%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT312+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:18 AM UTC 2025
% Result : Theorem 0.68s 0.86s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT312+1 : TPTP v9.0.0. Released v3.4.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:11:41 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.68/0.86 % SZS status Theorem
% 0.68/0.86 % SZS output start Proof
% 0.68/0.86 tff(k18_filter_2_type, type, (
% 0.68/0.86 k18_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(tptp_fun_B_1_type, type, (
% 0.68/0.86 tptp_fun_B_1: $i)).
% 0.68/0.86 tff(tptp_fun_A_0_type, type, (
% 0.68/0.86 tptp_fun_A_0: $i)).
% 0.68/0.86 tff(k19_filter_2_type, type, (
% 0.68/0.86 k19_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(tptp_fun_C_2_type, type, (
% 0.68/0.86 tptp_fun_C_2: $i)).
% 0.68/0.86 tff(k2_filter_0_type, type, (
% 0.68/0.86 k2_filter_0: ( $i * $i ) > $i)).
% 0.68/0.86 tff(g3_lattices_type, type, (
% 0.68/0.86 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.68/0.86 tff(u2_lattices_type, type, (
% 0.68/0.86 u2_lattices: $i > $i)).
% 0.68/0.86 tff(u1_lattices_type, type, (
% 0.68/0.86 u1_lattices: $i > $i)).
% 0.68/0.86 tff(u1_struct_0_type, type, (
% 0.68/0.86 u1_struct_0: $i > $i)).
% 0.68/0.86 tff(k3_filter_0_type, type, (
% 0.68/0.86 k3_filter_0: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k6_domain_1_type, type, (
% 0.68/0.86 k6_domain_1: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k2_filter_2_type, type, (
% 0.68/0.86 k2_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k5_filter_2_type, type, (
% 0.68/0.86 k5_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k1_lattice2_type, type, (
% 0.68/0.86 k1_lattice2: $i > $i)).
% 0.68/0.86 tff(m1_subset_1_type, type, (
% 0.68/0.86 m1_subset_1: ( $i * $i ) > $o)).
% 0.68/0.86 tff(v10_lattices_type, type, (
% 0.68/0.86 v10_lattices: $i > $o)).
% 0.68/0.86 tff(l3_lattices_type, type, (
% 0.68/0.86 l3_lattices: $i > $o)).
% 0.68/0.86 tff(v3_struct_0_type, type, (
% 0.68/0.86 v3_struct_0: $i > $o)).
% 0.68/0.86 tff(k1_zfmisc_1_type, type, (
% 0.68/0.86 k1_zfmisc_1: $i > $i)).
% 0.68/0.86 tff(v1_xboole_0_type, type, (
% 0.68/0.86 v1_xboole_0: $i > $o)).
% 0.68/0.86 tff(r1_filter_2_type, type, (
% 0.68/0.86 r1_filter_2: ( $i * $i * $i ) > $o)).
% 0.68/0.86 tff(v9_lattices_type, type, (
% 0.68/0.86 v9_lattices: $i > $o)).
% 0.68/0.86 tff(v8_lattices_type, type, (
% 0.68/0.86 v8_lattices: $i > $o)).
% 0.68/0.86 tff(v7_lattices_type, type, (
% 0.68/0.86 v7_lattices: $i > $o)).
% 0.68/0.86 tff(v6_lattices_type, type, (
% 0.68/0.86 v6_lattices: $i > $o)).
% 0.68/0.86 tff(v5_lattices_type, type, (
% 0.68/0.86 v5_lattices: $i > $o)).
% 0.68/0.86 tff(v4_lattices_type, type, (
% 0.68/0.86 v4_lattices: $i > $o)).
% 0.68/0.86 tff(v3_lattices_type, type, (
% 0.68/0.86 v3_lattices: $i > $o)).
% 0.68/0.86 tff(m1_relset_1_type, type, (
% 0.68/0.86 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.68/0.86 tff(k2_zfmisc_1_type, type, (
% 0.68/0.86 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.68/0.86 tff(m2_relset_1_type, type, (
% 0.68/0.86 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.68/0.86 tff(v1_funct_2_type, type, (
% 0.68/0.86 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.68/0.86 tff(v1_funct_1_type, type, (
% 0.68/0.86 v1_funct_1: $i > $o)).
% 0.68/0.86 tff(l1_lattices_type, type, (
% 0.68/0.86 l1_lattices: $i > $o)).
% 0.68/0.86 tff(l2_lattices_type, type, (
% 0.68/0.86 l2_lattices: $i > $o)).
% 0.68/0.86 tff(k3_filter_2_type, type, (
% 0.68/0.86 k3_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k7_filter_2_type, type, (
% 0.68/0.86 k7_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k8_filter_2_type, type, (
% 0.68/0.86 k8_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(k1_tarski_type, type, (
% 0.68/0.86 k1_tarski: $i > $i)).
% 0.68/0.86 tff(v1_realset1_type, type, (
% 0.68/0.86 v1_realset1: $i > $o)).
% 0.68/0.86 tff(v1_finset_1_type, type, (
% 0.68/0.86 v1_finset_1: $i > $o)).
% 0.68/0.86 tff(l1_struct_0_type, type, (
% 0.68/0.86 l1_struct_0: $i > $o)).
% 0.68/0.86 tff(m2_lattice4_type, type, (
% 0.68/0.86 m2_lattice4: ( $i * $i ) > $o)).
% 0.68/0.86 tff(m2_filter_2_type, type, (
% 0.68/0.86 m2_filter_2: ( $i * $i ) > $o)).
% 0.68/0.86 tff(a_2_0_filter_2_type, type, (
% 0.68/0.86 a_2_0_filter_2: ( $i * $i ) > $i)).
% 0.68/0.86 tff(1,plain,
% 0.68/0.86 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(2,plain,
% 0.68/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[1])).
% 0.68/0.86 tff(3,plain,
% 0.68/0.86 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(4,plain,
% 0.68/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[3])).
% 0.68/0.86 tff(5,plain,
% 0.68/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(transitivity,[status(thm)],[4, 2])).
% 0.68/0.86 tff(6,plain,
% 0.68/0.86 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(7,plain,
% 0.68/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[6])).
% 0.68/0.86 tff(8,plain,
% 0.68/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(9,plain,
% 0.68/0.86 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(bind,[status(th)],[])).
% 0.68/0.86 tff(10,plain,
% 0.68/0.86 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.68/0.86 inference(quant_intro,[status(thm)],[9])).
% 0.68/0.86 tff(11,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_filter_2')).
% 0.68/0.86 tff(12,plain,
% 0.68/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[11, 10])).
% 0.68/0.86 tff(13,plain,
% 0.68/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[12, 8])).
% 0.68/0.86 tff(14,plain,(
% 0.68/0.86 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.68/0.86 inference(skolemize,[status(sab)],[13])).
% 0.68/0.86 tff(15,plain,
% 0.68/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[14, 7])).
% 0.68/0.86 tff(16,plain,
% 0.68/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.68/0.86 inference(modus_ponens,[status(thm)],[15, 5])).
% 0.68/0.86 tff(17,plain,
% 0.68/0.86 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(18,plain,
% 0.68/0.86 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))) <=> (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(19,plain,
% 0.68/0.86 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[18])).
% 0.68/0.86 tff(20,plain,
% 0.68/0.86 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))))),
% 0.68/0.86 inference(monotonicity,[status(thm)],[19])).
% 0.68/0.86 tff(21,plain,
% 0.68/0.86 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.68/0.86 inference(transitivity,[status(thm)],[20, 17])).
% 0.68/0.86 tff(22,plain,
% 0.68/0.86 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(23,plain,
% 0.68/0.86 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B)) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 0.68/0.86 inference(rewrite,[status(thm)],[])).
% 0.68/0.86 tff(24,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => (r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B)) => r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t41_filter_2')).
% 0.71/0.86 tff(25,plain,
% 0.71/0.86 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[24, 23])).
% 0.71/0.86 tff(26,plain,
% 0.71/0.86 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[25, 22])).
% 0.71/0.86 tff(27,plain,
% 0.71/0.86 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[26, 22])).
% 0.71/0.86 tff(28,plain,
% 0.71/0.86 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : (r1_filter_2(u1_struct_0(A), k19_filter_2(A, C), k18_filter_2(A, B)) | (~r1_filter_2(u1_struct_0(A), C, k6_domain_1(u1_struct_0(A), B))) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[27, 22])).
% 0.71/0.86 tff(29,plain,
% 0.71/0.86 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[28, 21])).
% 0.71/0.86 tff(30,plain,
% 0.71/0.86 (l3_lattices(A!0)),
% 0.71/0.86 inference(and_elim,[status(thm)],[29])).
% 0.71/0.86 tff(31,plain,
% 0.71/0.86 (v10_lattices(A!0)),
% 0.71/0.86 inference(and_elim,[status(thm)],[29])).
% 0.71/0.86 tff(32,plain,
% 0.71/0.86 (~v3_struct_0(A!0)),
% 0.71/0.86 inference(and_elim,[status(thm)],[29])).
% 0.71/0.86 tff(33,plain,
% 0.71/0.86 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(34,plain,
% 0.71/0.86 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(35,plain,
% 0.71/0.86 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.71/0.86 tff(36,plain,
% 0.71/0.86 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[35, 32, 31, 30, 16])).
% 0.71/0.86 tff(37,plain,
% 0.71/0.86 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.71/0.86 inference(and_elim,[status(thm)],[29])).
% 0.71/0.86 tff(38,plain,
% 0.71/0.86 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(39,plain,
% 0.71/0.86 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(40,plain,
% 0.71/0.86 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.71/0.86 tff(41,plain,
% 0.71/0.86 (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[40, 37, 36])).
% 0.71/0.86 tff(42,plain,
% 0.71/0.86 (((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))) | (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))),
% 0.71/0.86 inference(tautology,[status(thm)],[])).
% 0.71/0.86 tff(43,plain,
% 0.71/0.86 (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.71/0.86 tff(44,plain,
% 0.71/0.86 (k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k18_filter_2(A!0, B!1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[43])).
% 0.71/0.86 tff(45,plain,
% 0.71/0.86 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(46,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[45])).
% 0.71/0.86 tff(47,plain,
% 0.71/0.86 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(48,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[47])).
% 0.71/0.86 tff(49,plain,
% 0.71/0.86 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(50,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[49])).
% 0.71/0.86 tff(51,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[50, 48])).
% 0.71/0.86 tff(52,plain,
% 0.71/0.86 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(53,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[52])).
% 0.71/0.86 tff(54,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(55,plain,
% 0.71/0.86 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(56,plain,
% 0.71/0.86 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[55])).
% 0.71/0.86 tff(57,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 0.71/0.86 tff(58,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.71/0.86 tff(59,plain,
% 0.71/0.86 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[58, 54])).
% 0.71/0.86 tff(60,plain,(
% 0.71/0.86 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[59])).
% 0.71/0.86 tff(61,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[60, 53])).
% 0.71/0.86 tff(62,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[61, 51])).
% 0.71/0.86 tff(63,plain,
% 0.71/0.86 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[62, 46])).
% 0.71/0.86 tff(64,plain,
% 0.71/0.86 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(65,plain,
% 0.71/0.86 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(66,plain,
% 0.71/0.86 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[65, 64])).
% 0.71/0.86 tff(67,plain,
% 0.71/0.86 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[66, 32, 31, 30, 63])).
% 0.71/0.86 tff(68,plain,
% 0.71/0.86 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(69,plain,
% 0.71/0.86 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(70,plain,
% 0.71/0.86 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.71/0.86 tff(71,plain,
% 0.71/0.86 (k5_filter_2(A!0, B!1) = B!1),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[70, 37, 67])).
% 0.71/0.86 tff(72,plain,
% 0.71/0.86 (B!1 = k5_filter_2(A!0, B!1)),
% 0.71/0.86 inference(symmetry,[status(thm)],[71])).
% 0.71/0.86 tff(73,plain,
% 0.71/0.86 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(74,plain,
% 0.71/0.86 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[73])).
% 0.71/0.86 tff(75,plain,
% 0.71/0.86 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(76,plain,
% 0.71/0.86 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(77,plain,
% 0.71/0.86 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[76])).
% 0.71/0.86 tff(78,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 0.71/0.86 tff(79,plain,
% 0.71/0.86 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.71/0.86 tff(80,plain,
% 0.71/0.86 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.71/0.86 tff(81,plain,(
% 0.71/0.86 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(skolemize,[status(sab)],[80])).
% 0.71/0.86 tff(82,plain,
% 0.71/0.86 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.71/0.86 tff(83,plain,
% 0.71/0.86 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(84,plain,
% 0.71/0.86 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(85,plain,
% 0.71/0.86 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.71/0.86 tff(86,plain,
% 0.71/0.86 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[85, 30, 82])).
% 0.71/0.86 tff(87,plain,
% 0.71/0.86 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.71/0.86 inference(symmetry,[status(thm)],[86])).
% 0.71/0.86 tff(88,plain,
% 0.71/0.86 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[87, 72])).
% 0.71/0.86 tff(89,plain,
% 0.71/0.86 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[87])).
% 0.71/0.86 tff(90,plain,
% 0.71/0.86 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.86 inference(symmetry,[status(thm)],[89])).
% 0.71/0.86 tff(91,plain,
% 0.71/0.86 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[71, 90])).
% 0.71/0.86 tff(92,plain,
% 0.71/0.86 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(93,plain,
% 0.71/0.86 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[92])).
% 0.71/0.86 tff(94,plain,
% 0.71/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(95,plain,
% 0.71/0.86 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[94])).
% 0.71/0.86 tff(96,plain,
% 0.71/0.86 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(97,plain,
% 0.71/0.86 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(98,plain,
% 0.71/0.87 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[97])).
% 0.71/0.87 tff(99,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 0.71/0.87 tff(100,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.71/0.87 tff(101,plain,
% 0.71/0.87 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[100, 96])).
% 0.71/0.87 tff(102,plain,(
% 0.71/0.87 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[101])).
% 0.71/0.87 tff(103,plain,
% 0.71/0.87 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[102, 95])).
% 0.71/0.87 tff(104,plain,
% 0.71/0.87 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[103, 93])).
% 0.71/0.87 tff(105,plain,
% 0.71/0.87 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(106,plain,
% 0.71/0.87 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(107,plain,
% 0.71/0.87 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[106])).
% 0.71/0.87 tff(108,plain,
% 0.71/0.87 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.87 inference(transitivity,[status(thm)],[107, 105])).
% 0.71/0.87 tff(109,plain,
% 0.71/0.87 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(110,plain,
% 0.71/0.87 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.71/0.87 tff(111,plain,
% 0.71/0.87 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[110, 32, 31, 30, 37, 104])).
% 0.71/0.87 tff(112,plain,
% 0.71/0.87 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[111, 91])).
% 0.71/0.87 tff(113,plain,
% 0.71/0.87 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[87])).
% 0.71/0.87 tff(114,plain,
% 0.71/0.87 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[113])).
% 0.71/0.87 tff(115,plain,
% 0.71/0.87 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(116,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[115])).
% 0.71/0.87 tff(117,plain,
% 0.71/0.87 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(118,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[117])).
% 0.71/0.87 tff(119,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(120,plain,
% 0.71/0.87 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(121,plain,
% 0.71/0.87 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[120])).
% 0.71/0.87 tff(122,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.71/0.87 tff(123,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.71/0.87 tff(124,plain,
% 0.71/0.87 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[123, 119])).
% 0.71/0.87 tff(125,plain,(
% 0.71/0.87 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[124])).
% 0.71/0.87 tff(126,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[125, 118])).
% 0.71/0.87 tff(127,plain,
% 0.71/0.87 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[126, 116])).
% 0.71/0.87 tff(128,plain,
% 0.71/0.87 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(129,plain,
% 0.71/0.87 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(130,plain,
% 0.71/0.87 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.71/0.87 tff(131,plain,
% 0.71/0.87 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[130, 32, 31, 30, 127])).
% 0.71/0.87 tff(132,plain,
% 0.71/0.87 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(133,plain,
% 0.71/0.87 (v10_lattices(k1_lattice2(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[132, 131])).
% 0.71/0.87 tff(134,plain,
% 0.71/0.87 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[133, 114])).
% 0.71/0.87 tff(135,plain,
% 0.71/0.87 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[87])).
% 0.71/0.87 tff(136,plain,
% 0.71/0.87 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.87 inference(symmetry,[status(thm)],[135])).
% 0.71/0.87 tff(137,plain,
% 0.71/0.87 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[136])).
% 0.71/0.87 tff(138,plain,
% 0.71/0.87 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(139,plain,
% 0.71/0.87 (~v3_struct_0(k1_lattice2(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[138, 131])).
% 0.71/0.87 tff(140,plain,
% 0.71/0.87 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[139, 137])).
% 0.71/0.87 tff(141,plain,
% 0.71/0.87 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(142,plain,
% 0.71/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[141])).
% 0.71/0.87 tff(143,plain,
% 0.71/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(144,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.71/0.87 tff(145,plain,
% 0.71/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.71/0.87 tff(146,plain,(
% 0.71/0.87 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.71/0.87 inference(skolemize,[status(sab)],[145])).
% 0.71/0.87 tff(147,plain,
% 0.71/0.87 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[146, 142])).
% 0.71/0.87 tff(148,plain,
% 0.71/0.87 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(149,plain,
% 0.71/0.87 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[148, 147])).
% 0.71/0.87 tff(150,plain,
% 0.71/0.87 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(151,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[150])).
% 0.71/0.87 tff(152,plain,
% 0.71/0.87 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(153,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[152])).
% 0.71/0.87 tff(154,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(155,plain,
% 0.71/0.87 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(156,plain,
% 0.71/0.87 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[155])).
% 0.71/0.87 tff(157,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.71/0.87 tff(158,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.71/0.87 tff(159,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.71/0.87 tff(160,plain,(
% 0.71/0.87 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.71/0.87 inference(skolemize,[status(sab)],[159])).
% 0.71/0.87 tff(161,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.71/0.87 tff(162,plain,
% 0.71/0.87 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[161, 151])).
% 0.71/0.87 tff(163,plain,
% 0.71/0.87 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(164,plain,
% 0.71/0.87 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(165,plain,
% 0.71/0.87 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[164, 163])).
% 0.71/0.87 tff(166,plain,
% 0.71/0.87 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[165, 30, 162])).
% 0.71/0.87 tff(167,plain,
% 0.71/0.87 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(168,plain,
% 0.71/0.87 (l1_lattices(A!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.71/0.87 tff(169,plain,
% 0.71/0.87 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(170,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[169])).
% 0.71/0.87 tff(171,plain,
% 0.71/0.87 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(172,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[171])).
% 0.71/0.87 tff(173,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(174,plain,
% 0.71/0.87 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(175,plain,
% 0.71/0.87 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[174])).
% 0.71/0.87 tff(176,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.71/0.87 tff(177,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.71/0.87 tff(178,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.71/0.87 tff(179,plain,(
% 0.71/0.87 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[178])).
% 0.71/0.87 tff(180,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.71/0.87 tff(181,plain,
% 0.71/0.87 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[180, 170])).
% 0.71/0.87 tff(182,plain,
% 0.71/0.87 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(183,plain,
% 0.71/0.87 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(184,plain,
% 0.71/0.87 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[183, 182])).
% 0.71/0.87 tff(185,plain,
% 0.71/0.87 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[184, 181])).
% 0.71/0.87 tff(186,plain,
% 0.71/0.87 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[185, 168])).
% 0.71/0.87 tff(187,plain,
% 0.71/0.87 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(188,plain,
% 0.71/0.87 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[187, 186])).
% 0.71/0.87 tff(189,plain,
% 0.71/0.87 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(190,plain,
% 0.71/0.87 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.71/0.87 tff(191,plain,
% 0.71/0.87 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[190, 149])).
% 0.71/0.87 tff(192,plain,
% 0.71/0.87 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(193,plain,
% 0.71/0.87 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[192, 147])).
% 0.71/0.87 tff(194,plain,
% 0.71/0.87 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.71/0.87 inference(tautology,[status(thm)],[])).
% 0.71/0.87 tff(195,plain,
% 0.71/0.87 (l2_lattices(A!0)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[194, 166])).
% 0.71/0.87 tff(196,plain,
% 0.71/0.87 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(197,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[196])).
% 0.71/0.87 tff(198,plain,
% 0.71/0.87 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(199,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[198])).
% 0.71/0.87 tff(200,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(201,plain,
% 0.71/0.87 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(202,plain,
% 0.71/0.87 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[201])).
% 0.71/0.87 tff(203,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.71/0.87 tff(204,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.71/0.87 tff(205,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.71/0.87 tff(206,plain,(
% 0.71/0.87 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.71/0.87 inference(skolemize,[status(sab)],[205])).
% 0.71/0.87 tff(207,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.71/0.87 tff(208,plain,
% 0.71/0.87 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[207, 197])).
% 0.71/0.87 tff(209,plain,
% 0.71/0.87 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(210,plain,
% 0.71/0.88 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(211,plain,
% 0.71/0.88 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.71/0.88 tff(212,plain,
% 0.71/0.88 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[211, 208])).
% 0.71/0.88 tff(213,plain,
% 0.71/0.88 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[212, 195])).
% 0.71/0.88 tff(214,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(215,plain,
% 0.71/0.88 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[214, 213])).
% 0.71/0.88 tff(216,plain,
% 0.71/0.88 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(217,plain,
% 0.71/0.88 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[216, 215])).
% 0.71/0.88 tff(218,plain,
% 0.71/0.88 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[217, 193])).
% 0.71/0.88 tff(219,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(220,plain,
% 0.71/0.88 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[219, 213])).
% 0.71/0.88 tff(221,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(222,plain,
% 0.71/0.88 (v1_funct_1(u2_lattices(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[221, 213])).
% 0.71/0.88 tff(223,plain,
% 0.71/0.88 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(224,plain,
% 0.71/0.88 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[223, 186])).
% 0.71/0.88 tff(225,plain,
% 0.71/0.88 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(226,plain,
% 0.71/0.88 (v1_funct_1(u1_lattices(A!0))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[225, 186])).
% 0.71/0.88 tff(227,plain,
% 0.71/0.88 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(228,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[227])).
% 0.71/0.88 tff(229,plain,
% 0.71/0.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(230,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[229])).
% 0.71/0.88 tff(231,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(232,plain,
% 0.71/0.88 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(233,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[232])).
% 0.71/0.88 tff(234,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 0.71/0.88 tff(235,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.71/0.88 tff(236,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[235, 231])).
% 0.71/0.88 tff(237,plain,(
% 0.71/0.88 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.71/0.88 inference(skolemize,[status(sab)],[236])).
% 0.71/0.88 tff(238,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[237, 230])).
% 0.71/0.88 tff(239,plain,
% 0.71/0.88 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[238, 228])).
% 0.71/0.88 tff(240,plain,
% 0.71/0.88 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(241,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(242,plain,
% 0.71/0.88 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(243,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[242])).
% 0.71/0.88 tff(244,plain,
% 0.71/0.88 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[243, 241])).
% 0.71/0.88 tff(245,plain,
% 0.71/0.88 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[244])).
% 0.71/0.88 tff(246,plain,
% 0.71/0.88 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(transitivity,[status(thm)],[245, 240])).
% 0.71/0.88 tff(247,plain,
% 0.71/0.88 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(248,plain,
% 0.71/0.88 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[247, 246])).
% 0.71/0.88 tff(249,plain,
% 0.71/0.88 ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[248, 239, 226, 224, 222, 220])).
% 0.71/0.88 tff(250,plain,
% 0.71/0.88 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[249, 218, 191])).
% 0.71/0.88 tff(251,plain,
% 0.71/0.88 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.88 inference(tautology,[status(thm)],[])).
% 0.71/0.88 tff(252,plain,
% 0.71/0.88 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.71/0.88 tff(253,plain,
% 0.71/0.88 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(254,plain,
% 0.71/0.88 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[253])).
% 0.71/0.88 tff(255,plain,
% 0.71/0.88 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(256,plain,
% 0.71/0.88 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[255])).
% 0.71/0.88 tff(257,plain,
% 0.71/0.88 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(258,plain,
% 0.71/0.88 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(259,plain,
% 0.71/0.88 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[258])).
% 0.71/0.88 tff(260,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 0.71/0.88 tff(261,plain,
% 0.71/0.88 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.71/0.88 tff(262,plain,
% 0.71/0.88 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[261, 257])).
% 0.71/0.88 tff(263,plain,(
% 0.71/0.88 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[262])).
% 0.71/0.88 tff(264,plain,
% 0.71/0.88 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[263, 256])).
% 0.71/0.88 tff(265,plain,
% 0.71/0.88 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[264, 254])).
% 0.71/0.88 tff(266,plain,
% 0.71/0.88 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(267,plain,
% 0.71/0.88 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(268,plain,
% 0.71/0.88 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[267])).
% 0.71/0.89 tff(269,plain,
% 0.71/0.89 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[268, 266])).
% 0.71/0.89 tff(270,plain,
% 0.71/0.89 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(271,plain,
% 0.71/0.89 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.71/0.89 tff(272,plain,
% 0.71/0.89 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[271, 265, 252, 140, 134, 112])).
% 0.71/0.89 tff(273,plain,
% 0.71/0.89 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.71/0.89 inference(symmetry,[status(thm)],[272])).
% 0.71/0.89 tff(274,plain,
% 0.71/0.89 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k18_filter_2(A!0, B!1)),
% 0.71/0.89 inference(transitivity,[status(thm)],[273, 88, 44])).
% 0.71/0.89 tff(275,plain,
% 0.71/0.89 (^[A: $i] : refl((~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A))))) <=> (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(276,plain,
% 0.71/0.89 (![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A))))) <=> ![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A)))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[275])).
% 0.71/0.89 tff(277,plain,
% 0.71/0.89 (^[A: $i] : rewrite(((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A))) <=> (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(278,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A))) <=> ![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A)))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[277])).
% 0.71/0.89 tff(279,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(280,plain,
% 0.71/0.89 (^[A: $i] : rewrite((((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A))) & v1_realset1(k1_tarski(A))) <=> ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(281,plain,
% 0.71/0.89 (![A: $i] : (((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A))) & v1_realset1(k1_tarski(A))) <=> ![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[280])).
% 0.71/0.89 tff(282,axiom,(![A: $i] : (((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A))) & v1_realset1(k1_tarski(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_realset1')).
% 0.71/0.89 tff(283,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[282, 281])).
% 0.71/0.89 tff(284,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[283, 279])).
% 0.71/0.89 tff(285,plain,(
% 0.71/0.89 ![A: $i] : ((~v1_xboole_0(k1_tarski(A))) & v1_finset_1(k1_tarski(A)) & v1_realset1(k1_tarski(A)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[284])).
% 0.71/0.89 tff(286,plain,
% 0.71/0.89 (![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A)))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[285, 278])).
% 0.71/0.89 tff(287,plain,
% 0.71/0.89 (![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A)))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[286, 276])).
% 0.71/0.89 tff(288,plain,
% 0.71/0.89 ((~![A: $i] : (~(v1_xboole_0(k1_tarski(A)) | (~v1_finset_1(k1_tarski(A))) | (~v1_realset1(k1_tarski(A)))))) | (~(v1_xboole_0(k1_tarski(B!1)) | (~v1_finset_1(k1_tarski(B!1))) | (~v1_realset1(k1_tarski(B!1)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(289,plain,
% 0.71/0.89 (~(v1_xboole_0(k1_tarski(B!1)) | (~v1_finset_1(k1_tarski(B!1))) | (~v1_realset1(k1_tarski(B!1))))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[288, 287])).
% 0.71/0.89 tff(290,plain,
% 0.71/0.89 ((v1_xboole_0(k1_tarski(B!1)) | (~v1_finset_1(k1_tarski(B!1))) | (~v1_realset1(k1_tarski(B!1)))) | (~v1_xboole_0(k1_tarski(B!1)))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(291,plain,
% 0.71/0.89 (~v1_xboole_0(k1_tarski(B!1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[290, 289])).
% 0.71/0.89 tff(292,plain,
% 0.71/0.89 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(293,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[292])).
% 0.71/0.89 tff(294,plain,
% 0.71/0.89 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(295,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[294])).
% 0.71/0.89 tff(296,plain,
% 0.71/0.89 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(297,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[296])).
% 0.71/0.89 tff(298,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[297, 295])).
% 0.71/0.89 tff(299,plain,
% 0.71/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(300,plain,
% 0.71/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[299])).
% 0.71/0.89 tff(301,plain,
% 0.71/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(302,plain,
% 0.71/0.89 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(303,plain,
% 0.71/0.89 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[302])).
% 0.71/0.89 tff(304,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 0.71/0.89 tff(305,plain,
% 0.71/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.71/0.89 tff(306,plain,
% 0.71/0.89 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.71/0.89 tff(307,plain,(
% 0.71/0.89 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[306])).
% 0.71/0.89 tff(308,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[307, 300])).
% 0.71/0.89 tff(309,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[308, 298])).
% 0.71/0.89 tff(310,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[309, 293])).
% 0.71/0.89 tff(311,plain,
% 0.71/0.89 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(312,plain,
% 0.71/0.89 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(313,plain,
% 0.71/0.89 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[312, 311])).
% 0.71/0.89 tff(314,plain,
% 0.71/0.89 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[313, 32, 31, 30, 310])).
% 0.71/0.89 tff(315,plain,
% 0.71/0.89 (~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (~((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.71/0.89 inference(and_elim,[status(thm)],[29])).
% 0.71/0.89 tff(316,plain,
% 0.71/0.89 ((~v1_xboole_0(C!2)) & m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.71/0.89 inference(or_elim,[status(thm)],[315])).
% 0.71/0.89 tff(317,plain,
% 0.71/0.89 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.71/0.89 inference(and_elim,[status(thm)],[316])).
% 0.71/0.89 tff(318,plain,
% 0.71/0.89 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(319,plain,
% 0.71/0.89 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(320,plain,
% 0.71/0.89 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, C!2) = C!2)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[319, 318])).
% 0.71/0.89 tff(321,plain,
% 0.71/0.89 (k7_filter_2(A!0, C!2) = C!2),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[320, 317, 314])).
% 0.71/0.89 tff(322,plain,
% 0.71/0.89 (C!2 = k7_filter_2(A!0, C!2)),
% 0.71/0.89 inference(symmetry,[status(thm)],[321])).
% 0.71/0.89 tff(323,plain,
% 0.71/0.89 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(324,plain,
% 0.71/0.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[323])).
% 0.71/0.89 tff(325,plain,
% 0.71/0.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(326,plain,
% 0.71/0.89 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(327,plain,
% 0.71/0.89 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[326])).
% 0.71/0.89 tff(328,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.71/0.89 tff(329,plain,
% 0.71/0.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.71/0.89 tff(330,plain,
% 0.71/0.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[329, 325])).
% 0.71/0.89 tff(331,plain,(
% 0.71/0.89 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[330])).
% 0.71/0.89 tff(332,plain,
% 0.71/0.89 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[331, 324])).
% 0.71/0.89 tff(333,plain,
% 0.71/0.89 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(334,plain,
% 0.71/0.89 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(335,plain,
% 0.71/0.89 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.71/0.89 tff(336,plain,
% 0.71/0.89 (l1_struct_0(A!0)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[335, 332, 195])).
% 0.71/0.89 tff(337,plain,
% 0.71/0.89 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(338,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[337])).
% 0.71/0.89 tff(339,plain,
% 0.71/0.89 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(340,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[339])).
% 0.71/0.89 tff(341,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(342,plain,
% 0.71/0.89 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(343,plain,
% 0.71/0.89 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[342])).
% 0.71/0.89 tff(344,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.71/0.89 tff(345,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[344, 343])).
% 0.71/0.89 tff(346,plain,
% 0.71/0.89 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[345, 341])).
% 0.71/0.89 tff(347,plain,(
% 0.71/0.89 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.71/0.89 inference(skolemize,[status(sab)],[346])).
% 0.71/0.89 tff(348,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[347, 340])).
% 0.71/0.89 tff(349,plain,
% 0.71/0.89 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[348, 338])).
% 0.71/0.89 tff(350,plain,
% 0.71/0.89 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(351,plain,
% 0.71/0.89 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(352,plain,
% 0.71/0.89 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[351])).
% 0.71/0.89 tff(353,plain,
% 0.71/0.89 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[352, 350])).
% 0.71/0.89 tff(354,plain,
% 0.71/0.89 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(355,plain,
% 0.71/0.89 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.71/0.89 tff(356,plain,
% 0.71/0.89 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[355, 32, 349])).
% 0.71/0.89 tff(357,plain,
% 0.71/0.89 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[356, 336])).
% 0.71/0.89 tff(358,plain,
% 0.71/0.89 (^[A: $i, B: $i] : refl((m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A))) <=> (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(359,plain,
% 0.71/0.89 (![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A))) <=> ![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[358])).
% 0.71/0.89 tff(360,plain,
% 0.71/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, A)) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A)))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(361,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[360])).
% 0.71/0.89 tff(362,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(363,plain,
% 0.71/0.89 (^[A: $i, B: $i] : rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, A)) => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(364,plain,
% 0.71/0.89 (![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[363])).
% 0.71/0.89 tff(365,axiom,(![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_domain_1')).
% 0.71/0.89 tff(366,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.71/0.89 tff(367,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[366, 362])).
% 0.71/0.89 tff(368,plain,(
% 0.71/0.89 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[367])).
% 0.71/0.89 tff(369,plain,
% 0.71/0.89 (![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[368, 361])).
% 0.71/0.89 tff(370,plain,
% 0.71/0.89 (![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[369, 359])).
% 0.71/0.89 tff(371,plain,
% 0.71/0.89 (((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(372,plain,
% 0.71/0.89 ((m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(373,plain,
% 0.71/0.89 (((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[372])).
% 0.71/0.89 tff(374,plain,
% 0.71/0.89 (((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[373, 371])).
% 0.71/0.89 tff(375,plain,
% 0.71/0.89 ((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(376,plain,
% 0.71/0.89 ((~![A: $i, B: $i] : (m1_subset_1(k6_domain_1(A, B), k1_zfmisc_1(A)) | v1_xboole_0(A) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[375, 374])).
% 0.71/0.89 tff(377,plain,
% 0.71/0.89 (v1_xboole_0(u1_struct_0(A!0)) | m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[376, 37, 370])).
% 0.71/0.89 tff(378,plain,
% 0.71/0.89 (m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[377, 357])).
% 0.71/0.89 tff(379,plain,
% 0.71/0.89 (^[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)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(380,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[379])).
% 0.71/0.89 tff(381,plain,
% 0.71/0.89 (^[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))))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(382,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[381])).
% 0.71/0.89 tff(383,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(384,plain,
% 0.71/0.89 (^[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)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(385,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[384])).
% 0.71/0.89 tff(386,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/sandbox2/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 0.71/0.89 tff(387,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.71/0.89 tff(388,plain,
% 0.71/0.89 (![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)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[387, 383])).
% 0.71/0.89 tff(389,plain,(
% 0.71/0.89 ![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)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[388])).
% 0.71/0.89 tff(390,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[389, 382])).
% 0.71/0.89 tff(391,plain,
% 0.71/0.89 (![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))))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[390, 380])).
% 0.71/0.89 tff(392,plain,
% 0.71/0.89 (((~![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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))))) <=> ((~![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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(393,plain,
% 0.71/0.89 ((v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(394,plain,
% 0.71/0.89 (((~![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), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), 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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[393])).
% 0.71/0.89 tff(395,plain,
% 0.71/0.89 (((~![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), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), 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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))))),
% 0.71/0.89 inference(transitivity,[status(thm)],[394, 392])).
% 0.71/0.89 tff(396,plain,
% 0.71/0.89 ((~![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), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(397,plain,
% 0.71/0.89 ((~![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(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[396, 395])).
% 0.71/0.89 tff(398,plain,
% 0.71/0.89 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A!0), B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[397, 317, 391])).
% 0.71/0.89 tff(399,plain,
% 0.71/0.89 (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[398, 378, 357])).
% 0.71/0.89 tff(400,plain,
% 0.71/0.89 (r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.89 inference(or_elim,[status(thm)],[315])).
% 0.71/0.89 tff(401,plain,
% 0.71/0.89 ((~(r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)))) | (~r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1))) | (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.89 inference(tautology,[status(thm)],[])).
% 0.71/0.89 tff(402,plain,
% 0.71/0.89 ((~(r1_filter_2(u1_struct_0(A!0), C!2, k6_domain_1(u1_struct_0(A!0), B!1)) <=> (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)))) | (C!2 = k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[401, 400])).
% 0.71/0.89 tff(403,plain,
% 0.71/0.89 (C!2 = k6_domain_1(u1_struct_0(A!0), B!1)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[402, 399])).
% 0.71/0.89 tff(404,plain,
% 0.71/0.89 (k6_domain_1(u1_struct_0(A!0), B!1) = C!2),
% 0.71/0.89 inference(symmetry,[status(thm)],[403])).
% 0.71/0.89 tff(405,plain,
% 0.71/0.89 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(406,plain,
% 0.71/0.89 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[405])).
% 0.71/0.89 tff(407,plain,
% 0.71/0.89 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, A)) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A)))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(408,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[407])).
% 0.71/0.89 tff(409,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(410,plain,
% 0.71/0.89 (^[A: $i, B: $i] : rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(411,plain,
% 0.71/0.89 (![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[410])).
% 0.71/0.89 tff(412,axiom,(![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k6_domain_1')).
% 0.71/0.89 tff(413,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.71/0.89 tff(414,plain,
% 0.71/0.89 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[413, 409])).
% 0.71/0.90 tff(415,plain,(
% 0.71/0.90 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.71/0.90 inference(skolemize,[status(sab)],[414])).
% 0.71/0.90 tff(416,plain,
% 0.71/0.90 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[415, 408])).
% 0.71/0.90 tff(417,plain,
% 0.71/0.90 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[416, 406])).
% 0.71/0.90 tff(418,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(419,plain,
% 0.71/0.90 ((v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(420,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[419])).
% 0.71/0.90 tff(421,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)))),
% 0.71/0.90 inference(transitivity,[status(thm)],[420, 418])).
% 0.71/0.90 tff(422,plain,
% 0.71/0.90 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(423,plain,
% 0.71/0.90 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.71/0.90 tff(424,plain,
% 0.71/0.90 (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[423, 37, 417])).
% 0.71/0.90 tff(425,plain,
% 0.71/0.90 (k6_domain_1(u1_struct_0(A!0), B!1) = k1_tarski(B!1)),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[424, 357])).
% 0.71/0.90 tff(426,plain,
% 0.71/0.90 (k1_tarski(B!1) = k6_domain_1(u1_struct_0(A!0), B!1)),
% 0.71/0.90 inference(symmetry,[status(thm)],[425])).
% 0.71/0.90 tff(427,plain,
% 0.71/0.90 (k1_tarski(B!1) = k7_filter_2(A!0, C!2)),
% 0.71/0.90 inference(transitivity,[status(thm)],[426, 404, 322])).
% 0.71/0.90 tff(428,plain,
% 0.71/0.90 (m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[427])).
% 0.71/0.90 tff(429,plain,
% 0.71/0.90 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.90 inference(symmetry,[status(thm)],[428])).
% 0.71/0.90 tff(430,plain,
% 0.71/0.90 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(431,plain,
% 0.71/0.90 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[430])).
% 0.71/0.90 tff(432,plain,
% 0.71/0.90 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(433,plain,
% 0.71/0.90 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[432])).
% 0.71/0.90 tff(434,plain,
% 0.71/0.90 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(435,plain,
% 0.71/0.90 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(436,plain,
% 0.71/0.90 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[435])).
% 0.71/0.90 tff(437,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_filter_2')).
% 0.71/0.90 tff(438,plain,
% 0.71/0.90 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[437, 436])).
% 0.71/0.90 tff(439,plain,
% 0.71/0.90 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[438, 434])).
% 0.71/0.90 tff(440,plain,(
% 0.71/0.90 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))),
% 0.71/0.90 inference(skolemize,[status(sab)],[439])).
% 0.71/0.90 tff(441,plain,
% 0.71/0.90 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[440, 433])).
% 0.71/0.90 tff(442,plain,
% 0.71/0.90 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[441, 431])).
% 0.71/0.90 tff(443,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(444,plain,
% 0.71/0.90 ((v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(445,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))))),
% 0.71/0.90 inference(monotonicity,[status(thm)],[444])).
% 0.71/0.90 tff(446,plain,
% 0.71/0.90 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[445, 443])).
% 0.71/0.90 tff(447,plain,
% 0.71/0.90 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(448,plain,
% 0.71/0.90 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k7_filter_2(A, B), k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.71/0.90 tff(449,plain,
% 0.71/0.90 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[448, 32, 31, 30, 317, 442])).
% 0.71/0.90 tff(450,plain,
% 0.71/0.90 (m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[449, 429])).
% 0.71/0.90 tff(451,plain,
% 0.71/0.90 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(452,plain,
% 0.71/0.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[451])).
% 0.71/0.90 tff(453,plain,
% 0.71/0.90 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(454,plain,
% 0.71/0.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[453])).
% 0.71/0.90 tff(455,plain,
% 0.71/0.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(transitivity,[status(thm)],[454, 452])).
% 0.71/0.90 tff(456,plain,
% 0.71/0.90 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) <=> (~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))))), rewrite((~(~(v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))))), ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))))), rewrite(((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), rewrite(((v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(457,plain,
% 0.71/0.90 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[456])).
% 0.71/0.90 tff(458,plain,
% 0.71/0.90 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(459,plain,
% 0.71/0.90 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)))), (((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> (((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), rewrite((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))), (((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))) <=> ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))) <=> ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(bind,[status(th)],[])).
% 0.71/0.90 tff(460,plain,
% 0.71/0.90 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.71/0.90 inference(quant_intro,[status(thm)],[459])).
% 0.71/0.90 tff(461,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) => ((((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t37_filter_2')).
% 0.71/0.90 tff(462,plain,
% 0.71/0.90 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[461, 460])).
% 0.71/0.90 tff(463,plain,
% 0.71/0.90 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[462, 458])).
% 0.71/0.90 tff(464,plain,(
% 0.71/0.90 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | ![C: $i] : ((~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))))) | ((k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B)) & (k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B))) & (k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C)) & (k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))),
% 0.71/0.90 inference(skolemize,[status(sab)],[463])).
% 0.71/0.90 tff(465,plain,
% 0.71/0.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[464, 457])).
% 0.71/0.90 tff(466,plain,
% 0.71/0.90 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[465, 455])).
% 0.71/0.90 tff(467,plain,
% 0.71/0.90 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))),
% 0.71/0.90 inference(rewrite,[status(thm)],[])).
% 0.71/0.90 tff(468,plain,
% 0.71/0.90 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))))),
% 0.71/0.90 inference(quant_inst,[status(thm)],[])).
% 0.71/0.90 tff(469,plain,
% 0.71/0.90 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (~((~(k3_filter_2(k1_lattice2(A), k7_filter_2(A, B)) = k19_filter_2(A, B))) | (~(k3_filter_2(A, B) = k19_filter_2(k1_lattice2(A), k7_filter_2(A, B)))) | (~(k3_filter_2(A, k8_filter_2(A, C)) = k19_filter_2(k1_lattice2(A), C))) | (~(k3_filter_2(k1_lattice2(A), C) = k19_filter_2(A, k8_filter_2(A, C)))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.71/0.90 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.71/0.90 tff(470,plain,
% 0.71/0.90 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.71/0.90 inference(unit_resolution,[status(thm)],[469, 32, 31, 30, 466])).
% 0.71/0.90 tff(471,plain,
% 0.71/0.90 (~v1_xboole_0(C!2)),
% 0.71/0.90 inference(and_elim,[status(thm)],[316])).
% 0.71/0.90 tff(472,plain,
% 0.71/0.90 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(473,plain,
% 0.71/0.91 ((v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))))))) <=> (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(474,plain,
% 0.71/0.91 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[473])).
% 0.71/0.91 tff(475,plain,
% 0.71/0.91 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))))),
% 0.71/0.91 inference(transitivity,[status(thm)],[474, 472])).
% 0.71/0.91 tff(476,plain,
% 0.71/0.91 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(477,plain,
% 0.71/0.91 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)) = k19_filter_2(A!0, B))) | (~(k3_filter_2(A!0, B) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, B)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | ![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[476, 475])).
% 0.71/0.91 tff(478,plain,
% 0.71/0.91 (![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[477, 471, 317, 470])).
% 0.71/0.91 tff(479,plain,
% 0.71/0.91 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(480,plain,
% 0.71/0.91 ((v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))))))) <=> (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(481,plain,
% 0.71/0.91 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1)))))))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[480])).
% 0.71/0.91 tff(482,plain,
% 0.71/0.91 (((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) <=> ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))))))),
% 0.71/0.91 inference(transitivity,[status(thm)],[481, 479])).
% 0.71/0.91 tff(483,plain,
% 0.71/0.91 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))),
% 0.71/0.91 inference(quant_inst,[status(thm)],[])).
% 0.71/0.91 tff(484,plain,
% 0.71/0.91 ((~![C: $i] : (v1_xboole_0(C) | (~m1_subset_1(C, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(A!0, k8_filter_2(A!0, C)) = k19_filter_2(k1_lattice2(A!0), C))) | (~(k3_filter_2(k1_lattice2(A!0), C) = k19_filter_2(A!0, k8_filter_2(A!0, C)))) | (~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))))))) | v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1)))))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[483, 482])).
% 0.71/0.91 tff(485,plain,
% 0.71/0.91 (v1_xboole_0(k1_tarski(B!1)) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1)))))))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[484, 478])).
% 0.71/0.91 tff(486,plain,
% 0.71/0.91 (~((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))))))),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[485, 450, 291])).
% 0.71/0.91 tff(487,plain,
% 0.71/0.91 (((~(k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))) | (~(k3_filter_2(A!0, C!2) = k19_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)))) | (~(k3_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1))) = k19_filter_2(k1_lattice2(A!0), k1_tarski(B!1)))) | (~(k3_filter_2(k1_lattice2(A!0), k1_tarski(B!1)) = k19_filter_2(A!0, k8_filter_2(A!0, k1_tarski(B!1)))))) | (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2))),
% 0.71/0.91 inference(tautology,[status(thm)],[])).
% 0.71/0.91 tff(488,plain,
% 0.71/0.91 (k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2)) = k19_filter_2(A!0, C!2)),
% 0.71/0.91 inference(unit_resolution,[status(thm)],[487, 486])).
% 0.71/0.91 tff(489,plain,
% 0.71/0.91 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_2(k1_lattice2(A!0), k7_filter_2(A!0, C!2))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[87, 427])).
% 0.71/0.91 tff(490,plain,
% 0.71/0.91 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[89])).
% 0.71/0.91 tff(491,plain,
% 0.71/0.91 (m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.91 inference(monotonicity,[status(thm)],[427, 490])).
% 0.71/0.91 tff(492,plain,
% 0.71/0.91 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.91 inference(symmetry,[status(thm)],[491])).
% 0.71/0.91 tff(493,plain,
% 0.71/0.91 (m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[449, 492])).
% 0.71/0.91 tff(494,plain,
% 0.71/0.91 (^[A: $i, B: $i] : refl((v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(495,plain,
% 0.71/0.91 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[494])).
% 0.71/0.91 tff(496,plain,
% 0.71/0.91 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k3_filter_2(A, B) = k3_filter_0(A, B))))), rewrite(((v1_xboole_0(B) | v3_struct_0(A) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(497,plain,
% 0.71/0.91 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[496])).
% 0.71/0.91 tff(498,plain,
% 0.71/0.91 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(499,plain,
% 0.71/0.91 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))))),
% 0.71/0.91 inference(bind,[status(th)],[])).
% 0.71/0.91 tff(500,plain,
% 0.71/0.91 (![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.71/0.91 inference(quant_intro,[status(thm)],[499])).
% 0.71/0.91 tff(501,axiom,(![A: $i, B: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & (~v1_xboole_0(B))) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (k3_filter_2(A, B) = k3_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_filter_2')).
% 0.71/0.91 tff(502,plain,
% 0.71/0.91 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.71/0.91 tff(503,plain,
% 0.71/0.91 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[502, 498])).
% 0.71/0.91 tff(504,plain,(
% 0.71/0.91 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & (~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (k3_filter_2(A, B) = k3_filter_0(A, B)))),
% 0.71/0.91 inference(skolemize,[status(sab)],[503])).
% 0.71/0.91 tff(505,plain,
% 0.71/0.91 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[504, 497])).
% 0.71/0.91 tff(506,plain,
% 0.71/0.91 (![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.91 inference(modus_ponens,[status(thm)],[505, 495])).
% 0.71/0.91 tff(507,plain,
% 0.71/0.91 (((~![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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(B) | v3_struct_0(A) | (k3_filter_2(A, B) = k3_filter_0(A, B)) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(508,plain,
% 0.71/0.91 ((v1_xboole_0(k1_tarski(B!1)) | 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)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), 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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.91 inference(rewrite,[status(thm)],[])).
% 0.71/0.91 tff(509,plain,
% 0.71/0.91 (((~![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(k1_tarski(B!1)) | 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)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), 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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[508])).
% 0.71/0.92 tff(510,plain,
% 0.71/0.92 (((~![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(k1_tarski(B!1)) | 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)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), 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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.92 inference(transitivity,[status(thm)],[509, 507])).
% 0.71/0.92 tff(511,plain,
% 0.71/0.92 ((~![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(k1_tarski(B!1)) | 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)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(512,plain,
% 0.71/0.92 ((~![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(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.71/0.92 tff(513,plain,
% 0.71/0.92 (v1_xboole_0(k1_tarski(B!1)) | (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))) | (~m1_subset_1(k1_tarski(B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[512, 506, 252, 140, 134])).
% 0.71/0.92 tff(514,plain,
% 0.71/0.92 (k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[513, 493, 291])).
% 0.71/0.92 tff(515,plain,
% 0.71/0.92 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1)) = k3_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))),
% 0.71/0.92 inference(symmetry,[status(thm)],[514])).
% 0.71/0.92 tff(516,plain,
% 0.71/0.92 (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))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[90])).
% 0.71/0.92 tff(517,plain,
% 0.71/0.92 (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))))),
% 0.71/0.92 inference(symmetry,[status(thm)],[516])).
% 0.71/0.92 tff(518,plain,
% 0.71/0.92 (((~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)))),
% 0.71/0.92 inference(tautology,[status(thm)],[])).
% 0.71/0.92 tff(519,plain,
% 0.71/0.92 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[518, 250])).
% 0.71/0.92 tff(520,plain,
% 0.71/0.92 (^[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))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(521,plain,
% 0.71/0.92 (![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)))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[520])).
% 0.71/0.92 tff(522,plain,
% 0.71/0.92 (![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)))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(523,plain,
% 0.71/0.92 (^[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)))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(524,plain,
% 0.71/0.92 (![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)))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[523])).
% 0.71/0.92 tff(525,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 0.71/0.92 tff(526,plain,
% 0.71/0.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.71/0.92 tff(527,plain,
% 0.71/0.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[526, 522])).
% 0.71/0.92 tff(528,plain,(
% 0.71/0.92 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.92 inference(skolemize,[status(sab)],[527])).
% 0.71/0.92 tff(529,plain,
% 0.71/0.92 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[528, 521])).
% 0.71/0.92 tff(530,plain,
% 0.71/0.92 (((~![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))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(531,plain,
% 0.71/0.92 (((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))))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(532,plain,
% 0.71/0.92 (((~![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)))))))),
% 0.71/0.92 inference(monotonicity,[status(thm)],[531])).
% 0.71/0.92 tff(533,plain,
% 0.71/0.92 (((~![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))))))),
% 0.71/0.92 inference(transitivity,[status(thm)],[532, 530])).
% 0.71/0.92 tff(534,plain,
% 0.71/0.92 ((~![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)))))),
% 0.71/0.92 inference(quant_inst,[status(thm)],[])).
% 0.71/0.92 tff(535,plain,
% 0.71/0.92 ((~![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)))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[534, 533])).
% 0.71/0.92 tff(536,plain,
% 0.71/0.92 ((~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)))))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[535, 529])).
% 0.71/0.92 tff(537,plain,
% 0.71/0.92 (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))))),
% 0.71/0.92 inference(unit_resolution,[status(thm)],[536, 252, 519])).
% 0.71/0.92 tff(538,plain,
% 0.71/0.92 (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))))),
% 0.71/0.92 inference(transitivity,[status(thm)],[537, 517])).
% 0.71/0.92 tff(539,plain,
% 0.71/0.92 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(540,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[539])).
% 0.71/0.92 tff(541,plain,
% 0.71/0.92 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(542,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[541])).
% 0.71/0.92 tff(543,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(transitivity,[status(thm)],[542, 540])).
% 0.71/0.92 tff(544,plain,
% 0.71/0.92 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(545,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[544])).
% 0.71/0.92 tff(546,plain,
% 0.71/0.92 (![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))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(547,plain,
% 0.71/0.92 (^[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))))))),
% 0.71/0.92 inference(bind,[status(th)],[])).
% 0.71/0.92 tff(548,plain,
% 0.71/0.92 (![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))))),
% 0.71/0.92 inference(quant_intro,[status(thm)],[547])).
% 0.71/0.92 tff(549,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.71/0.92 tff(550,plain,
% 0.71/0.92 (![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))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[549, 548])).
% 0.71/0.92 tff(551,plain,
% 0.71/0.92 (![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))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[550, 546])).
% 0.71/0.92 tff(552,plain,(
% 0.71/0.92 ![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))))),
% 0.71/0.92 inference(skolemize,[status(sab)],[551])).
% 0.71/0.92 tff(553,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[552, 545])).
% 0.71/0.92 tff(554,plain,
% 0.71/0.92 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.71/0.92 inference(modus_ponens,[status(thm)],[553, 543])).
% 0.71/0.92 tff(555,plain,
% 0.71/0.92 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(556,plain,
% 0.71/0.92 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.71/0.92 inference(rewrite,[status(thm)],[])).
% 0.71/0.92 tff(557,plain,
% 0.71/0.92 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[556])).
% 0.71/0.93 tff(558,plain,
% 0.71/0.93 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.71/0.93 inference(transitivity,[status(thm)],[557, 555])).
% 0.71/0.93 tff(559,plain,
% 0.71/0.93 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(560,plain,
% 0.71/0.93 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.71/0.93 tff(561,plain,
% 0.71/0.93 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[560, 554, 226, 224, 222, 220])).
% 0.71/0.93 tff(562,plain,
% 0.71/0.93 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[561, 218, 191])).
% 0.71/0.93 tff(563,plain,
% 0.71/0.93 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(564,plain,
% 0.71/0.93 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.71/0.93 inference(quant_inst,[status(thm)],[])).
% 0.71/0.93 tff(565,plain,
% 0.71/0.93 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[564, 563])).
% 0.71/0.93 tff(566,plain,
% 0.71/0.93 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[565, 562])).
% 0.71/0.93 tff(567,plain,
% 0.71/0.93 (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[566, 538])).
% 0.71/0.93 tff(568,plain,
% 0.71/0.93 (((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 0.71/0.93 inference(tautology,[status(thm)],[])).
% 0.71/0.93 tff(569,plain,
% 0.71/0.93 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 0.71/0.93 inference(unit_resolution,[status(thm)],[568, 567])).
% 0.71/0.93 tff(570,plain,
% 0.71/0.93 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(A!0)),
% 0.71/0.93 inference(symmetry,[status(thm)],[569])).
% 0.71/0.93 tff(571,plain,
% 0.71/0.93 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 0.71/0.93 inference(transitivity,[status(thm)],[89, 570])).
% 0.71/0.93 tff(572,plain,
% 0.71/0.93 (k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1) = k6_domain_1(u1_struct_0(A!0), B!1)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[571])).
% 0.71/0.93 tff(573,plain,
% 0.71/0.93 (k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1) = k1_tarski(B!1)),
% 0.71/0.93 inference(transitivity,[status(thm)],[572, 425])).
% 0.71/0.93 tff(574,plain,
% 0.71/0.93 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k1_tarski(B!1))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[573])).
% 0.71/0.93 tff(575,plain,
% 0.71/0.93 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k19_filter_2(A!0, C!2)),
% 0.71/0.93 inference(transitivity,[status(thm)],[574, 515, 489, 488])).
% 0.71/0.93 tff(576,plain,
% 0.71/0.93 ((k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[575, 274])).
% 0.71/0.93 tff(577,plain,
% 0.71/0.93 (v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) <=> v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[572])).
% 0.71/0.93 tff(578,plain,
% 0.71/0.93 (v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1)) <=> v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1))),
% 0.71/0.93 inference(symmetry,[status(thm)],[577])).
% 0.71/0.93 tff(579,plain,
% 0.71/0.93 ((~v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1))) <=> (~v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[578])).
% 0.71/0.93 tff(580,plain,
% 0.71/0.93 (v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1)) <=> v1_xboole_0(C!2)),
% 0.71/0.93 inference(monotonicity,[status(thm)],[404])).
% 0.71/0.93 tff(581,plain,
% 0.71/0.93 (v1_xboole_0(C!2) <=> v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.93 inference(symmetry,[status(thm)],[580])).
% 0.71/0.93 tff(582,plain,
% 0.71/0.93 ((~v1_xboole_0(C!2)) <=> (~v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1)))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[581])).
% 0.71/0.93 tff(583,plain,
% 0.71/0.93 (~v1_xboole_0(k6_domain_1(u1_struct_0(A!0), B!1))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[471, 582])).
% 0.71/0.93 tff(584,plain,
% 0.71/0.93 (~v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[583, 579])).
% 0.71/0.93 tff(585,plain,
% 0.71/0.93 (k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1) = k7_filter_2(A!0, C!2)),
% 0.71/0.93 inference(transitivity,[status(thm)],[572, 404, 322])).
% 0.71/0.93 tff(586,plain,
% 0.71/0.93 (m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 0.71/0.93 inference(monotonicity,[status(thm)],[585, 490])).
% 0.71/0.93 tff(587,plain,
% 0.71/0.93 (m1_subset_1(k7_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.93 inference(symmetry,[status(thm)],[586])).
% 0.71/0.93 tff(588,plain,
% 0.71/0.93 (m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[449, 587])).
% 0.71/0.93 tff(589,plain,
% 0.71/0.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(590,plain,
% 0.71/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[589])).
% 0.71/0.93 tff(591,plain,
% 0.71/0.93 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(592,plain,
% 0.71/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[591])).
% 0.71/0.93 tff(593,plain,
% 0.71/0.93 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(594,plain,
% 0.71/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[593])).
% 0.71/0.93 tff(595,plain,
% 0.71/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.71/0.93 inference(transitivity,[status(thm)],[594, 592])).
% 0.71/0.93 tff(596,plain,
% 0.71/0.93 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(597,plain,
% 0.71/0.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[596])).
% 0.71/0.93 tff(598,plain,
% 0.71/0.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.71/0.93 inference(rewrite,[status(thm)],[])).
% 0.71/0.93 tff(599,plain,
% 0.71/0.93 (^[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(trans(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(rewrite(((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B))) <=> ((~(C = k6_domain_1(u1_struct_0(A), B))) | (k3_filter_0(A, C) = k2_filter_0(A, B)))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))) <=> (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((~(C = k6_domain_1(u1_struct_0(A), B))) | (k3_filter_0(A, C) = k2_filter_0(A, B)))))), rewrite((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((~(C = k6_domain_1(u1_struct_0(A), B))) | (k3_filter_0(A, C) = k2_filter_0(A, B)))) <=> ((k3_filter_0(A, C) = k2_filter_0(A, B)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | (~(C = k6_domain_1(u1_struct_0(A), B))))), ((((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))) <=> ((k3_filter_0(A, C) = k2_filter_0(A, B)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | (~(C = k6_domain_1(u1_struct_0(A), B))))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))) <=> ![C: $i] : ((k3_filter_0(A, C) = k2_filter_0(A, B)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | (~(C = k6_domain_1(u1_struct_0(A), B)))))), trans(der(![C: $i] : ((k3_filter_0(A, C) = k2_filter_0(A, B)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | (~(C = k6_domain_1(u1_struct_0(A), B)))) <=> ![C: $i] : ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))), elim_unused(![C: $i] : ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) <=> ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))), (![C: $i] : ((k3_filter_0(A, C) = k2_filter_0(A, B)) | (~((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A))))) | (~(C = k6_domain_1(u1_struct_0(A), B)))) <=> ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))), (![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))) <=> ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ((k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))))),
% 0.71/0.93 inference(bind,[status(th)],[])).
% 0.71/0.93 tff(600,plain,
% 0.71/0.93 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.71/0.93 inference(quant_intro,[status(thm)],[599])).
% 0.71/0.93 tff(601,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (((~v1_xboole_0(C)) & m1_subset_1(C, k1_zfmisc_1(u1_struct_0(A)))) => ((C = k6_domain_1(u1_struct_0(A), B)) => (k3_filter_0(A, C) = k2_filter_0(A, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_filter_0')).
% 0.71/0.93 tff(602,plain,
% 0.71/0.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.71/0.93 inference(modus_ponens,[status(thm)],[601, 600])).
% 0.71/0.93 tff(603,plain,
% 0.71/0.93 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[602, 598])).
% 0.79/0.93 tff(604,plain,(
% 0.79/0.93 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.79/0.93 inference(skolemize,[status(sab)],[603])).
% 0.79/0.93 tff(605,plain,
% 0.79/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[604, 597])).
% 0.79/0.93 tff(606,plain,
% 0.79/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))) | (~v10_lattices(A)))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[605, 595])).
% 0.79/0.93 tff(607,plain,
% 0.79/0.93 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[606, 590])).
% 0.79/0.93 tff(608,plain,
% 0.79/0.93 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B))))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(609,plain,
% 0.79/0.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B))))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(610,plain,
% 0.79/0.93 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k3_filter_0(A, k6_domain_1(u1_struct_0(A), B)) = k2_filter_0(A, B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(A), B), k1_zfmisc_1(u1_struct_0(A)))) | v1_xboole_0(k6_domain_1(u1_struct_0(A), B))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[609, 608])).
% 0.79/0.93 tff(611,plain,
% 0.79/0.93 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[610, 607, 252, 140, 134])).
% 0.79/0.93 tff(612,plain,
% 0.79/0.93 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))) | ((~m1_subset_1(B!1, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))) | (~m1_subset_1(B!1, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(613,plain,
% 0.79/0.94 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))) | ((~m1_subset_1(B!1, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(614,plain,
% 0.79/0.94 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B)))) | (~m1_subset_1(B!1, u1_struct_0(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)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[613, 612])).
% 0.79/0.94 tff(615,plain,
% 0.79/0.94 ((k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | v1_xboole_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[614, 611, 112])).
% 0.79/0.94 tff(616,plain,
% 0.79/0.94 (k3_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1)) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[615, 588, 584])).
% 0.79/0.94 tff(617,plain,
% 0.79/0.94 (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[616, 576])).
% 0.79/0.94 tff(618,plain,
% 0.79/0.94 (^[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))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(619,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[618])).
% 0.79/0.94 tff(620,plain,
% 0.79/0.94 (^[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)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(621,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[620])).
% 0.79/0.94 tff(622,plain,
% 0.79/0.94 (![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))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(623,plain,
% 0.79/0.94 (^[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))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(624,plain,
% 0.79/0.94 (![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))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[623])).
% 0.79/0.94 tff(625,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/sandbox2/benchmark/theBenchmark.p','dt_k19_filter_2')).
% 0.79/0.94 tff(626,plain,
% 0.79/0.94 (![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))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.79/0.94 tff(627,plain,
% 0.79/0.94 (![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))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[626, 622])).
% 0.79/0.94 tff(628,plain,(
% 0.79/0.94 ![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))),
% 0.79/0.94 inference(skolemize,[status(sab)],[627])).
% 0.79/0.94 tff(629,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[628, 621])).
% 0.79/0.94 tff(630,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[629, 619])).
% 0.79/0.94 tff(631,plain,
% 0.79/0.94 (((~![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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), 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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(632,plain,
% 0.79/0.94 ((v1_xboole_0(C!2) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, C!2), 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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(633,plain,
% 0.79/0.94 (((~![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(C!2) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, C!2), 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] : (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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0)))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[632])).
% 0.79/0.94 tff(634,plain,
% 0.79/0.94 (((~![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(C!2) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, C!2), 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] : (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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0))),
% 0.79/0.94 inference(transitivity,[status(thm)],[633, 631])).
% 0.79/0.94 tff(635,plain,
% 0.79/0.94 ((~![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(C!2) | v3_struct_0(A!0) | m2_filter_2(k19_filter_2(A!0, C!2), A!0) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(636,plain,
% 0.79/0.94 ((~![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) | v1_xboole_0(C!2) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | m2_filter_2(k19_filter_2(A!0, C!2), A!0)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[635, 634])).
% 0.79/0.94 tff(637,plain,
% 0.79/0.94 (m2_filter_2(k19_filter_2(A!0, C!2), A!0)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[636, 32, 31, 30, 471, 317, 630])).
% 0.79/0.94 tff(638,plain,
% 0.79/0.94 (^[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)))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(639,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[638])).
% 0.79/0.94 tff(640,plain,
% 0.79/0.94 (^[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)))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(641,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[640])).
% 0.79/0.94 tff(642,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(transitivity,[status(thm)],[641, 639])).
% 0.79/0.94 tff(643,plain,
% 0.79/0.94 (^[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))))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(644,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[643])).
% 0.79/0.94 tff(645,plain,
% 0.79/0.94 (![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))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(646,plain,
% 0.79/0.94 (^[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))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(647,plain,
% 0.79/0.94 (![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))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[646])).
% 0.79/0.94 tff(648,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/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.79/0.94 tff(649,plain,
% 0.79/0.94 (![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))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.79/0.94 tff(650,plain,
% 0.79/0.94 (![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))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[649, 645])).
% 0.79/0.94 tff(651,plain,(
% 0.79/0.94 ![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))))),
% 0.79/0.94 inference(skolemize,[status(sab)],[650])).
% 0.79/0.94 tff(652,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[651, 644])).
% 0.79/0.94 tff(653,plain,
% 0.79/0.94 (![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))))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[652, 642])).
% 0.79/0.94 tff(654,plain,
% 0.79/0.94 (((~![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))))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(655,plain,
% 0.79/0.94 ((~![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))))))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(656,plain,
% 0.79/0.94 ((~![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)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[655, 654])).
% 0.79/0.94 tff(657,plain,
% 0.79/0.94 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[656, 32, 31, 30, 653])).
% 0.79/0.94 tff(658,plain,
% 0.79/0.94 (((~![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, C!2), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, 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, C!2), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, C!2), A!0)))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(659,plain,
% 0.79/0.94 ((~![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, C!2), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, C!2), A!0)))))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(660,plain,
% 0.79/0.94 ((~![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, C!2), A!0)) | (~(v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, C!2), A!0))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.79/0.94 tff(661,plain,
% 0.79/0.94 (~(v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, C!2), A!0)))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[660, 657, 637])).
% 0.79/0.94 tff(662,plain,
% 0.79/0.94 ((v1_xboole_0(k19_filter_2(A!0, C!2)) | (~m2_lattice4(k19_filter_2(A!0, C!2), A!0))) | m2_lattice4(k19_filter_2(A!0, C!2), A!0)),
% 0.79/0.94 inference(tautology,[status(thm)],[])).
% 0.79/0.94 tff(663,plain,
% 0.79/0.94 (m2_lattice4(k19_filter_2(A!0, C!2), A!0)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[662, 661])).
% 0.79/0.94 tff(664,plain,
% 0.79/0.94 (^[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))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(665,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[664])).
% 0.79/0.94 tff(666,plain,
% 0.79/0.94 (^[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))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(667,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[666])).
% 0.79/0.94 tff(668,plain,
% 0.79/0.94 (^[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))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(669,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[668])).
% 0.79/0.94 tff(670,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[669, 667])).
% 0.79/0.94 tff(671,plain,
% 0.79/0.94 (^[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)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(672,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[671])).
% 0.79/0.94 tff(673,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(674,plain,
% 0.79/0.94 (^[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)))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(675,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[674])).
% 0.79/0.94 tff(676,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.79/0.94 tff(677,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[676, 675])).
% 0.79/0.94 tff(678,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[677, 673])).
% 0.79/0.94 tff(679,plain,(
% 0.79/0.94 ![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)))))),
% 0.79/0.94 inference(skolemize,[status(sab)],[678])).
% 0.79/0.94 tff(680,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[679, 672])).
% 0.79/0.94 tff(681,plain,
% 0.79/0.94 (![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)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[680, 670])).
% 0.79/0.94 tff(682,plain,
% 0.79/0.94 (![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)))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[681, 665])).
% 0.79/0.94 tff(683,plain,
% 0.79/0.94 (((~![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)))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(684,plain,
% 0.79/0.94 ((~![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)))))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(685,plain,
% 0.79/0.94 ((~![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))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[684, 683])).
% 0.79/0.94 tff(686,plain,
% 0.79/0.94 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[685, 32, 31, 30, 682])).
% 0.79/0.94 tff(687,plain,
% 0.79/0.94 (((~![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, C!2), A!0)) | m1_subset_1(k19_filter_2(A!0, 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, C!2), A!0)) | m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(688,plain,
% 0.79/0.94 ((~![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, C!2), A!0)) | m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(689,plain,
% 0.79/0.94 ((~![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, C!2), A!0)) | m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[688, 687])).
% 0.79/0.94 tff(690,plain,
% 0.79/0.94 (m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[689, 686, 663])).
% 0.79/0.94 tff(691,plain,
% 0.79/0.94 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(692,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[691])).
% 0.79/0.94 tff(693,plain,
% 0.79/0.94 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(694,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[693])).
% 0.79/0.94 tff(695,plain,
% 0.79/0.94 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(696,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[695])).
% 0.79/0.94 tff(697,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[696, 694])).
% 0.79/0.94 tff(698,plain,
% 0.79/0.94 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(699,plain,
% 0.79/0.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[698])).
% 0.79/0.94 tff(700,plain,
% 0.79/0.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(701,plain,
% 0.79/0.94 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(702,plain,
% 0.79/0.94 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[701])).
% 0.79/0.94 tff(703,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_filter_2')).
% 0.79/0.94 tff(704,plain,
% 0.79/0.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[703, 702])).
% 0.79/0.94 tff(705,plain,
% 0.79/0.94 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[704, 700])).
% 0.79/0.94 tff(706,plain,(
% 0.79/0.94 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.94 inference(skolemize,[status(sab)],[705])).
% 0.79/0.94 tff(707,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[706, 699])).
% 0.79/0.94 tff(708,plain,
% 0.79/0.94 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))) | (~v10_lattices(A)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[707, 697])).
% 0.79/0.95 tff(709,plain,
% 0.79/0.95 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[708, 692])).
% 0.79/0.95 tff(710,plain,
% 0.79/0.95 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(711,plain,
% 0.79/0.95 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B))))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(712,plain,
% 0.79/0.95 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k18_filter_2(A, B) = a_2_0_filter_2(A, B))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[711, 710])).
% 0.79/0.95 tff(713,plain,
% 0.79/0.95 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[712, 32, 31, 30, 709])).
% 0.79/0.95 tff(714,plain,
% 0.79/0.95 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(715,plain,
% 0.79/0.95 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(716,plain,
% 0.79/0.95 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k18_filter_2(A!0, B) = a_2_0_filter_2(A!0, B)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[715, 714])).
% 0.79/0.95 tff(717,plain,
% 0.79/0.95 (k18_filter_2(A!0, B!1) = a_2_0_filter_2(A!0, B!1)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[716, 37, 713])).
% 0.79/0.95 tff(718,plain,
% 0.79/0.95 (a_2_0_filter_2(A!0, B!1) = k18_filter_2(A!0, B!1)),
% 0.79/0.95 inference(symmetry,[status(thm)],[717])).
% 0.79/0.95 tff(719,plain,
% 0.79/0.95 (m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[718])).
% 0.79/0.95 tff(720,plain,
% 0.79/0.95 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0) <=> m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(monotonicity,[status(thm)],[718])).
% 0.79/0.95 tff(721,plain,
% 0.79/0.95 (m2_lattice4(k18_filter_2(A!0, B!1), A!0) <=> m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(symmetry,[status(thm)],[720])).
% 0.79/0.95 tff(722,plain,
% 0.79/0.95 (^[A: $i, B: $i] : refl((m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(723,plain,
% 0.79/0.95 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[722])).
% 0.79/0.95 tff(724,plain,
% 0.79/0.95 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(725,plain,
% 0.79/0.95 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[724])).
% 0.79/0.95 tff(726,plain,
% 0.79/0.95 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(727,plain,
% 0.79/0.95 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(728,plain,
% 0.79/0.95 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[727])).
% 0.79/0.95 tff(729,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k18_filter_2')).
% 0.79/0.95 tff(730,plain,
% 0.79/0.95 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.79/0.95 tff(731,plain,
% 0.79/0.95 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[730, 726])).
% 0.79/0.95 tff(732,plain,(
% 0.79/0.95 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.79/0.95 inference(skolemize,[status(sab)],[731])).
% 0.79/0.95 tff(733,plain,
% 0.79/0.95 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[732, 725])).
% 0.79/0.95 tff(734,plain,
% 0.79/0.95 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[733, 723])).
% 0.79/0.95 tff(735,plain,
% 0.79/0.95 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(736,plain,
% 0.79/0.95 ((m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(737,plain,
% 0.79/0.95 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[736])).
% 0.79/0.95 tff(738,plain,
% 0.79/0.95 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0))),
% 0.79/0.95 inference(transitivity,[status(thm)],[737, 735])).
% 0.79/0.95 tff(739,plain,
% 0.79/0.95 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, B!1), A!0) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(740,plain,
% 0.79/0.95 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[739, 738])).
% 0.79/0.95 tff(741,plain,
% 0.79/0.95 (m2_filter_2(k18_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[740, 32, 31, 30, 37, 734])).
% 0.79/0.95 tff(742,plain,
% 0.79/0.95 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(743,plain,
% 0.79/0.95 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(744,plain,
% 0.79/0.95 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, B!1), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[743, 742])).
% 0.79/0.95 tff(745,plain,
% 0.79/0.95 (~(v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0)))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[744, 657, 741])).
% 0.79/0.95 tff(746,plain,
% 0.79/0.95 ((v1_xboole_0(k18_filter_2(A!0, B!1)) | (~m2_lattice4(k18_filter_2(A!0, B!1), A!0))) | m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(tautology,[status(thm)],[])).
% 0.79/0.95 tff(747,plain,
% 0.79/0.95 (m2_lattice4(k18_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[746, 745])).
% 0.79/0.95 tff(748,plain,
% 0.79/0.95 (m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[747, 721])).
% 0.79/0.95 tff(749,plain,
% 0.79/0.95 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, 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(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(750,plain,
% 0.79/0.95 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(751,plain,
% 0.79/0.95 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[750, 749])).
% 0.79/0.95 tff(752,plain,
% 0.79/0.95 ((~m2_lattice4(a_2_0_filter_2(A!0, B!1), A!0)) | m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[751, 686])).
% 0.79/0.95 tff(753,plain,
% 0.79/0.95 (m1_subset_1(a_2_0_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[752, 748])).
% 0.79/0.95 tff(754,plain,
% 0.79/0.95 (m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[753, 719])).
% 0.79/0.95 tff(755,plain,
% 0.79/0.95 (((~![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(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))))) <=> ((~![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(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(756,plain,
% 0.79/0.95 ((v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(757,plain,
% 0.79/0.95 (((~![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, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, B!1), 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(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[756])).
% 0.79/0.95 tff(758,plain,
% 0.79/0.95 (((~![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, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, B!1), 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(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))))),
% 0.79/0.96 inference(transitivity,[status(thm)],[757, 755])).
% 0.79/0.96 tff(759,plain,
% 0.79/0.96 ((~![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, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(760,plain,
% 0.79/0.96 ((~![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(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[759, 758])).
% 0.79/0.96 tff(761,plain,
% 0.79/0.96 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, B!1), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k19_filter_2(A!0, C!2), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[760, 391])).
% 0.79/0.96 tff(762,plain,
% 0.79/0.96 (r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[761, 754, 357, 690])).
% 0.79/0.96 tff(763,plain,
% 0.79/0.96 (~r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1))),
% 0.79/0.96 inference(or_elim,[status(thm)],[315])).
% 0.79/0.96 tff(764,plain,
% 0.79/0.96 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))) | r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) | (~(k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))),
% 0.79/0.96 inference(tautology,[status(thm)],[])).
% 0.79/0.96 tff(765,plain,
% 0.79/0.96 ((~(r1_filter_2(u1_struct_0(A!0), k19_filter_2(A!0, C!2), k18_filter_2(A!0, B!1)) <=> (k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))) | (~(k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1)))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[764, 763])).
% 0.79/0.96 tff(766,plain,
% 0.79/0.96 (~(k19_filter_2(A!0, C!2) = k18_filter_2(A!0, B!1))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[765, 762])).
% 0.79/0.96 tff(767,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[766, 617])).
% 0.79/0.96 % SZS output end Proof
% 0.79/0.96 % E exiting
%------------------------------------------------------------------------------