636,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : m1_filter_0(B, A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','existence_m1_filter_0')).
% 265.87/266.16 tff(637,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[636, 635])).
% 265.87/266.16 tff(638,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : m1_filter_0(B, A))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[637, 633])).
% 265.87/266.16 tff(639,plain,(
% 265.87/266.16 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(tptp_fun_B_7(A), A))),
% 265.87/266.16 inference(skolemize,[status(sab)],[638])).
% 265.87/266.16 tff(640,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[639, 632])).
% 265.87/266.16 tff(641,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[640, 630])).
% 265.87/266.16 tff(642,plain,
% 265.87/266.16 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(643,plain,
% 265.87/266.16 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(644,plain,
% 265.87/266.16 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)))),
% 265.87/266.16 inference(monotonicity,[status(thm)],[643])).
% 265.87/266.16 tff(645,plain,
% 265.87/266.16 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0))),
% 265.87/266.16 inference(transitivity,[status(thm)],[644, 642])).
% 265.87/266.16 tff(646,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0) | (~v10_lattices(A!0)))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(647,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | m1_filter_0(tptp_fun_B_7(A), A) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[646, 645])).
% 265.87/266.16 tff(648,plain,
% 265.87/266.16 (m1_filter_0(tptp_fun_B_7(A!0), A!0)),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[647, 28, 27, 26, 641])).
% 265.87/266.16 tff(649,plain,
% 265.87/266.16 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(650,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[649])).
% 265.87/266.16 tff(651,plain,
% 265.87/266.16 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(652,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[651])).
% 265.87/266.16 tff(653,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(transitivity,[status(thm)],[652, 650])).
% 265.87/266.16 tff(654,plain,
% 265.87/266.16 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(655,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[654])).
% 265.87/266.16 tff(656,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(657,plain,
% 265.87/266.16 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(658,plain,
% 265.87/266.16 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[657])).
% 265.87/266.16 tff(659,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 265.87/266.16 tff(660,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[659, 658])).
% 265.87/266.16 tff(661,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[660, 656])).
% 265.87/266.16 tff(662,plain,(
% 265.87/266.16 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 265.87/266.16 inference(skolemize,[status(sab)],[661])).
% 265.87/266.16 tff(663,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[662, 655])).
% 265.87/266.16 tff(664,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[663, 653])).
% 265.87/266.16 tff(665,plain,
% 265.87/266.16 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(666,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(667,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[666, 665])).
% 265.87/266.16 tff(668,plain,
% 265.87/266.16 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[667, 28, 27, 26, 664])).
% 265.87/266.16 tff(669,plain,
% 265.87/266.16 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(670,plain,
% 265.87/266.16 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(671,plain,
% 265.87/266.16 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(tptp_fun_B_7(A!0), A!0)) | (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[670, 669])).
% 265.87/266.16 tff(672,plain,
% 265.87/266.16 (~(v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[671, 668, 648])).
% 265.87/266.16 tff(673,plain,
% 265.87/266.16 ((v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.87/266.16 inference(tautology,[status(thm)],[])).
% 265.87/266.16 tff(674,plain,
% 265.87/266.16 (m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[673, 672])).
% 265.87/266.16 tff(675,plain,
% 265.87/266.16 ((v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | (~v1_xboole_0(tptp_fun_B_7(A!0)))),
% 265.87/266.16 inference(tautology,[status(thm)],[])).
% 265.87/266.16 tff(676,plain,
% 265.87/266.16 (~v1_xboole_0(tptp_fun_B_7(A!0))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[675, 672])).
% 265.87/266.16 tff(677,plain,
% 265.87/266.16 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(678,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[677])).
% 265.87/266.16 tff(679,plain,
% 265.87/266.16 (^[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((m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A)))) <=> (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(680,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[679])).
% 265.87/266.16 tff(681,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(682,plain,
% 265.87/266.16 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(683,plain,
% 265.87/266.16 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[682])).
% 265.87/266.16 tff(684,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rc1_lattice4')).
% 265.87/266.16 tff(685,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[684, 683])).
% 265.87/266.16 tff(686,plain,
% 265.87/266.16 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ?[B: $i] : (m2_lattice4(B, A) & (~v1_xboole_0(B))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[685, 681])).
% 265.87/266.16 tff(687,plain,(
% 265.87/266.16 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (m2_lattice4(tptp_fun_B_19(A), A) & (~v1_xboole_0(tptp_fun_B_19(A)))))),
% 265.87/266.16 inference(skolemize,[status(sab)],[686])).
% 265.87/266.16 tff(688,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[687, 680])).
% 265.87/266.16 tff(689,plain,
% 265.87/266.16 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[688, 678])).
% 265.87/266.16 tff(690,plain,
% 265.87/266.16 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(691,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(692,plain,
% 265.87/266.16 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v1_xboole_0(tptp_fun_B_19(A)) | (~m2_lattice4(tptp_fun_B_19(A), A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[691, 690])).
% 265.87/266.16 tff(693,plain,
% 265.87/266.16 (~(v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[692, 28, 27, 26, 689])).
% 265.87/266.16 tff(694,plain,
% 265.87/266.16 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))) | m2_lattice4(tptp_fun_B_19(A!0), A!0)),
% 265.87/266.16 inference(tautology,[status(thm)],[])).
% 265.87/266.16 tff(695,plain,
% 265.87/266.16 (m2_lattice4(tptp_fun_B_19(A!0), A!0)),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[694, 693])).
% 265.87/266.16 tff(696,plain,
% 265.87/266.16 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.87/266.16 inference(rewrite,[status(thm)],[])).
% 265.87/266.16 tff(697,plain,
% 265.87/266.16 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.87/266.16 inference(quant_inst,[status(thm)],[])).
% 265.87/266.16 tff(698,plain,
% 265.87/266.16 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0)) | m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.87/266.16 inference(modus_ponens,[status(thm)],[697, 696])).
% 265.87/266.16 tff(699,plain,
% 265.87/266.16 (m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[698, 72, 695])).
% 265.87/266.16 tff(700,plain,
% 265.87/266.16 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m2_lattice4(tptp_fun_B_19(A!0), A!0))) | (~v1_xboole_0(tptp_fun_B_19(A!0)))),
% 265.87/266.16 inference(tautology,[status(thm)],[])).
% 265.87/266.16 tff(701,plain,
% 265.87/266.16 (~v1_xboole_0(tptp_fun_B_19(A!0))),
% 265.87/266.16 inference(unit_resolution,[status(thm)],[700, 693])).
% 265.87/266.16 tff(702,plain,
% 265.87/266.16 (^[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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(703,plain,
% 265.87/266.16 (![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[702])).
% 265.87/266.16 tff(704,plain,
% 265.87/266.16 (^[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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))),
% 265.87/266.16 inference(bind,[status(th)],[])).
% 265.87/266.16 tff(705,plain,
% 265.87/266.16 (![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.16 inference(quant_intro,[status(thm)],[704])).
% 265.87/266.16 tff(706,plain,
% 265.87/266.16 (![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> ![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.16 inference(transitivity,[status(thm)],[705, 703])).
% 265.87/266.16 tff(707,plain,
% 265.87/266.16 (^[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(A)))) <=> (~(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))))) <=> (~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(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)))))), ((~((~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))))))), quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), rewrite(((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), (((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), rewrite(((v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), (((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), rewrite(((v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), rewrite(((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), 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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))), (![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))))), 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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))), (((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))))),
% 265.87/266.17 inference(bind,[status(th)],[])).
% 265.87/266.17 tff(708,plain,
% 265.87/266.17 (![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.17 inference(quant_intro,[status(thm)],[707])).
% 265.87/266.17 tff(709,plain,
% 265.87/266.17 (![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 265.87/266.17 inference(rewrite,[status(thm)],[])).
% 265.87/266.17 tff(710,plain,
% 265.87/266.17 (^[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(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(monotonicity(rewrite((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))))), (((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> (((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), rewrite((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))), (((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))) <=> ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), ((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), rewrite((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))), ((((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), (![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))) <=> ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), ((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), rewrite((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))), ((((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), (![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))) <=> ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))) <=> ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), ((((~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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> (((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), 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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))), ((((~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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), (![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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))) <=> ![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((((~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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> (((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))))), 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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), (((((~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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ((~((~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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.17 inference(bind,[status(th)],[])).
% 265.87/266.17 tff(711,plain,
% 265.87/266.17 (![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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E)))))))) <=> ![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 265.87/266.17 inference(quant_intro,[status(thm)],[710])).
% 265.87/266.17 tff(712,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(A)))) => ![D: $i] : (((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ![E: $i] : (((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t45_filter_2')).
% 265.87/266.17 tff(713,plain,
% 265.87/266.17 (![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 265.87/266.17 inference(modus_ponens,[status(thm)],[712, 711])).
% 265.87/266.17 tff(714,plain,
% 265.87/266.17 (![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 265.87/266.17 inference(modus_ponens,[status(thm)],[713, 709])).
% 265.87/266.17 tff(715,plain,(
% 265.87/266.17 ![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(A))))) | ![D: $i] : ((~((~v1_xboole_0(D)) & m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ![E: $i] : ((~((~v1_xboole_0(E)) & m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C))) & (k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C)) & (k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E))) & (k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))),
% 265.87/266.17 inference(skolemize,[status(sab)],[714])).
% 265.87/266.17 tff(716,plain,
% 265.87/266.17 (![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.17 inference(modus_ponens,[status(thm)],[715, 708])).
% 265.87/266.17 tff(717,plain,
% 265.87/266.17 (![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))),
% 265.87/266.17 inference(modus_ponens,[status(thm)],[716, 706])).
% 265.87/266.17 tff(718,plain,
% 265.87/266.17 (((~![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | (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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))) <=> ((~![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | 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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))),
% 265.87/266.17 inference(rewrite,[status(thm)],[])).
% 265.87/266.17 tff(719,plain,
% 265.87/266.17 ((~![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | (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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))))),
% 265.87/266.17 inference(quant_inst,[status(thm)],[])).
% 265.87/266.17 tff(720,plain,
% 265.87/266.17 ((~![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(A)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k20_filter_2(A, B, C) = k5_filter_0(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)))) | (~(k20_filter_2(k1_lattice2(A), k7_filter_2(A, B), k7_filter_2(A, C)) = k5_filter_0(A, B, C))) | (~(k20_filter_2(k1_lattice2(A), D, E) = k5_filter_0(A, k8_filter_2(A, D), k8_filter_2(A, E)))) | (~(k20_filter_2(A, k8_filter_2(A, D), k8_filter_2(A, E)) = k5_filter_0(k1_lattice2(A), D, E))))))))))) | 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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 265.87/266.17 inference(modus_ponens,[status(thm)],[719, 718])).
% 265.87/266.17 tff(721,plain,
% 265.87/266.17 (![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 265.87/266.17 inference(unit_resolution,[status(thm)],[720, 28, 27, 26, 717])).
% 265.87/266.17 tff(722,plain,
% 265.87/266.17 (((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 265.87/266.18 inference(rewrite,[status(thm)],[])).
% 265.87/266.18 tff(723,plain,
% 265.87/266.18 ((v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))))))))) <=> (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 265.87/266.18 inference(rewrite,[status(thm)],[])).
% 265.87/266.18 tff(724,plain,
% 265.87/266.18 (((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) <=> ((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))))),
% 265.87/266.18 inference(monotonicity,[status(thm)],[723])).
% 265.87/266.18 tff(725,plain,
% 265.87/266.18 (((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) <=> ((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C)))))))))),
% 265.87/266.18 inference(transitivity,[status(thm)],[724, 722])).
% 265.87/266.18 tff(726,plain,
% 265.87/266.18 ((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | (v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))),
% 265.92/266.18 inference(quant_inst,[status(thm)],[])).
% 265.92/266.18 tff(727,plain,
% 265.92/266.18 ((~![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(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, B, C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B), k7_filter_2(A!0, C)) = k5_filter_0(A!0, B, C))) | (~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E)))))))))) | v1_xboole_0(tptp_fun_B_19(A!0)) | (~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 265.92/266.18 inference(modus_ponens,[status(thm)],[726, 725])).
% 265.92/266.18 tff(728,plain,
% 265.92/266.18 ((~m1_subset_1(tptp_fun_B_19(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 265.92/266.18 inference(unit_resolution,[status(thm)],[727, 721, 701])).
% 265.92/266.18 tff(729,plain,
% 265.92/266.18 (![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))),
% 265.92/266.18 inference(unit_resolution,[status(thm)],[728, 699])).
% 265.92/266.18 tff(730,plain,
% 265.92/266.18 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | (v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))),
% 265.92/266.18 inference(rewrite,[status(thm)],[])).
% 265.92/266.18 tff(731,plain,
% 265.92/266.18 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | (v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))))),
% 265.92/266.18 inference(quant_inst,[status(thm)],[])).
% 265.92/266.18 tff(732,plain,
% 265.92/266.18 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), C) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, C)) = k5_filter_0(A!0, tptp_fun_B_19(A!0), C))))))))) | v1_xboole_0(tptp_fun_B_7(A!0)) | (~m1_subset_1(tptp_fun_B_7(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | ![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 265.92/266.18 inference(modus_ponens,[status(thm)],[731, 730])).
% 265.92/266.18 tff(733,plain,
% 265.92/266.18 (![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 265.92/266.18 inference(unit_resolution,[status(thm)],[732, 729, 676, 674])).
% 265.92/266.18 tff(734,plain,
% 265.92/266.18 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 265.92/266.18 inference(rewrite,[status(thm)],[])).
% 265.92/266.18 tff(735,plain,
% 265.92/266.18 ((v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, 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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 265.92/266.18 inference(rewrite,[status(thm)],[])).
% 265.92/266.18 tff(736,plain,
% 265.92/266.18 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))))),
% 265.92/266.18 inference(monotonicity,[status(thm)],[735])).
% 265.92/266.18 tff(737,plain,
% 265.92/266.18 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1))))),
% 265.92/266.18 inference(transitivity,[status(thm)],[736, 734])).
% 265.92/266.18 tff(738,plain,
% 265.92/266.18 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v1_xboole_0(B!1) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, B!1))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.18 inference(quant_inst,[status(thm)],[])).
% 265.92/266.18 tff(739,plain,
% 265.92/266.18 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 265.92/266.18 inference(modus_ponens,[status(thm)],[738, 737])).
% 265.92/266.18 tff(740,plain,
% 265.92/266.18 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(B!1) | (~v1_xboole_0(k7_filter_2(A!0, B!1)))),
% 265.92/266.18 inference(unit_resolution,[status(thm)],[739, 28, 27, 26, 254])).
% 265.92/266.18 tff(741,plain,
% 265.92/266.18 (~v1_xboole_0(k7_filter_2(A!0, B!1))),
% 265.92/266.18 inference(unit_resolution,[status(thm)],[740, 76, 39])).
% 265.92/266.18 tff(742,plain,
% 265.92/266.18 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 265.92/266.19 inference(rewrite,[status(thm)],[])).
% 265.92/266.19 tff(743,plain,
% 265.92/266.19 ((v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))))))) <=> (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 265.92/266.19 inference(rewrite,[status(thm)],[])).
% 265.92/266.19 tff(744,plain,
% 265.92/266.19 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))))),
% 265.92/266.19 inference(monotonicity,[status(thm)],[743])).
% 265.92/266.19 tff(745,plain,
% 265.92/266.19 (((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) <=> ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E)))))))),
% 265.92/266.19 inference(transitivity,[status(thm)],[744, 742])).
% 265.92/266.19 tff(746,plain,
% 265.92/266.19 ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | (v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))),
% 265.92/266.19 inference(quant_inst,[status(thm)],[])).
% 265.92/266.19 tff(747,plain,
% 265.92/266.19 ((~![D: $i] : (v1_xboole_0(D) | (~m1_subset_1(D, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(k1_lattice2(A!0), D, E) = k5_filter_0(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, D), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), D, E))) | (~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0))))))))) | v1_xboole_0(k7_filter_2(A!0, B!1)) | (~m1_subset_1(k7_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | ![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))),
% 265.92/266.19 inference(modus_ponens,[status(thm)],[746, 745])).
% 265.92/266.19 tff(748,plain,
% 265.92/266.19 (![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))),
% 265.92/266.19 inference(unit_resolution,[status(thm)],[747, 622, 741, 733])).
% 265.92/266.19 tff(749,plain,
% 265.92/266.19 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 265.92/266.19 inference(rewrite,[status(thm)],[])).
% 265.92/266.19 tff(750,plain,
% 265.92/266.19 ((v1_xboole_0(C!2) | v3_struct_0(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 265.92/266.19 inference(rewrite,[status(thm)],[])).
% 265.92/266.19 tff(751,plain,
% 265.92/266.19 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(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(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~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] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))))),
% 265.92/266.19 inference(monotonicity,[status(thm)],[750])).
% 265.92/266.19 tff(752,plain,
% 265.92/266.19 (((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(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(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~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] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2))))),
% 265.92/266.19 inference(transitivity,[status(thm)],[751, 749])).
% 265.92/266.19 tff(753,plain,
% 265.92/266.19 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(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(A!0) | (~v1_xboole_0(k7_filter_2(A!0, C!2))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.19 inference(quant_inst,[status(thm)],[])).
% 265.92/266.19 tff(754,plain,
% 265.92/266.19 ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (~v1_xboole_0(k7_filter_2(A, B))) | (~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)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 265.92/266.19 inference(modus_ponens,[status(thm)],[753, 752])).
% 265.92/266.19 tff(755,plain,
% 265.92/266.19 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | v1_xboole_0(C!2) | (~v1_xboole_0(k7_filter_2(A!0, C!2)))),
% 265.92/266.19 inference(unit_resolution,[status(thm)],[754, 28, 27, 26, 254])).
% 265.92/266.19 tff(756,plain,
% 265.92/266.19 (~v1_xboole_0(k7_filter_2(A!0, C!2))),
% 265.92/266.19 inference(unit_resolution,[status(thm)],[755, 82, 47])).
% 265.92/266.19 tff(757,plain,
% 265.92/266.19 (((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))) <=> ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 265.92/266.19 inference(rewrite,[status(thm)],[])).
% 265.92/266.19 tff(758,plain,
% 265.92/266.19 ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))))),
% 265.92/266.19 inference(quant_inst,[status(thm)],[])).
% 265.92/266.19 tff(759,plain,
% 265.92/266.19 ((~![E: $i] : (v1_xboole_0(E) | (~m1_subset_1(E, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, E)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), E))))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[758, 757])).
% 265.92/266.20 tff(760,plain,
% 265.92/266.20 (~((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[759, 581, 756, 748])).
% 265.92/266.20 tff(761,plain,
% 265.92/266.20 (((~(k20_filter_2(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, tptp_fun_B_19(A!0)), k7_filter_2(A!0, tptp_fun_B_7(A!0))) = k5_filter_0(A!0, tptp_fun_B_19(A!0), tptp_fun_B_7(A!0)))) | (~(k20_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))))) | (~(k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))) | (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 265.92/266.20 inference(tautology,[status(thm)],[])).
% 265.92/266.20 tff(762,plain,
% 265.92/266.20 (k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2))) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[761, 760])).
% 265.92/266.20 tff(763,plain,
% 265.92/266.20 (k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k20_filter_2(A!0, k8_filter_2(A!0, k7_filter_2(A!0, B!1)), k8_filter_2(A!0, k7_filter_2(A!0, C!2)))),
% 265.92/266.20 inference(symmetry,[status(thm)],[762])).
% 265.92/266.20 tff(764,plain,
% 265.92/266.20 (k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k5_filter_0(k1_lattice2(A!0), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 265.92/266.20 inference(monotonicity,[status(thm)],[362])).
% 265.92/266.20 tff(765,plain,
% 265.92/266.20 (k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k20_filter_2(A!0, B!1, C!2)),
% 265.92/266.20 inference(transitivity,[status(thm)],[764, 763, 628])).
% 265.92/266.20 tff(766,plain,
% 265.92/266.20 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k20_filter_2(A!0, B!1, C!2))),
% 265.92/266.20 inference(monotonicity,[status(thm)],[765])).
% 265.92/266.20 tff(767,plain,
% 265.92/266.20 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(768,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[767])).
% 265.92/266.20 tff(769,plain,
% 265.92/266.20 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(770,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[769])).
% 265.92/266.20 tff(771,plain,
% 265.92/266.20 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(772,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[771])).
% 265.92/266.20 tff(773,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(transitivity,[status(thm)],[772, 770])).
% 265.92/266.20 tff(774,plain,
% 265.92/266.20 (^[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_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(775,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[774])).
% 265.92/266.20 tff(776,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(777,plain,
% 265.92/266.20 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(778,plain,
% 265.92/266.20 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[777])).
% 265.92/266.20 tff(779,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 265.92/266.20 tff(780,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[779, 778])).
% 265.92/266.20 tff(781,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[780, 776])).
% 265.92/266.20 tff(782,plain,(
% 265.92/266.20 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(skolemize,[status(sab)],[781])).
% 265.92/266.20 tff(783,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[782, 775])).
% 265.92/266.20 tff(784,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[783, 773])).
% 265.92/266.20 tff(785,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[784, 768])).
% 265.92/266.20 tff(786,plain,
% 265.92/266.20 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(787,plain,
% 265.92/266.20 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.92/266.20 inference(quant_inst,[status(thm)],[])).
% 265.92/266.20 tff(788,plain,
% 265.92/266.20 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[787, 786])).
% 265.92/266.20 tff(789,plain,
% 265.92/266.20 (![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[788, 785, 465, 547, 541])).
% 265.92/266.20 tff(790,plain,
% 265.92/266.20 ((~![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.92/266.20 inference(quant_inst,[status(thm)],[])).
% 265.92/266.20 tff(791,plain,
% 265.92/266.20 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[790, 789])).
% 265.92/266.20 tff(792,plain,
% 265.92/266.20 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(793,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[792])).
% 265.92/266.20 tff(794,plain,
% 265.92/266.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(795,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[794])).
% 265.92/266.20 tff(796,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(797,plain,
% 265.92/266.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(798,plain,
% 265.92/266.20 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[797])).
% 265.92/266.20 tff(799,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 265.92/266.20 tff(800,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[799, 798])).
% 265.92/266.20 tff(801,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[800, 796])).
% 265.92/266.20 tff(802,plain,(
% 265.92/266.20 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 265.92/266.20 inference(skolemize,[status(sab)],[801])).
% 265.92/266.20 tff(803,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[802, 795])).
% 265.92/266.20 tff(804,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[803, 793])).
% 265.92/266.20 tff(805,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(806,plain,
% 265.92/266.20 ((v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(807,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))))),
% 265.92/266.20 inference(monotonicity,[status(thm)],[806])).
% 265.92/266.20 tff(808,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)))),
% 265.92/266.20 inference(transitivity,[status(thm)],[807, 805])).
% 265.92/266.20 tff(809,plain,
% 265.92/266.20 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.20 inference(quant_inst,[status(thm)],[])).
% 265.92/266.20 tff(810,plain,
% 265.92/266.20 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[809, 808])).
% 265.92/266.20 tff(811,plain,
% 265.92/266.20 (k15_filter_2(A!0, B!1) = k7_filter_2(A!0, B!1)),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[810, 28, 27, 26, 33, 804])).
% 265.92/266.20 tff(812,plain,
% 265.92/266.20 (k7_filter_2(A!0, B!1) = k15_filter_2(A!0, B!1)),
% 265.92/266.20 inference(symmetry,[status(thm)],[811])).
% 265.92/266.20 tff(813,plain,
% 265.92/266.20 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 265.92/266.20 inference(monotonicity,[status(thm)],[812, 362])).
% 265.92/266.20 tff(814,plain,
% 265.92/266.20 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.20 inference(symmetry,[status(thm)],[813])).
% 265.92/266.20 tff(815,plain,
% 265.92/266.20 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(816,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[815])).
% 265.92/266.20 tff(817,plain,
% 265.92/266.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(818,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[817])).
% 265.92/266.20 tff(819,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(820,plain,
% 265.92/266.20 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(821,plain,
% 265.92/266.20 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[820])).
% 265.92/266.20 tff(822,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k15_filter_2')).
% 265.92/266.20 tff(823,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[822, 821])).
% 265.92/266.20 tff(824,plain,
% 265.92/266.20 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[823, 819])).
% 265.92/266.20 tff(825,plain,(
% 265.92/266.20 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)))),
% 265.92/266.20 inference(skolemize,[status(sab)],[824])).
% 265.92/266.20 tff(826,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[825, 818])).
% 265.92/266.20 tff(827,plain,
% 265.92/266.20 (![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[826, 816])).
% 265.92/266.20 tff(828,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(829,plain,
% 265.92/266.20 ((v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(830,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))))),
% 265.92/266.20 inference(monotonicity,[status(thm)],[829])).
% 265.92/266.20 tff(831,plain,
% 265.92/266.20 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)))),
% 265.92/266.20 inference(transitivity,[status(thm)],[830, 828])).
% 265.92/266.20 tff(832,plain,
% 265.92/266.20 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0)) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.20 inference(quant_inst,[status(thm)],[])).
% 265.92/266.20 tff(833,plain,
% 265.92/266.20 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(B!1, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[832, 831])).
% 265.92/266.20 tff(834,plain,
% 265.92/266.20 (m1_filter_2(k15_filter_2(A!0, B!1), k1_lattice2(A!0))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[833, 28, 27, 26, 33, 827])).
% 265.92/266.20 tff(835,plain,
% 265.92/266.20 (m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.20 inference(modus_ponens,[status(thm)],[834, 814])).
% 265.92/266.20 tff(836,plain,
% 265.92/266.20 ((~(m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.20 inference(tautology,[status(thm)],[])).
% 265.92/266.20 tff(837,plain,
% 265.92/266.20 (m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.20 inference(unit_resolution,[status(thm)],[836, 835, 791])).
% 265.92/266.20 tff(838,plain,
% 265.92/266.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(839,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[838])).
% 265.92/266.20 tff(840,plain,
% 265.92/266.20 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(841,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[840])).
% 265.92/266.20 tff(842,plain,
% 265.92/266.20 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(843,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[842])).
% 265.92/266.20 tff(844,plain,
% 265.92/266.20 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.20 inference(transitivity,[status(thm)],[843, 841])).
% 265.92/266.20 tff(845,plain,
% 265.92/266.20 (^[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_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))))),
% 265.92/266.20 inference(bind,[status(th)],[])).
% 265.92/266.20 tff(846,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.20 inference(quant_intro,[status(thm)],[845])).
% 265.92/266.20 tff(847,plain,
% 265.92/266.20 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.20 inference(rewrite,[status(thm)],[])).
% 265.92/266.20 tff(848,plain,
% 265.92/266.20 (^[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] : rewrite((m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))) <=> ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))), (![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))) <=> ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))), ((m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) <=> (m1_filter_0(B, A) => ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))), rewrite((m1_filter_0(B, A) => ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))), ((m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) <=> ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))))), (![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))))),
% 265.92/266.21 inference(bind,[status(th)],[])).
% 265.92/266.21 tff(849,plain,
% 265.92/266.21 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.21 inference(quant_intro,[status(thm)],[848])).
% 265.92/266.21 tff(850,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ![C: $i] : (m1_filter_0(C, A) => (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t50_filter_0')).
% 265.92/266.21 tff(851,plain,
% 265.92/266.21 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[850, 849])).
% 265.92/266.21 tff(852,plain,
% 265.92/266.21 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[851, 847])).
% 265.92/266.21 tff(853,plain,(
% 265.92/266.21 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.21 inference(skolemize,[status(sab)],[852])).
% 265.92/266.21 tff(854,plain,
% 265.92/266.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[853, 846])).
% 265.92/266.21 tff(855,plain,
% 265.92/266.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))) | (~v10_lattices(A)))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[854, 844])).
% 265.92/266.21 tff(856,plain,
% 265.92/266.21 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[855, 839])).
% 265.92/266.21 tff(857,plain,
% 265.92/266.21 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(858,plain,
% 265.92/266.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C))))))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(859,plain,
% 265.92/266.21 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | ![C: $i] : ((~m1_filter_0(C, A)) | (k3_filter_0(A, k4_subset_1(u1_struct_0(A), B, C)) = k3_filter_0(A, k5_filter_0(A, B, C))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[858, 857])).
% 265.92/266.21 tff(860,plain,
% 265.92/266.21 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[859, 856, 465, 547, 541])).
% 265.92/266.21 tff(861,plain,
% 265.92/266.21 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(862,plain,
% 265.92/266.21 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))) | ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C)))))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(863,plain,
% 265.92/266.21 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C)))))) | (~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[862, 861])).
% 265.92/266.21 tff(864,plain,
% 265.92/266.21 ((~m1_filter_0(k7_filter_2(A!0, B!1), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[863, 860])).
% 265.92/266.21 tff(865,plain,
% 265.92/266.21 (![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[864, 837])).
% 265.92/266.21 tff(866,plain,
% 265.92/266.21 ((~![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(867,plain,
% 265.92/266.21 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[866, 789])).
% 265.92/266.21 tff(868,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(869,plain,
% 265.92/266.21 ((v3_struct_0(A!0) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(870,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))))),
% 265.92/266.21 inference(monotonicity,[status(thm)],[869])).
% 265.92/266.21 tff(871,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)))),
% 265.92/266.21 inference(transitivity,[status(thm)],[870, 868])).
% 265.92/266.21 tff(872,plain,
% 265.92/266.21 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(873,plain,
% 265.92/266.21 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[872, 871])).
% 265.92/266.21 tff(874,plain,
% 265.92/266.21 (k15_filter_2(A!0, C!2) = k7_filter_2(A!0, C!2)),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[873, 28, 27, 26, 41, 804])).
% 265.92/266.21 tff(875,plain,
% 265.92/266.21 (k7_filter_2(A!0, C!2) = k15_filter_2(A!0, C!2)),
% 265.92/266.21 inference(symmetry,[status(thm)],[874])).
% 265.92/266.21 tff(876,plain,
% 265.92/266.21 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 265.92/266.21 inference(monotonicity,[status(thm)],[875, 362])).
% 265.92/266.21 tff(877,plain,
% 265.92/266.21 (m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) <=> m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.21 inference(symmetry,[status(thm)],[876])).
% 265.92/266.21 tff(878,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(879,plain,
% 265.92/266.21 ((v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(880,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))))),
% 265.92/266.21 inference(monotonicity,[status(thm)],[879])).
% 265.92/266.21 tff(881,plain,
% 265.92/266.21 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)))),
% 265.92/266.21 inference(transitivity,[status(thm)],[880, 878])).
% 265.92/266.21 tff(882,plain,
% 265.92/266.21 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0)) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(883,plain,
% 265.92/266.21 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_filter_2(k15_filter_2(A, B), k1_lattice2(A)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m2_filter_2(C!2, A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[882, 881])).
% 265.92/266.21 tff(884,plain,
% 265.92/266.21 (m1_filter_2(k15_filter_2(A!0, C!2), k1_lattice2(A!0))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[883, 28, 27, 26, 41, 827])).
% 265.92/266.21 tff(885,plain,
% 265.92/266.21 (m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[884, 877])).
% 265.92/266.21 tff(886,plain,
% 265.92/266.21 ((~(m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_filter_2(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.21 inference(tautology,[status(thm)],[])).
% 265.92/266.21 tff(887,plain,
% 265.92/266.21 (m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[886, 885, 867])).
% 265.92/266.21 tff(888,plain,
% 265.92/266.21 (((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))) | ((~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))) <=> ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))) | (~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 265.92/266.21 inference(rewrite,[status(thm)],[])).
% 265.92/266.21 tff(889,plain,
% 265.92/266.21 ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))) | ((~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 265.92/266.21 inference(quant_inst,[status(thm)],[])).
% 265.92/266.21 tff(890,plain,
% 265.92/266.21 ((~![C: $i] : ((~m1_filter_0(C, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), C)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), C))))) | (~m1_filter_0(k7_filter_2(A!0, C!2), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))),
% 265.92/266.21 inference(modus_ponens,[status(thm)],[889, 888])).
% 265.92/266.21 tff(891,plain,
% 265.92/266.21 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 265.92/266.21 inference(unit_resolution,[status(thm)],[890, 887, 865])).
% 265.92/266.21 tff(892,plain,
% 265.92/266.21 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(A!0)),
% 265.92/266.21 inference(symmetry,[status(thm)],[515])).
% 265.92/266.21 tff(893,plain,
% 265.92/266.21 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 265.92/266.21 inference(transitivity,[status(thm)],[364, 892])).
% 265.92/266.21 tff(894,plain,
% 265.92/266.21 (k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k4_subset_1(u1_struct_0(A!0), B!1, C!2)),
% 265.92/266.21 inference(monotonicity,[status(thm)],[893, 614, 573])).
% 265.92/266.21 tff(895,plain,
% 265.92/266.21 (k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 265.92/266.21 inference(symmetry,[status(thm)],[894])).
% 265.92/266.21 tff(896,plain,
% 265.92/266.21 (^[A: $i, B: $i, C: $i] : refl(((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 265.92/266.21 inference(bind,[status(th)],[])).
% 265.92/266.21 tff(897,plain,
% 265.92/266.21 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[896])).
% 265.92/266.22 tff(898,plain,
% 265.92/266.22 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(899,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[898])).
% 265.92/266.22 tff(900,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(901,plain,
% 265.92/266.22 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(902,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[901])).
% 265.92/266.22 tff(903,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k4_subset_1')).
% 265.92/266.22 tff(904,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[903, 902])).
% 265.92/266.22 tff(905,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[904, 900])).
% 265.92/266.22 tff(906,plain,(
% 265.92/266.22 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (k4_subset_1(A, B, C) = k2_xboole_0(B, C)))),
% 265.92/266.22 inference(skolemize,[status(sab)],[905])).
% 265.92/266.22 tff(907,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[906, 899])).
% 265.92/266.22 tff(908,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[907, 897])).
% 265.92/266.22 tff(909,plain,
% 265.92/266.22 (((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(910,plain,
% 265.92/266.22 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(quant_inst,[status(thm)],[])).
% 265.92/266.22 tff(911,plain,
% 265.92/266.22 ((~![A: $i, B: $i, C: $i] : ((k4_subset_1(A, B, C) = k2_xboole_0(B, C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[910, 909])).
% 265.92/266.22 tff(912,plain,
% 265.92/266.22 ((k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[911, 908])).
% 265.92/266.22 tff(913,plain,
% 265.92/266.22 (k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k2_xboole_0(B!1, C!2)),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[912, 76, 82])).
% 265.92/266.22 tff(914,plain,
% 265.92/266.22 (k2_xboole_0(B!1, C!2) = k4_subset_1(u1_struct_0(A!0), B!1, C!2)),
% 265.92/266.22 inference(symmetry,[status(thm)],[913])).
% 265.92/266.22 tff(915,plain,
% 265.92/266.22 (k2_xboole_0(B!1, C!2) = k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))),
% 265.92/266.22 inference(transitivity,[status(thm)],[914, 895])).
% 265.92/266.22 tff(916,plain,
% 265.92/266.22 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k4_subset_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[915])).
% 265.92/266.22 tff(917,plain,
% 265.92/266.22 (k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))) = k1_zfmisc_1(u1_struct_0(A!0))),
% 265.92/266.22 inference(symmetry,[status(thm)],[516])).
% 265.92/266.22 tff(918,plain,
% 265.92/266.22 (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(A!0))),
% 265.92/266.22 inference(transitivity,[status(thm)],[365, 917])).
% 265.92/266.22 tff(919,plain,
% 265.92/266.22 (m1_subset_1(k2_xboole_0(B!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(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[914, 918])).
% 265.92/266.22 tff(920,plain,
% 265.92/266.22 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.92/266.22 inference(symmetry,[status(thm)],[919])).
% 265.92/266.22 tff(921,plain,
% 265.92/266.22 (^[A: $i, B: $i, C: $i] : refl((m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(922,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[921])).
% 265.92/266.22 tff(923,plain,
% 265.92/266.22 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> ((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))), rewrite((((~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(924,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[923])).
% 265.92/266.22 tff(925,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(926,plain,
% 265.92/266.22 (^[A: $i, B: $i, C: $i] : rewrite(((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(927,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A))) <=> ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[926])).
% 265.92/266.22 tff(928,axiom,(![A: $i, B: $i, C: $i] : ((m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_subset_1')).
% 265.92/266.22 tff(929,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[928, 927])).
% 265.92/266.22 tff(930,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[929, 925])).
% 265.92/266.22 tff(931,plain,(
% 265.92/266.22 ![A: $i, B: $i, C: $i] : ((~(m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)))),
% 265.92/266.22 inference(skolemize,[status(sab)],[930])).
% 265.92/266.22 tff(932,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[931, 924])).
% 265.92/266.22 tff(933,plain,
% 265.92/266.22 (![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[932, 922])).
% 265.92/266.22 tff(934,plain,
% 265.92/266.22 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(935,plain,
% 265.92/266.22 ((m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(936,plain,
% 265.92/266.22 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[935])).
% 265.92/266.22 tff(937,plain,
% 265.92/266.22 (((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(transitivity,[status(thm)],[936, 934])).
% 265.92/266.22 tff(938,plain,
% 265.92/266.22 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 265.92/266.22 inference(quant_inst,[status(thm)],[])).
% 265.92/266.22 tff(939,plain,
% 265.92/266.22 ((~![A: $i, B: $i, C: $i] : (m1_subset_1(k4_subset_1(A, B, C), k1_zfmisc_1(A)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[938, 937])).
% 265.92/266.22 tff(940,plain,
% 265.92/266.22 ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[939, 933])).
% 265.92/266.22 tff(941,plain,
% 265.92/266.22 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[940, 82, 76])).
% 265.92/266.22 tff(942,plain,
% 265.92/266.22 (m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[941, 920])).
% 265.92/266.22 tff(943,plain,
% 265.92/266.22 (v1_xboole_0(k2_xboole_0(B!1, C!2)) <=> v1_xboole_0(k4_subset_1(u1_struct_0(A!0), B!1, C!2))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[914])).
% 265.92/266.22 tff(944,plain,
% 265.92/266.22 (v1_xboole_0(k4_subset_1(u1_struct_0(A!0), B!1, C!2)) <=> v1_xboole_0(k2_xboole_0(B!1, C!2))),
% 265.92/266.22 inference(symmetry,[status(thm)],[943])).
% 265.92/266.22 tff(945,plain,
% 265.92/266.22 (k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k2_xboole_0(B!1, C!2)),
% 265.92/266.22 inference(monotonicity,[status(thm)],[614, 573])).
% 265.92/266.22 tff(946,plain,
% 265.92/266.22 (k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)) = k4_subset_1(u1_struct_0(A!0), B!1, C!2)),
% 265.92/266.22 inference(transitivity,[status(thm)],[945, 914])).
% 265.92/266.22 tff(947,plain,
% 265.92/266.22 (v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) <=> v1_xboole_0(k4_subset_1(u1_struct_0(A!0), B!1, C!2))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[946])).
% 265.92/266.22 tff(948,plain,
% 265.92/266.22 (v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))) <=> v1_xboole_0(k2_xboole_0(B!1, C!2))),
% 265.92/266.22 inference(transitivity,[status(thm)],[947, 944])).
% 265.92/266.22 tff(949,plain,
% 265.92/266.22 ((~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))) <=> (~v1_xboole_0(k2_xboole_0(B!1, C!2)))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[948])).
% 265.92/266.22 tff(950,plain,
% 265.92/266.22 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A)))) <=> (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A)))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(951,plain,
% 265.92/266.22 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[950])).
% 265.92/266.22 tff(952,plain,
% 265.92/266.22 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(953,plain,
% 265.92/266.22 (^[A: $i, B: $i] : rewrite(((~v1_xboole_0(A)) => (~v1_xboole_0(k2_xboole_0(B, A)))) <=> (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A)))))),
% 265.92/266.22 inference(bind,[status(th)],[])).
% 265.92/266.22 tff(954,plain,
% 265.92/266.22 (![A: $i, B: $i] : ((~v1_xboole_0(A)) => (~v1_xboole_0(k2_xboole_0(B, A)))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(quant_intro,[status(thm)],[953])).
% 265.92/266.22 tff(955,axiom,(![A: $i, B: $i] : ((~v1_xboole_0(A)) => (~v1_xboole_0(k2_xboole_0(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc3_xboole_0')).
% 265.92/266.22 tff(956,plain,
% 265.92/266.22 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[955, 954])).
% 265.92/266.22 tff(957,plain,
% 265.92/266.22 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[956, 952])).
% 265.92/266.22 tff(958,plain,(
% 265.92/266.22 ![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(skolemize,[status(sab)],[957])).
% 265.92/266.22 tff(959,plain,
% 265.92/266.22 (![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[958, 951])).
% 265.92/266.22 tff(960,plain,
% 265.92/266.22 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(961,plain,
% 265.92/266.22 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))) | (v1_xboole_0(k7_filter_2(A!0, C!2)) | (~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))))),
% 265.92/266.22 inference(quant_inst,[status(thm)],[])).
% 265.92/266.22 tff(962,plain,
% 265.92/266.22 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (~v1_xboole_0(k2_xboole_0(B, A))))) | v1_xboole_0(k7_filter_2(A!0, C!2)) | (~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[961, 960])).
% 265.92/266.22 tff(963,plain,
% 265.92/266.22 (~v1_xboole_0(k2_xboole_0(k7_filter_2(A!0, B!1), k7_filter_2(A!0, C!2)))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[962, 959, 756])).
% 265.92/266.22 tff(964,plain,
% 265.92/266.22 (~v1_xboole_0(k2_xboole_0(B!1, C!2))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[963, 949])).
% 265.92/266.22 tff(965,plain,
% 265.92/266.22 (((~![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)))) | ((~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))))) <=> ((~![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)))) | (~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(966,plain,
% 265.92/266.22 ((v1_xboole_0(k2_xboole_0(B!1, 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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))) | (~m1_subset_1(k2_xboole_0(B!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))))) <=> ((~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))))),
% 265.92/266.22 inference(rewrite,[status(thm)],[])).
% 265.92/266.22 tff(967,plain,
% 265.92/266.22 (((~![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(k2_xboole_0(B!1, 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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))) | (~m1_subset_1(k2_xboole_0(B!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)))) | ((~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2)))))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[966])).
% 265.92/266.22 tff(968,plain,
% 265.92/266.22 (((~![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(k2_xboole_0(B!1, 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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))) | (~m1_subset_1(k2_xboole_0(B!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)))) | (~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))))),
% 265.92/266.22 inference(transitivity,[status(thm)],[967, 965])).
% 265.92/266.22 tff(969,plain,
% 265.92/266.22 ((~![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(k2_xboole_0(B!1, 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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))) | (~m1_subset_1(k2_xboole_0(B!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)))))),
% 265.92/266.22 inference(quant_inst,[status(thm)],[])).
% 265.92/266.22 tff(970,plain,
% 265.92/266.22 ((~![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)))) | (~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))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2)))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[969, 968])).
% 265.92/266.22 tff(971,plain,
% 265.92/266.22 ((~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_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)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2)))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[970, 560, 465, 547, 541, 964])).
% 265.92/266.22 tff(972,plain,
% 265.92/266.22 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[971, 942])).
% 265.92/266.22 tff(973,plain,
% 265.92/266.22 (k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k2_xboole_0(B!1, C!2))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[361])).
% 265.92/266.22 tff(974,plain,
% 265.92/266.22 (m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.22 inference(monotonicity,[status(thm)],[914, 917])).
% 265.92/266.22 tff(975,plain,
% 265.92/266.22 (m1_subset_1(k4_subset_1(u1_struct_0(A!0), B!1, C!2), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.92/266.22 inference(symmetry,[status(thm)],[974])).
% 265.92/266.22 tff(976,plain,
% 265.92/266.22 (m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 265.92/266.22 inference(modus_ponens,[status(thm)],[941, 975])).
% 265.92/266.22 tff(977,plain,
% 265.92/266.22 ((v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m2_lattice4(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), A!0))) | (~v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 265.92/266.22 inference(tautology,[status(thm)],[])).
% 265.92/266.22 tff(978,plain,
% 265.92/266.22 (~v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))),
% 265.92/266.22 inference(unit_resolution,[status(thm)],[977, 149])).
% 265.92/266.22 tff(979,plain,
% 265.92/266.22 (((~![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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))))),
% 265.92/266.23 inference(rewrite,[status(thm)],[])).
% 265.92/266.23 tff(980,plain,
% 265.92/266.23 ((v1_xboole_0(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))))),
% 265.92/266.23 inference(rewrite,[status(thm)],[])).
% 265.92/266.23 tff(981,plain,
% 265.92/266.23 (((~![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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))))),
% 265.92/266.23 inference(monotonicity,[status(thm)],[980])).
% 265.92/266.23 tff(982,plain,
% 265.92/266.23 (((~![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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))))),
% 265.92/266.23 inference(transitivity,[status(thm)],[981, 979])).
% 265.92/266.23 tff(983,plain,
% 265.92/266.23 ((~![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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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))))))))),
% 265.92/266.23 inference(quant_inst,[status(thm)],[])).
% 265.92/266.23 tff(984,plain,
% 265.92/266.23 ((~![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(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.92/266.23 inference(modus_ponens,[status(thm)],[983, 982])).
% 265.92/266.23 tff(985,plain,
% 265.92/266.23 ((~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.92/266.23 inference(unit_resolution,[status(thm)],[984, 301, 978])).
% 265.92/266.23 tff(986,plain,
% 265.92/266.23 (![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.92/266.23 inference(unit_resolution,[status(thm)],[985, 155])).
% 265.92/266.23 tff(987,plain,
% 265.92/266.23 (((~![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, 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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))))))),
% 265.92/266.23 inference(rewrite,[status(thm)],[])).
% 265.92/266.23 tff(988,plain,
% 265.92/266.23 ((v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))))) <=> (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))))))),
% 265.92/266.23 inference(rewrite,[status(thm)],[])).
% 265.92/266.23 tff(989,plain,
% 265.92/266.23 (((~![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2)))))))))),
% 265.92/266.23 inference(monotonicity,[status(thm)],[988])).
% 265.92/266.23 tff(990,plain,
% 265.92/266.23 (((~![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, 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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))))))),
% 265.92/266.24 inference(transitivity,[status(thm)],[989, 987])).
% 265.92/266.24 tff(991,plain,
% 265.92/266.24 ((~![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | (v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))),
% 265.92/266.24 inference(quant_inst,[status(thm)],[])).
% 265.92/266.24 tff(992,plain,
% 265.92/266.24 ((~![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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))))))) | v1_xboole_0(k2_xboole_0(B!1, C!2)) | (~m1_subset_1(k2_xboole_0(B!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, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2)))))))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[991, 990])).
% 265.92/266.24 tff(993,plain,
% 265.92/266.24 (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))))),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[992, 964, 986, 976])).
% 265.92/266.24 tff(994,plain,
% 265.92/266.24 (((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) = k19_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k3_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k19_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)))) | (~(k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2)))))) | (k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))))),
% 265.92/266.24 inference(tautology,[status(thm)],[])).
% 265.92/266.24 tff(995,plain,
% 265.92/266.24 (k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2)))),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[994, 993])).
% 265.92/266.24 tff(996,plain,
% 265.92/266.24 (k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2))) = k3_filter_2(k1_lattice2(A!0), k2_xboole_0(B!1, C!2))),
% 265.92/266.24 inference(symmetry,[status(thm)],[995])).
% 265.92/266.24 tff(997,plain,
% 265.92/266.24 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2)))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2)))),
% 265.92/266.24 inference(rewrite,[status(thm)],[])).
% 265.92/266.24 tff(998,plain,
% 265.92/266.24 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2)))),
% 265.92/266.24 inference(quant_inst,[status(thm)],[])).
% 265.92/266.24 tff(999,plain,
% 265.92/266.24 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[998, 997])).
% 265.92/266.24 tff(1000,plain,
% 265.92/266.24 ((~m1_subset_1(k2_xboole_0(B!1, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2))),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[999, 604])).
% 265.92/266.24 tff(1001,plain,
% 265.92/266.24 (k8_filter_2(A!0, k2_xboole_0(B!1, C!2)) = k2_xboole_0(B!1, C!2)),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[1000, 976])).
% 265.92/266.24 tff(1002,plain,
% 265.92/266.24 (k2_xboole_0(B!1, C!2) = k8_filter_2(A!0, k2_xboole_0(B!1, C!2))),
% 265.92/266.24 inference(symmetry,[status(thm)],[1001])).
% 265.92/266.24 tff(1003,plain,
% 265.92/266.24 (k4_subset_1(u1_struct_0(A!0), B!1, C!2) = k8_filter_2(A!0, k2_xboole_0(B!1, C!2))),
% 265.92/266.24 inference(transitivity,[status(thm)],[913, 1002])).
% 265.92/266.24 tff(1004,plain,
% 265.92/266.24 (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k8_filter_2(A!0, k2_xboole_0(B!1, C!2)))),
% 265.92/266.24 inference(monotonicity,[status(thm)],[1003])).
% 265.92/266.24 tff(1005,plain,
% 265.92/266.24 (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))),
% 265.92/266.24 inference(transitivity,[status(thm)],[1004, 996, 973, 972, 916, 891, 766, 568, 363, 347, 318])).
% 265.92/266.24 tff(1006,plain,
% 265.92/266.24 (m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.24 inference(monotonicity,[status(thm)],[1005])).
% 265.92/266.24 tff(1007,plain,
% 265.92/266.24 (m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.24 inference(symmetry,[status(thm)],[1006])).
% 265.92/266.24 tff(1008,plain,
% 265.92/266.24 (m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[155, 1007])).
% 265.92/266.24 tff(1009,plain,
% 265.92/266.24 (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))),
% 265.92/266.24 inference(or_elim,[status(thm)],[40])).
% 265.92/266.24 tff(1010,plain,
% 265.92/266.24 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) | (~(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 265.92/266.24 inference(tautology,[status(thm)],[])).
% 265.92/266.24 tff(1011,plain,
% 265.92/266.24 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))) | (~(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[1010, 1009])).
% 265.92/266.24 tff(1012,plain,
% 265.92/266.24 (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 265.92/266.24 inference(unit_resolution,[status(thm)],[1011, 1005])).
% 265.92/266.24 tff(1013,plain,
% 265.92/266.24 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 265.92/266.24 inference(bind,[status(th)],[])).
% 265.92/266.24 tff(1014,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.24 inference(quant_intro,[status(thm)],[1013])).
% 265.92/266.24 tff(1015,plain,
% 265.92/266.24 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 265.92/266.24 inference(bind,[status(th)],[])).
% 265.92/266.24 tff(1016,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.24 inference(quant_intro,[status(thm)],[1015])).
% 265.92/266.24 tff(1017,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 265.92/266.24 inference(rewrite,[status(thm)],[])).
% 265.92/266.24 tff(1018,plain,
% 265.92/266.24 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))))),
% 265.92/266.24 inference(bind,[status(th)],[])).
% 265.92/266.24 tff(1019,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 265.92/266.24 inference(quant_intro,[status(thm)],[1018])).
% 265.92/266.24 tff(1020,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 265.92/266.24 tff(1021,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[1020, 1019])).
% 265.92/266.24 tff(1022,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[1021, 1017])).
% 265.92/266.24 tff(1023,plain,(
% 265.92/266.24 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 265.92/266.24 inference(skolemize,[status(sab)],[1022])).
% 265.92/266.24 tff(1024,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[1023, 1016])).
% 265.92/266.24 tff(1025,plain,
% 265.92/266.24 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 265.92/266.24 inference(modus_ponens,[status(thm)],[1024, 1014])).
% 265.92/266.24 tff(1026,plain,
% 265.92/266.24 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))),
% 265.92/266.24 inference(rewrite,[status(thm)],[])).
% 265.92/266.24 tff(1027,plain,
% 265.92/266.24 ((v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))),
% 265.92/266.24 inference(rewrite,[status(thm)],[])).
% 265.92/266.24 tff(1028,plain,
% 265.92/266.24 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))))),
% 267.14/267.40 inference(monotonicity,[status(thm)],[1027])).
% 267.14/267.40 tff(1029,plain,
% 267.14/267.40 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))))),
% 267.14/267.40 inference(transitivity,[status(thm)],[1028, 1026])).
% 267.14/267.40 tff(1030,plain,
% 267.14/267.40 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 267.14/267.40 inference(quant_inst,[status(thm)],[])).
% 267.14/267.40 tff(1031,plain,
% 267.14/267.40 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 267.14/267.40 inference(modus_ponens,[status(thm)],[1030, 1029])).
% 267.14/267.40 tff(1032,plain,
% 267.14/267.40 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)), k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))) <=> (k19_filter_2(A!0, k4_subset_1(u1_struct_0(A!0), B!1, C!2)) = k19_filter_2(A!0, k20_filter_2(A!0, B!1, C!2))))),
% 267.14/267.40 inference(unit_resolution,[status(thm)],[1031, 1025])).
% 267.14/267.40 tff(1033,plain,
% 267.14/267.40 ($false),
% 267.14/267.40 inference(unit_resolution,[status(thm)],[1032, 1012, 1008, 209, 155])).
% 267.14/267.40 % SZS output end Proof
% 267.14/267.40 % E exiting
%------------------------------------------------------------------------------