%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT297+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:13 AM UTC 2025
% Result : Theorem 0.19s 0.51s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT297+1 : TPTP v9.0.0. Released v3.4.0.
% 0.12/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n010.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 20:07:11 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.51 % SZS status Theorem
% 0.19/0.51 % SZS output start Proof
% 0.19/0.51 tff(r2_hidden_type, type, (
% 0.19/0.51 r2_hidden: ( $i * $i ) > $o)).
% 0.19/0.51 tff(tptp_fun_B_1_type, type, (
% 0.19/0.51 tptp_fun_B_1: $i)).
% 0.19/0.51 tff(k4_lattices_type, type, (
% 0.19/0.51 k4_lattices: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_C_2_type, type, (
% 0.19/0.51 tptp_fun_C_2: ( $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_A_0_type, type, (
% 0.19/0.51 tptp_fun_A_0: $i)).
% 0.19/0.51 tff(k3_lattices_type, type, (
% 0.19/0.51 k3_lattices: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(tptp_fun_D_3_type, type, (
% 0.19/0.51 tptp_fun_D_3: ( $i * $i ) > $i)).
% 0.19/0.51 tff(k2_lattices_type, type, (
% 0.19/0.51 k2_lattices: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(k1_lattices_type, type, (
% 0.19/0.51 k1_lattices: ( $i * $i * $i ) > $i)).
% 0.19/0.51 tff(m1_subset_1_type, type, (
% 0.19/0.51 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.51 tff(u1_struct_0_type, type, (
% 0.19/0.51 u1_struct_0: $i > $i)).
% 0.19/0.51 tff(m2_lattice4_type, type, (
% 0.19/0.51 m2_lattice4: ( $i * $i ) > $o)).
% 0.19/0.51 tff(k1_zfmisc_1_type, type, (
% 0.19/0.51 k1_zfmisc_1: $i > $i)).
% 0.19/0.51 tff(v10_lattices_type, type, (
% 0.19/0.51 v10_lattices: $i > $o)).
% 0.19/0.51 tff(l3_lattices_type, type, (
% 0.19/0.51 l3_lattices: $i > $o)).
% 0.19/0.51 tff(v3_struct_0_type, type, (
% 0.19/0.51 v3_struct_0: $i > $o)).
% 0.19/0.51 tff(v9_lattices_type, type, (
% 0.19/0.51 v9_lattices: $i > $o)).
% 0.19/0.51 tff(tptp_fun_B_4_type, type, (
% 0.19/0.51 tptp_fun_B_4: $i > $i)).
% 0.19/0.51 tff(tptp_fun_C_5_type, type, (
% 0.19/0.51 tptp_fun_C_5: $i > $i)).
% 0.19/0.51 tff(v8_lattices_type, type, (
% 0.19/0.51 v8_lattices: $i > $o)).
% 0.19/0.51 tff(v7_lattices_type, type, (
% 0.19/0.51 v7_lattices: $i > $o)).
% 0.19/0.51 tff(v6_lattices_type, type, (
% 0.19/0.51 v6_lattices: $i > $o)).
% 0.19/0.51 tff(v5_lattices_type, type, (
% 0.19/0.51 v5_lattices: $i > $o)).
% 0.19/0.51 tff(v4_lattices_type, type, (
% 0.19/0.51 v4_lattices: $i > $o)).
% 0.19/0.51 tff(k2_binop_1_type, type, (
% 0.19/0.51 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.19/0.51 tff(u2_lattices_type, type, (
% 0.19/0.51 u2_lattices: $i > $i)).
% 0.19/0.51 tff(l2_lattices_type, type, (
% 0.19/0.51 l2_lattices: $i > $o)).
% 0.19/0.51 tff(l1_lattices_type, type, (
% 0.19/0.51 l1_lattices: $i > $o)).
% 0.19/0.51 tff(m1_relset_1_type, type, (
% 0.19/0.51 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(k2_zfmisc_1_type, type, (
% 0.19/0.51 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.19/0.51 tff(m2_relset_1_type, type, (
% 0.19/0.51 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(v1_funct_2_type, type, (
% 0.19/0.51 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(v1_funct_1_type, type, (
% 0.19/0.51 v1_funct_1: $i > $o)).
% 0.19/0.51 tff(v1_xboole_0_type, type, (
% 0.19/0.51 v1_xboole_0: $i > $o)).
% 0.19/0.51 tff(l1_struct_0_type, type, (
% 0.19/0.51 l1_struct_0: $i > $o)).
% 0.19/0.51 tff(v2_binop_1_type, type, (
% 0.19/0.51 v2_binop_1: ( $i * $i ) > $o)).
% 0.19/0.51 tff(v1_partfun1_type, type, (
% 0.19/0.51 v1_partfun1: ( $i * $i * $i ) > $o)).
% 0.19/0.51 tff(v1_relat_1_type, type, (
% 0.19/0.51 v1_relat_1: $i > $o)).
% 0.19/0.51 tff(1,plain,
% 0.19/0.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(2,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.51 tff(3,plain,
% 0.19/0.51 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(4,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.51 tff(5,plain,
% 0.19/0.51 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(6,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[5])).
% 0.19/0.51 tff(7,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[6, 4])).
% 0.19/0.51 tff(8,plain,
% 0.19/0.51 (^[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, k1_zfmisc_1(u1_struct_0(A)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), B))))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))), (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), B))))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), B)))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(9,plain,
% 0.19/0.51 (![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)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), 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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[8])).
% 0.19/0.51 tff(10,plain,
% 0.19/0.51 (![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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, 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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(11,plain,
% 0.19/0.51 (^[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(rewrite((m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)))))) <=> (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B))))))) <=> (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))), rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))))), ((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B))))))) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))))))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B))))))) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, 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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))))),
% 0.19/0.51 inference(bind,[status(th)],[])).
% 0.19/0.51 tff(12,plain,
% 0.19/0.51 (![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))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), 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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))),
% 0.19/0.51 inference(quant_intro,[status(thm)],[11])).
% 0.19/0.51 tff(13,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (m2_lattice4(B, A) <=> ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) => (r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d10_lattice4')).
% 0.19/0.51 tff(14,plain,
% 0.19/0.51 (![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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.19/0.51 tff(15,plain,
% 0.19/0.51 (![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)))) | (m2_lattice4(B, A) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[14, 10])).
% 0.19/0.51 tff(16,plain,(
% 0.19/0.51 ![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)))) | (((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((r2_hidden(k4_lattices(A, C, D), B) & r2_hidden(k3_lattices(A, C, D), B)) | (~m1_subset_1(D, u1_struct_0(A))) | (~(r2_hidden(C, B) & r2_hidden(D, B)))))) & (m2_lattice4(B, A) | (m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A)) & (~((r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B) & r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~(r2_hidden(tptp_fun_C_2(B, A), B) & r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(skolemize,[status(sab)],[15])).
% 0.19/0.51 tff(17,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[16, 9])).
% 0.19/0.51 tff(18,plain,
% 0.19/0.51 (![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)))) | (~((~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)))))) | (~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[17, 7])).
% 0.19/0.52 tff(19,plain,
% 0.19/0.52 (![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[18, 2])).
% 0.19/0.52 tff(20,plain,
% 0.19/0.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(21,plain,
% 0.19/0.52 (((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) <=> ((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(22,plain,
% 0.19/0.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[21])).
% 0.19/0.52 tff(23,plain,
% 0.19/0.52 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[22, 20])).
% 0.19/0.52 tff(24,plain,
% 0.19/0.52 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(25,plain,
% 0.19/0.52 ((~![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))) => (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))) => m2_lattice4(B, A))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(26,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))) => (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B)))) => m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t13_filter_2')).
% 0.19/0.52 tff(27,plain,
% 0.19/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.19/0.52 tff(28,plain,
% 0.19/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.19/0.52 tff(29,plain,
% 0.19/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.19/0.52 tff(30,plain,
% 0.19/0.52 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_lattice4(B, A) | (~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | ((r2_hidden(C, B) & r2_hidden(D, B)) <=> r2_hidden(k4_lattices(A, C, D), B))))) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.19/0.52 tff(31,plain,
% 0.19/0.52 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~m2_lattice4(B!1, A!0)) & ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) & m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.19/0.52 tff(32,plain,
% 0.19/0.52 (l3_lattices(A!0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(33,plain,
% 0.19/0.52 (v10_lattices(A!0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(34,plain,
% 0.19/0.52 (~v3_struct_0(A!0)),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(35,plain,
% 0.19/0.52 (((~![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), 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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B))))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(36,plain,
% 0.19/0.52 ((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)))) | (~((~(m2_lattice4(B, A!0) | (~((~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~r2_hidden(tptp_fun_D_3(B, A!0), B)))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B))))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(37,plain,
% 0.19/0.52 (((~![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~r2_hidden(tptp_fun_D_3(B, A!0), B)))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))))),
% 0.19/0.52 inference(monotonicity,[status(thm)],[36])).
% 0.19/0.52 tff(38,plain,
% 0.19/0.52 (((~![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~r2_hidden(tptp_fun_D_3(B, A!0), B)))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B))))))))))))),
% 0.19/0.52 inference(transitivity,[status(thm)],[37, 35])).
% 0.19/0.52 tff(39,plain,
% 0.19/0.52 ((~![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~r2_hidden(tptp_fun_D_3(B, A!0), B)))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B))))))))))),
% 0.19/0.52 inference(quant_inst,[status(thm)],[])).
% 0.19/0.52 tff(40,plain,
% 0.19/0.52 ((~![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)))) | (~((~(m2_lattice4(B, A) | (~((~m1_subset_1(tptp_fun_C_2(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_3(B, A), u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)) | (~r2_hidden(k3_lattices(A, tptp_fun_C_2(B, A), tptp_fun_D_3(B, A)), B)))) | (~r2_hidden(tptp_fun_C_2(B, A), B)) | (~r2_hidden(tptp_fun_D_3(B, A), B)))))) | (~((~m2_lattice4(B, A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A))) | (~((~r2_hidden(k4_lattices(A, C, D), B)) | (~r2_hidden(k3_lattices(A, C, D), B)))) | (~r2_hidden(C, B)) | (~r2_hidden(D, 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)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))),
% 0.19/0.52 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.19/0.52 tff(41,plain,
% 0.19/0.52 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))),
% 0.19/0.52 inference(unit_resolution,[status(thm)],[40, 34, 33, 32, 19])).
% 0.19/0.52 tff(42,plain,
% 0.19/0.52 (m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.19/0.52 inference(and_elim,[status(thm)],[31])).
% 0.19/0.52 tff(43,plain,
% 0.19/0.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(44,plain,
% 0.19/0.52 (((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1))))))))))) <=> ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))),
% 0.19/0.52 inference(rewrite,[status(thm)],[])).
% 0.19/0.52 tff(45,plain,
% 0.19/0.52 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1))))))))))))),
% 0.19/0.53 inference(monotonicity,[status(thm)],[44])).
% 0.19/0.53 tff(46,plain,
% 0.19/0.53 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[45, 43])).
% 0.19/0.53 tff(47,plain,
% 0.19/0.53 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | ((~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))))),
% 0.19/0.53 inference(quant_inst,[status(thm)],[])).
% 0.19/0.53 tff(48,plain,
% 0.19/0.53 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B, A!0) | (~((~r2_hidden(tptp_fun_D_3(B, A!0), B)) | (~r2_hidden(tptp_fun_C_2(B, A!0), B)) | (~m1_subset_1(tptp_fun_D_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B, A!0), u1_struct_0(A!0))) | (~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B, A!0), tptp_fun_D_3(B, A!0)), B)))))))) | (~((~m2_lattice4(B, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B)) | (~r2_hidden(D, B)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B)) | (~r2_hidden(k3_lattices(A!0, C, D), B)))))))))))) | (~m1_subset_1(B!1, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1))))))))))),
% 0.19/0.53 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.19/0.53 tff(49,plain,
% 0.19/0.53 (~((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1)))))))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[48, 42, 41])).
% 0.19/0.53 tff(50,plain,
% 0.19/0.53 (((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~m2_lattice4(B!1, A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1)) | (~((~r2_hidden(k4_lattices(A!0, C, D), B!1)) | (~r2_hidden(k3_lattices(A!0, C, D), B!1))))))))) | (m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(51,plain,
% 0.19/0.53 (m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[50, 49])).
% 0.19/0.53 tff(52,plain,
% 0.19/0.53 (~m2_lattice4(B!1, A!0)),
% 0.19/0.53 inference(and_elim,[status(thm)],[31])).
% 0.19/0.53 tff(53,plain,
% 0.19/0.53 ((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(54,plain,
% 0.19/0.53 ((~(m2_lattice4(B!1, A!0) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))))) | (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.19/0.53 tff(55,plain,
% 0.19/0.53 (~((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[54, 51])).
% 0.19/0.53 tff(56,plain,
% 0.19/0.53 (((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))),
% 0.19/0.53 inference(tautology,[status(thm)],[])).
% 0.19/0.53 tff(57,plain,
% 0.19/0.53 (m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))),
% 0.19/0.53 inference(unit_resolution,[status(thm)],[56, 55])).
% 0.19/0.53 tff(58,plain,
% 0.19/0.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(59,plain,
% 0.19/0.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.53 tff(60,plain,
% 0.19/0.53 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(61,plain,
% 0.19/0.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[60])).
% 0.19/0.53 tff(62,plain,
% 0.19/0.53 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(63,plain,
% 0.19/0.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[62])).
% 0.19/0.53 tff(64,plain,
% 0.19/0.53 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.53 inference(transitivity,[status(thm)],[63, 61])).
% 0.19/0.53 tff(65,plain,
% 0.19/0.53 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A))))), trans(monotonicity(rewrite(((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) <=> ((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))), rewrite((v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) <=> (v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))), ((((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))) <=> (((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))), rewrite((((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) <=> (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))), ((((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))) <=> (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A))) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A))) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))))),
% 0.19/0.53 inference(bind,[status(th)],[])).
% 0.19/0.53 tff(66,plain,
% 0.19/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.53 inference(quant_intro,[status(thm)],[65])).
% 0.19/0.53 tff(67,plain,
% 0.19/0.53 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(68,plain,
% 0.19/0.54 (^[A: $i] : trans(monotonicity(rewrite((v9_lattices(A) <=> ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) <=> (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) <=> (((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))), rewrite((((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(69,plain,
% 0.19/0.54 (![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[68])).
% 0.19/0.54 tff(70,axiom,(![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => (v9_lattices(A) <=> ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d9_lattices')).
% 0.19/0.54 tff(71,plain,
% 0.19/0.54 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[70, 69])).
% 0.19/0.54 tff(72,plain,
% 0.19/0.54 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (v9_lattices(A) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[71, 67])).
% 0.19/0.54 tff(73,plain,(
% 0.19/0.54 ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | (((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B)))) & (v9_lattices(A) | (m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A))))))))),
% 0.19/0.54 inference(skolemize,[status(sab)],[72])).
% 0.19/0.54 tff(74,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[73, 66])).
% 0.19/0.54 tff(75,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))) | (~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[74, 64])).
% 0.19/0.54 tff(76,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[75, 59])).
% 0.19/0.54 tff(77,plain,
% 0.19/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(78,plain,
% 0.19/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(79,plain,
% 0.19/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~((~(v9_lattices(A) | (~((~m1_subset_1(tptp_fun_B_4(A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_C_5(A), u1_struct_0(A))) | (k2_lattices(A, tptp_fun_B_4(A), k1_lattices(A, tptp_fun_B_4(A), tptp_fun_C_5(A))) = tptp_fun_B_4(A)))))) | (~((~v9_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, k1_lattices(A, B, C)) = B))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.19/0.54 tff(80,plain,
% 0.19/0.54 (~((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[79, 34, 32, 76])).
% 0.19/0.54 tff(81,plain,
% 0.19/0.54 (((~(v9_lattices(A!0) | (~((~m1_subset_1(tptp_fun_B_4(A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_5(A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_B_4(A!0), k1_lattices(A!0, tptp_fun_B_4(A!0), tptp_fun_C_5(A!0))) = tptp_fun_B_4(A!0)))))) | (~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))))) | ((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(82,plain,
% 0.19/0.54 ((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[81, 80])).
% 0.19/0.54 tff(83,plain,
% 0.19/0.54 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(84,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[83])).
% 0.19/0.54 tff(85,plain,
% 0.19/0.54 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))))), rewrite(((~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), ((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(86,plain,
% 0.19/0.54 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[85])).
% 0.19/0.54 tff(87,plain,
% 0.19/0.54 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(88,plain,
% 0.19/0.54 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(89,plain,
% 0.19/0.54 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[88])).
% 0.19/0.54 tff(90,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 0.19/0.54 tff(91,plain,
% 0.19/0.54 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.19/0.54 tff(92,plain,
% 0.19/0.54 (![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.19/0.54 tff(93,plain,(
% 0.19/0.54 ![A: $i] : (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))) | (~l3_lattices(A)))),
% 0.19/0.54 inference(skolemize,[status(sab)],[92])).
% 0.19/0.54 tff(94,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.19/0.54 tff(95,plain,
% 0.19/0.54 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.19/0.54 tff(96,plain,
% 0.19/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(97,plain,
% 0.19/0.54 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(98,plain,
% 0.19/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 0.19/0.54 inference(monotonicity,[status(thm)],[97])).
% 0.19/0.54 tff(99,plain,
% 0.19/0.54 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 0.19/0.54 inference(transitivity,[status(thm)],[98, 96])).
% 0.19/0.54 tff(100,plain,
% 0.19/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(101,plain,
% 0.19/0.54 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.19/0.54 tff(102,plain,
% 0.19/0.54 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[101, 34, 33, 32, 95])).
% 0.19/0.54 tff(103,plain,
% 0.19/0.54 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v9_lattices(A!0)),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(104,plain,
% 0.19/0.54 (v9_lattices(A!0)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[103, 102])).
% 0.19/0.54 tff(105,plain,
% 0.19/0.54 ((~((~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B))))) | (~v9_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(106,plain,
% 0.19/0.54 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[105, 104, 82])).
% 0.19/0.54 tff(107,plain,
% 0.19/0.54 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0))))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(108,plain,
% 0.19/0.54 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0))))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(109,plain,
% 0.19/0.54 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, B, k1_lattices(A!0, B, C)) = B)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.54 tff(110,plain,
% 0.19/0.54 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[109, 106, 57])).
% 0.19/0.54 tff(111,plain,
% 0.19/0.54 (((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))),
% 0.19/0.54 inference(tautology,[status(thm)],[])).
% 0.19/0.54 tff(112,plain,
% 0.19/0.54 (m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[111, 55])).
% 0.19/0.54 tff(113,plain,
% 0.19/0.54 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = tptp_fun_C_2(B!1, A!0)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = tptp_fun_C_2(B!1, A!0)))),
% 0.19/0.54 inference(rewrite,[status(thm)],[])).
% 0.19/0.54 tff(114,plain,
% 0.19/0.54 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = tptp_fun_C_2(B!1, A!0)))),
% 0.19/0.54 inference(quant_inst,[status(thm)],[])).
% 0.19/0.54 tff(115,plain,
% 0.19/0.54 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C)) = tptp_fun_C_2(B!1, A!0)))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = tptp_fun_C_2(B!1, A!0))),
% 0.19/0.54 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.19/0.54 tff(116,plain,
% 0.19/0.54 (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = tptp_fun_C_2(B!1, A!0)),
% 0.19/0.54 inference(unit_resolution,[status(thm)],[115, 112, 110])).
% 0.19/0.54 tff(117,plain,
% 0.19/0.54 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(118,plain,
% 0.19/0.54 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.54 inference(quant_intro,[status(thm)],[117])).
% 0.19/0.54 tff(119,plain,
% 0.19/0.54 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.54 inference(bind,[status(th)],[])).
% 0.19/0.54 tff(120,plain,
% 0.19/0.54 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.55 tff(121,plain,
% 0.19/0.55 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(122,plain,
% 0.19/0.55 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(123,plain,
% 0.19/0.55 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[122])).
% 0.19/0.55 tff(124,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.19/0.55 tff(125,plain,
% 0.19/0.55 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.19/0.55 tff(126,plain,
% 0.19/0.55 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.19/0.55 tff(127,plain,(
% 0.19/0.55 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.55 inference(skolemize,[status(sab)],[126])).
% 0.19/0.55 tff(128,plain,
% 0.19/0.55 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.19/0.55 tff(129,plain,
% 0.19/0.55 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[128, 118])).
% 0.19/0.55 tff(130,plain,
% 0.19/0.55 (((~![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)))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(131,plain,
% 0.19/0.55 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(132,plain,
% 0.19/0.55 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.19/0.55 tff(133,plain,
% 0.19/0.55 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[132, 32, 129])).
% 0.19/0.55 tff(134,plain,
% 0.19/0.55 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.19/0.55 inference(tautology,[status(thm)],[])).
% 0.19/0.55 tff(135,plain,
% 0.19/0.55 (l2_lattices(A!0)),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[134, 133])).
% 0.19/0.55 tff(136,plain,
% 0.19/0.55 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(137,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[136])).
% 0.19/0.55 tff(138,plain,
% 0.19/0.55 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(139,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[138])).
% 0.19/0.55 tff(140,plain,
% 0.19/0.55 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(141,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[140])).
% 0.19/0.55 tff(142,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(transitivity,[status(thm)],[141, 139])).
% 0.19/0.55 tff(143,plain,
% 0.19/0.55 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(144,plain,
% 0.19/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[143])).
% 0.19/0.55 tff(145,plain,
% 0.19/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(146,plain,
% 0.19/0.55 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(147,plain,
% 0.19/0.55 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[146])).
% 0.19/0.55 tff(148,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_lattices')).
% 0.19/0.55 tff(149,plain,
% 0.19/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[148, 147])).
% 0.19/0.55 tff(150,plain,
% 0.19/0.55 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[149, 145])).
% 0.19/0.55 tff(151,plain,(
% 0.19/0.55 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(skolemize,[status(sab)],[150])).
% 0.19/0.55 tff(152,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[151, 144])).
% 0.19/0.55 tff(153,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[152, 142])).
% 0.19/0.55 tff(154,plain,
% 0.19/0.55 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[153, 137])).
% 0.19/0.55 tff(155,plain,
% 0.19/0.55 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(156,plain,
% 0.19/0.55 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(157,plain,
% 0.19/0.55 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.19/0.55 tff(158,plain,
% 0.19/0.55 ((~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[157, 34, 154])).
% 0.19/0.55 tff(159,plain,
% 0.19/0.55 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[158, 135])).
% 0.19/0.55 tff(160,plain,
% 0.19/0.55 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(161,plain,
% 0.19/0.55 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(162,plain,
% 0.19/0.55 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.55 tff(163,plain,
% 0.19/0.55 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[162, 159, 57])).
% 0.19/0.55 tff(164,plain,
% 0.19/0.55 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(165,plain,
% 0.19/0.55 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(166,plain,
% 0.19/0.55 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), C)))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.19/0.55 tff(167,plain,
% 0.19/0.55 (k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[166, 112, 163])).
% 0.19/0.55 tff(168,plain,
% 0.19/0.55 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))),
% 0.19/0.55 inference(symmetry,[status(thm)],[167])).
% 0.19/0.55 tff(169,plain,
% 0.19/0.55 (k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))),
% 0.19/0.55 inference(monotonicity,[status(thm)],[168])).
% 0.19/0.55 tff(170,plain,
% 0.19/0.55 (^[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)))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(171,plain,
% 0.19/0.55 (![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))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[170])).
% 0.19/0.55 tff(172,plain,
% 0.19/0.55 (![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))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(173,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')).
% 0.19/0.55 tff(174,plain,
% 0.19/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.19/0.55 tff(175,plain,(
% 0.19/0.55 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.55 inference(skolemize,[status(sab)],[174])).
% 0.19/0.55 tff(176,plain,
% 0.19/0.55 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[175, 171])).
% 0.19/0.55 tff(177,plain,
% 0.19/0.55 ((~![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)))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(178,plain,
% 0.19/0.55 (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))),
% 0.19/0.55 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.19/0.55 tff(179,plain,
% 0.19/0.55 (^[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)))))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(180,plain,
% 0.19/0.55 (![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))))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[179])).
% 0.19/0.55 tff(181,plain,
% 0.19/0.55 (^[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)))))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(182,plain,
% 0.19/0.55 (![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))))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[181])).
% 0.19/0.55 tff(183,plain,
% 0.19/0.55 (![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))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(184,plain,
% 0.19/0.55 (^[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))))))),
% 0.19/0.55 inference(bind,[status(th)],[])).
% 0.19/0.55 tff(185,plain,
% 0.19/0.55 (![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))))),
% 0.19/0.55 inference(quant_intro,[status(thm)],[184])).
% 0.19/0.55 tff(186,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')).
% 0.19/0.55 tff(187,plain,
% 0.19/0.55 (![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))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.55 tff(188,plain,
% 0.19/0.55 (![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))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.19/0.55 tff(189,plain,(
% 0.19/0.55 ![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))))),
% 0.19/0.55 inference(skolemize,[status(sab)],[188])).
% 0.19/0.55 tff(190,plain,
% 0.19/0.55 (![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))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.19/0.55 tff(191,plain,
% 0.19/0.55 (![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))))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[190, 180])).
% 0.19/0.55 tff(192,plain,
% 0.19/0.55 (((~![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))))))),
% 0.19/0.55 inference(rewrite,[status(thm)],[])).
% 0.19/0.55 tff(193,plain,
% 0.19/0.55 ((~![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))))))),
% 0.19/0.55 inference(quant_inst,[status(thm)],[])).
% 0.19/0.55 tff(194,plain,
% 0.19/0.55 ((~![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)))))),
% 0.19/0.55 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.19/0.55 tff(195,plain,
% 0.19/0.55 ((~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)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[194, 191])).
% 0.19/0.56 tff(196,plain,
% 0.19/0.56 (~((~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))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[195, 135])).
% 0.19/0.56 tff(197,plain,
% 0.19/0.56 (((~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))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(198,plain,
% 0.19/0.56 (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))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.19/0.56 tff(199,plain,
% 0.19/0.56 ((~(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))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(200,plain,
% 0.19/0.56 ((~(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))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[199, 198])).
% 0.19/0.56 tff(201,plain,
% 0.19/0.56 (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))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[200, 178])).
% 0.19/0.56 tff(202,plain,
% 0.19/0.56 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(203,plain,
% 0.19/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[202])).
% 0.19/0.56 tff(204,plain,
% 0.19/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(205,plain,
% 0.19/0.56 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(206,plain,
% 0.19/0.56 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.56 tff(207,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.19/0.56 tff(208,plain,
% 0.19/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[207, 206])).
% 0.19/0.56 tff(209,plain,
% 0.19/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[208, 204])).
% 0.19/0.56 tff(210,plain,(
% 0.19/0.56 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(skolemize,[status(sab)],[209])).
% 0.19/0.56 tff(211,plain,
% 0.19/0.56 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[210, 203])).
% 0.19/0.56 tff(212,plain,
% 0.19/0.56 (((~![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)))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(213,plain,
% 0.19/0.56 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(214,plain,
% 0.19/0.56 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[213, 212])).
% 0.19/0.56 tff(215,plain,
% 0.19/0.56 (l1_struct_0(A!0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[214, 211, 135])).
% 0.19/0.56 tff(216,plain,
% 0.19/0.56 (^[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))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(217,plain,
% 0.19/0.56 (![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)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[216])).
% 0.19/0.56 tff(218,plain,
% 0.19/0.56 (^[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)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(219,plain,
% 0.19/0.56 (![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)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[218])).
% 0.19/0.56 tff(220,plain,
% 0.19/0.56 (![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))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(221,plain,
% 0.19/0.56 (^[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)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(222,plain,
% 0.19/0.56 (![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))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[221])).
% 0.19/0.56 tff(223,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')).
% 0.19/0.56 tff(224,plain,
% 0.19/0.56 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[223, 222])).
% 0.19/0.56 tff(225,plain,
% 0.19/0.56 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[224, 220])).
% 0.19/0.56 tff(226,plain,(
% 0.19/0.56 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.19/0.56 inference(skolemize,[status(sab)],[225])).
% 0.19/0.56 tff(227,plain,
% 0.19/0.56 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[226, 219])).
% 0.19/0.56 tff(228,plain,
% 0.19/0.56 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[227, 217])).
% 0.19/0.56 tff(229,plain,
% 0.19/0.56 (((~![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))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(230,plain,
% 0.19/0.56 ((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))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(231,plain,
% 0.19/0.56 (((~![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)))))),
% 0.19/0.56 inference(monotonicity,[status(thm)],[230])).
% 0.19/0.56 tff(232,plain,
% 0.19/0.56 (((~![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))))),
% 0.19/0.56 inference(transitivity,[status(thm)],[231, 229])).
% 0.19/0.56 tff(233,plain,
% 0.19/0.56 ((~![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)))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(234,plain,
% 0.19/0.56 ((~![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)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.19/0.56 tff(235,plain,
% 0.19/0.56 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[234, 34, 228])).
% 0.19/0.56 tff(236,plain,
% 0.19/0.56 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[235, 215])).
% 0.19/0.56 tff(237,plain,
% 0.19/0.56 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v5_lattices(A!0)),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(238,plain,
% 0.19/0.56 (v5_lattices(A!0)),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[237, 102])).
% 0.19/0.56 tff(239,plain,
% 0.19/0.56 (^[A: $i] : refl((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(240,plain,
% 0.19/0.56 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[239])).
% 0.19/0.56 tff(241,plain,
% 0.19/0.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))), ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)))), ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))))), rewrite((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A))) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))), (((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(242,plain,
% 0.19/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[241])).
% 0.19/0.56 tff(243,plain,
% 0.19/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(244,plain,
% 0.19/0.56 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))), trans(monotonicity(trans(monotonicity(rewrite(((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> ((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)))), ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) <=> (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))))), (((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> ((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), rewrite(((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), (((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A)) => (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), (((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(245,plain,
% 0.19/0.56 (![A: $i] : ((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[244])).
% 0.19/0.56 tff(246,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v5_lattices(A)) & l2_lattices(A)) => ((((v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A))) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & v2_binop_1(u2_lattices(A), u1_struct_0(A))) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc3_lattice2')).
% 0.19/0.56 tff(247,plain,
% 0.19/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[246, 245])).
% 0.19/0.56 tff(248,plain,
% 0.19/0.56 (![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[247, 243])).
% 0.19/0.56 tff(249,plain,(
% 0.19/0.56 ![A: $i] : ((~((~v3_struct_0(A)) & v5_lattices(A) & l2_lattices(A))) | (v1_relat_1(u2_lattices(A)) & v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & v2_binop_1(u2_lattices(A), u1_struct_0(A)) & v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.56 inference(skolemize,[status(sab)],[248])).
% 0.19/0.56 tff(250,plain,
% 0.19/0.56 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[249, 242])).
% 0.19/0.56 tff(251,plain,
% 0.19/0.56 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[250, 240])).
% 0.19/0.56 tff(252,plain,
% 0.19/0.56 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(253,plain,
% 0.19/0.56 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))))),
% 0.19/0.56 inference(quant_inst,[status(thm)],[])).
% 0.19/0.56 tff(254,plain,
% 0.19/0.56 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | (~v5_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v1_relat_1(u2_lattices(A))) | (~v1_partfun1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~v2_binop_1(u2_lattices(A), u1_struct_0(A))))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v5_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.19/0.56 tff(255,plain,
% 0.19/0.56 ((~l2_lattices(A!0)) | (~v5_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[254, 34, 251])).
% 0.19/0.56 tff(256,plain,
% 0.19/0.56 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0))))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[255, 135, 238])).
% 0.19/0.56 tff(257,plain,
% 0.19/0.56 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(258,plain,
% 0.19/0.56 (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))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[257, 256])).
% 0.19/0.56 tff(259,plain,
% 0.19/0.56 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_relat_1(u2_lattices(A!0))) | (~v1_partfun1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v2_binop_1(u2_lattices(A!0), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 0.19/0.56 inference(tautology,[status(thm)],[])).
% 0.19/0.56 tff(260,plain,
% 0.19/0.56 (v1_funct_1(u2_lattices(A!0))),
% 0.19/0.56 inference(unit_resolution,[status(thm)],[259, 256])).
% 0.19/0.56 tff(261,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : refl((m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(262,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[261])).
% 0.19/0.56 tff(263,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) <=> (~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))))), rewrite((~(~(v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) <=> (v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite(((v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))), (((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(264,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[263])).
% 0.19/0.56 tff(265,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 0.19/0.56 inference(rewrite,[status(thm)],[])).
% 0.19/0.56 tff(266,plain,
% 0.19/0.56 (^[A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C))), (((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C))), ((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A))), (((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))), ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) <=> ((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> (((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)))), rewrite((((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), (((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))))),
% 0.19/0.56 inference(bind,[status(th)],[])).
% 0.19/0.56 tff(267,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C)) <=> ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 0.19/0.56 inference(quant_intro,[status(thm)],[266])).
% 0.19/0.56 tff(268,axiom,(![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((((((((~v1_xboole_0(A)) & (~v1_xboole_0(B))) & v1_funct_1(D)) & v1_funct_2(D, k2_zfmisc_1(A, B), C)) & m1_relset_1(D, k2_zfmisc_1(A, B), C)) & m1_subset_1(E, A)) & m1_subset_1(F, B)) => m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k2_binop_1')).
% 0.19/0.56 tff(269,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.19/0.56 tff(270,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.19/0.56 tff(271,plain,(
% 0.19/0.56 ![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : ((~((~v1_xboole_0(A)) & (~v1_xboole_0(B)) & v1_funct_1(D) & v1_funct_2(D, k2_zfmisc_1(A, B), C) & m1_relset_1(D, k2_zfmisc_1(A, B), C) & m1_subset_1(E, A) & m1_subset_1(F, B))) | m1_subset_1(k2_binop_1(A, B, C, D, E, F), C))),
% 0.19/0.56 inference(skolemize,[status(sab)],[270])).
% 0.19/0.56 tff(272,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.19/0.56 tff(273,plain,
% 0.19/0.56 (![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))),
% 0.19/0.56 inference(modus_ponens,[status(thm)],[272, 262])).
% 0.19/0.56 tff(274,plain,
% 0.19/0.56 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(275,plain,
% 0.19/0.57 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, 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))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(276,plain,
% 0.19/0.57 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[275])).
% 0.19/0.57 tff(277,plain,
% 0.19/0.57 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.19/0.57 inference(transitivity,[status(thm)],[276, 274])).
% 0.19/0.57 tff(278,plain,
% 0.19/0.57 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))),
% 0.19/0.57 inference(quant_inst,[status(thm)],[])).
% 0.19/0.57 tff(279,plain,
% 0.19/0.57 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.19/0.57 tff(280,plain,
% 0.19/0.57 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[279, 273, 260, 258, 236, 201, 57, 112])).
% 0.19/0.57 tff(281,plain,
% 0.19/0.57 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v6_lattices(A!0)),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(282,plain,
% 0.19/0.57 (v6_lattices(A!0)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[281, 102])).
% 0.19/0.57 tff(283,plain,
% 0.19/0.57 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.19/0.57 inference(tautology,[status(thm)],[])).
% 0.19/0.57 tff(284,plain,
% 0.19/0.57 (l1_lattices(A!0)),
% 0.19/0.57 inference(unit_resolution,[status(thm)],[283, 133])).
% 0.19/0.57 tff(285,plain,
% 0.19/0.57 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(286,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[285])).
% 0.19/0.57 tff(287,plain,
% 0.19/0.57 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(288,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[287])).
% 0.19/0.57 tff(289,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(290,plain,
% 0.19/0.57 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 0.19/0.57 inference(bind,[status(th)],[])).
% 0.19/0.57 tff(291,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.19/0.57 inference(quant_intro,[status(thm)],[290])).
% 0.19/0.57 tff(292,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 0.19/0.57 tff(293,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.19/0.57 tff(294,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.19/0.57 tff(295,plain,(
% 0.19/0.57 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.19/0.57 inference(skolemize,[status(sab)],[294])).
% 0.19/0.57 tff(296,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.19/0.57 tff(297,plain,
% 0.19/0.57 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.19/0.57 inference(modus_ponens,[status(thm)],[296, 286])).
% 0.19/0.57 tff(298,plain,
% 0.19/0.57 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(299,plain,
% 0.19/0.57 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))))),
% 0.19/0.57 inference(rewrite,[status(thm)],[])).
% 0.19/0.57 tff(300,plain,
% 0.19/0.57 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))))),
% 0.19/0.57 inference(monotonicity,[status(thm)],[299])).
% 0.19/0.57 tff(301,plain,
% 0.19/0.57 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[300, 298])).
% 0.19/0.58 tff(302,plain,
% 0.19/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(303,plain,
% 0.19/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.19/0.58 tff(304,plain,
% 0.19/0.58 ((~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[303, 34, 297, 284, 282, 57])).
% 0.19/0.58 tff(305,plain,
% 0.19/0.58 (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) = k2_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[304, 280])).
% 0.19/0.58 tff(306,plain,
% 0.19/0.58 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v4_lattices(A!0)),
% 0.19/0.58 inference(tautology,[status(thm)],[])).
% 0.19/0.58 tff(307,plain,
% 0.19/0.58 (v4_lattices(A!0)),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[306, 102])).
% 0.19/0.58 tff(308,plain,
% 0.19/0.58 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(309,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[308])).
% 0.19/0.58 tff(310,plain,
% 0.19/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(311,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[310])).
% 0.19/0.58 tff(312,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(313,plain,
% 0.19/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(314,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[313])).
% 0.19/0.58 tff(315,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_lattices')).
% 0.19/0.58 tff(316,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[315, 314])).
% 0.19/0.58 tff(317,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[316, 312])).
% 0.19/0.58 tff(318,plain,(
% 0.19/0.58 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.19/0.58 inference(skolemize,[status(sab)],[317])).
% 0.19/0.58 tff(319,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[318, 311])).
% 0.19/0.58 tff(320,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[319, 309])).
% 0.19/0.58 tff(321,plain,
% 0.19/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(322,plain,
% 0.19/0.58 ((v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.58 inference(rewrite,[status(thm)],[])).
% 0.19/0.58 tff(323,plain,
% 0.19/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))))),
% 0.19/0.58 inference(monotonicity,[status(thm)],[322])).
% 0.19/0.58 tff(324,plain,
% 0.19/0.58 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))))),
% 0.19/0.58 inference(transitivity,[status(thm)],[323, 321])).
% 0.19/0.58 tff(325,plain,
% 0.19/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))),
% 0.19/0.58 inference(quant_inst,[status(thm)],[])).
% 0.19/0.58 tff(326,plain,
% 0.19/0.58 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))),
% 0.19/0.58 inference(modus_ponens,[status(thm)],[325, 324])).
% 0.19/0.58 tff(327,plain,
% 0.19/0.58 (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k1_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))),
% 0.19/0.58 inference(unit_resolution,[status(thm)],[326, 34, 320, 135, 307, 57, 112])).
% 0.19/0.58 tff(328,plain,
% 0.19/0.58 (^[A: $i, B: $i, C: $i] : refl(((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.19/0.58 tff(329,plain,
% 0.19/0.58 (![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.19/0.58 inference(quant_intro,[status(thm)],[328])).
% 0.19/0.58 tff(330,plain,
% 0.19/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 0.19/0.58 inference(bind,[status(th)],[])).
% 0.42/0.58 tff(331,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.42/0.58 inference(quant_intro,[status(thm)],[330])).
% 0.42/0.58 tff(332,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(333,plain,
% 0.42/0.58 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))))),
% 0.42/0.58 inference(bind,[status(th)],[])).
% 0.42/0.58 tff(334,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))),
% 0.42/0.58 inference(quant_intro,[status(thm)],[333])).
% 0.42/0.58 tff(335,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k3_lattices(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k3_lattices')).
% 0.42/0.58 tff(336,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.42/0.58 tff(337,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[336, 332])).
% 0.42/0.58 tff(338,plain,(
% 0.42/0.58 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k3_lattices(A, C, B)))),
% 0.42/0.58 inference(skolemize,[status(sab)],[337])).
% 0.42/0.58 tff(339,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[338, 331])).
% 0.42/0.58 tff(340,plain,
% 0.42/0.58 (![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.42/0.58 inference(modus_ponens,[status(thm)],[339, 329])).
% 0.42/0.58 tff(341,plain,
% 0.42/0.58 (((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(342,plain,
% 0.42/0.58 (((k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.58 inference(rewrite,[status(thm)],[])).
% 0.42/0.58 tff(343,plain,
% 0.42/0.58 (((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[342])).
% 0.42/0.59 tff(344,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(transitivity,[status(thm)],[343, 341])).
% 0.42/0.59 tff(345,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(346,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i] : ((k3_lattices(A, B, C) = k3_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[345, 344])).
% 0.42/0.59 tff(347,plain,
% 0.42/0.59 (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[346, 34, 340, 135, 307, 57, 112])).
% 0.42/0.59 tff(348,plain,
% 0.42/0.59 (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))),
% 0.42/0.59 inference(symmetry,[status(thm)],[347])).
% 0.42/0.59 tff(349,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(350,plain,
% 0.42/0.59 ((v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(351,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[350])).
% 0.42/0.59 tff(352,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(transitivity,[status(thm)],[351, 349])).
% 0.42/0.59 tff(353,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(354,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.42/0.59 tff(355,plain,
% 0.42/0.59 (k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[354, 34, 320, 135, 307, 57, 112])).
% 0.42/0.59 tff(356,plain,
% 0.42/0.59 (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k3_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.42/0.59 inference(symmetry,[status(thm)],[355])).
% 0.42/0.59 tff(357,plain,
% 0.42/0.59 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(358,plain,
% 0.42/0.59 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(359,plain,
% 0.42/0.59 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[358, 357])).
% 0.42/0.59 tff(360,plain,
% 0.42/0.59 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[359, 159, 112])).
% 0.42/0.59 tff(361,plain,
% 0.42/0.59 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(362,plain,
% 0.42/0.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(363,plain,
% 0.42/0.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), C)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))),
% 0.42/0.59 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.42/0.59 tff(364,plain,
% 0.42/0.59 (k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.42/0.59 inference(unit_resolution,[status(thm)],[363, 57, 360])).
% 0.42/0.59 tff(365,plain,
% 0.42/0.59 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k1_lattices(A!0, tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.42/0.59 inference(symmetry,[status(thm)],[364])).
% 0.42/0.59 tff(366,plain,
% 0.42/0.59 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0))),
% 0.42/0.59 inference(transitivity,[status(thm)],[365, 356, 348, 327, 167])).
% 0.42/0.59 tff(367,plain,
% 0.42/0.59 (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[366])).
% 0.42/0.59 tff(368,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(369,plain,
% 0.42/0.59 ((m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, 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))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)))),
% 0.42/0.59 inference(rewrite,[status(thm)],[])).
% 0.42/0.59 tff(370,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))))),
% 0.42/0.59 inference(monotonicity,[status(thm)],[369])).
% 0.42/0.59 tff(371,plain,
% 0.42/0.59 (((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)))),
% 0.42/0.59 inference(transitivity,[status(thm)],[370, 368])).
% 0.42/0.59 tff(372,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0)) | v1_xboole_0(u1_struct_0(A!0)) | v1_xboole_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_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))),
% 0.42/0.59 inference(quant_inst,[status(thm)],[])).
% 0.42/0.59 tff(373,plain,
% 0.42/0.59 ((~![A: $i, B: $i, C: $i, D: $i, E: $i, F: $i] : (m1_subset_1(k2_binop_1(A, B, C, D, E, F), C) | v1_xboole_0(B) | v1_xboole_0(A) | (~v1_funct_1(D)) | (~v1_funct_2(D, k2_zfmisc_1(A, B), C)) | (~m1_relset_1(D, k2_zfmisc_1(A, B), C)) | (~m1_subset_1(E, A)) | (~m1_subset_1(F, B)))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | v1_xboole_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_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[372, 371])).
% 0.42/0.60 tff(374,plain,
% 0.42/0.60 (m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))),
% 0.42/0.60 inference(unit_resolution,[status(thm)],[373, 273, 260, 258, 236, 201, 57, 112])).
% 0.42/0.60 tff(375,plain,
% 0.42/0.60 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(376,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[375])).
% 0.42/0.60 tff(377,plain,
% 0.42/0.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(378,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[377])).
% 0.42/0.60 tff(379,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 0.42/0.60 inference(rewrite,[status(thm)],[])).
% 0.42/0.60 tff(380,plain,
% 0.42/0.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))))),
% 0.42/0.60 inference(bind,[status(th)],[])).
% 0.42/0.60 tff(381,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 0.42/0.60 inference(quant_intro,[status(thm)],[380])).
% 0.42/0.60 tff(382,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k4_lattices(A, C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 0.42/0.60 tff(383,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[382, 381])).
% 0.42/0.60 tff(384,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[383, 379])).
% 0.42/0.60 tff(385,plain,(
% 0.42/0.60 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)))),
% 0.42/0.60 inference(skolemize,[status(sab)],[384])).
% 0.42/0.60 tff(386,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[385, 378])).
% 0.42/0.60 tff(387,plain,
% 0.42/0.60 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.42/0.60 inference(modus_ponens,[status(thm)],[386, 376])).
% 0.42/0.60 tff(388,plain,
% 0.42/0.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(389,plain,
% 0.44/0.60 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))))),
% 0.44/0.60 inference(rewrite,[status(thm)],[])).
% 0.44/0.60 tff(390,plain,
% 0.44/0.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0)))))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[389])).
% 0.44/0.60 tff(391,plain,
% 0.44/0.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))))),
% 0.44/0.60 inference(transitivity,[status(thm)],[390, 388])).
% 0.44/0.60 tff(392,plain,
% 0.44/0.60 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)))),
% 0.44/0.60 inference(quant_inst,[status(thm)],[])).
% 0.44/0.60 tff(393,plain,
% 0.44/0.60 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k4_lattices(A, C, B)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0)))),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[392, 391])).
% 0.44/0.60 tff(394,plain,
% 0.44/0.60 (k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[393, 34, 387, 284, 282, 57, 374])).
% 0.44/0.60 tff(395,plain,
% 0.44/0.60 (k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0)) = k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)))),
% 0.44/0.60 inference(symmetry,[status(thm)],[394])).
% 0.44/0.60 tff(396,plain,
% 0.44/0.60 (k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0))),
% 0.44/0.60 inference(transitivity,[status(thm)],[347, 355, 364])).
% 0.44/0.60 tff(397,plain,
% 0.44/0.60 (k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)) = k4_lattices(A!0, k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), tptp_fun_D_3(B!1, A!0), tptp_fun_C_2(B!1, A!0)), tptp_fun_C_2(B!1, A!0))),
% 0.44/0.60 inference(monotonicity,[status(thm)],[396])).
% 0.44/0.60 tff(398,plain,
% 0.44/0.60 (k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)) = tptp_fun_C_2(B!1, A!0)),
% 0.44/0.60 inference(transitivity,[status(thm)],[397, 395, 367, 305, 169, 116])).
% 0.44/0.60 tff(399,plain,
% 0.44/0.60 (r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1) <=> r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)),
% 0.44/0.60 inference(monotonicity,[status(thm)],[398])).
% 0.44/0.60 tff(400,plain,
% 0.44/0.60 (r2_hidden(tptp_fun_C_2(B!1, A!0), B!1) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)),
% 0.44/0.60 inference(symmetry,[status(thm)],[399])).
% 0.44/0.60 tff(401,plain,
% 0.44/0.60 (((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)),
% 0.44/0.60 inference(tautology,[status(thm)],[])).
% 0.44/0.60 tff(402,plain,
% 0.44/0.60 (r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)),
% 0.44/0.60 inference(unit_resolution,[status(thm)],[401, 55])).
% 0.44/0.60 tff(403,plain,
% 0.44/0.60 (r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)),
% 0.44/0.60 inference(modus_ponens,[status(thm)],[402, 400])).
% 0.44/0.60 tff(404,plain,
% 0.44/0.60 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 0.44/0.60 inference(bind,[status(th)],[])).
% 0.44/0.60 tff(405,plain,
% 0.44/0.60 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.44/0.60 inference(quant_intro,[status(thm)],[404])).
% 0.44/0.60 tff(406,plain,
% 0.44/0.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(407,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[406])).
% 0.44/0.61 tff(408,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(409,plain,
% 0.44/0.61 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(410,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[409])).
% 0.44/0.61 tff(411,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k3_lattices')).
% 0.44/0.61 tff(412,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.44/0.61 tff(413,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[412, 408])).
% 0.44/0.61 tff(414,plain,(
% 0.44/0.61 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)))),
% 0.44/0.61 inference(skolemize,[status(sab)],[413])).
% 0.44/0.61 tff(415,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[414, 407])).
% 0.44/0.61 tff(416,plain,
% 0.44/0.61 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[415, 405])).
% 0.44/0.61 tff(417,plain,
% 0.44/0.61 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(418,plain,
% 0.44/0.61 ((v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(419,plain,
% 0.44/0.61 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[418])).
% 0.44/0.61 tff(420,plain,
% 0.44/0.61 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)))),
% 0.44/0.61 inference(transitivity,[status(thm)],[419, 417])).
% 0.44/0.61 tff(421,plain,
% 0.44/0.61 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(422,plain,
% 0.44/0.61 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k3_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.44/0.61 tff(423,plain,
% 0.44/0.61 (m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[422, 34, 416, 135, 307, 57, 112])).
% 0.44/0.61 tff(424,plain,
% 0.44/0.61 (^[C: $i] : refl(((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(425,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[424])).
% 0.44/0.61 tff(426,plain,
% 0.44/0.61 (^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(427,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[426])).
% 0.44/0.61 tff(428,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(transitivity,[status(thm)],[427, 425])).
% 0.44/0.61 tff(429,plain,
% 0.44/0.61 (^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))))),
% 0.44/0.61 inference(bind,[status(th)],[])).
% 0.44/0.61 tff(430,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(quant_intro,[status(thm)],[429])).
% 0.44/0.61 tff(431,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | ((r2_hidden(C, B!1) & r2_hidden(D, B!1)) <=> r2_hidden(k4_lattices(A!0, C, D), B!1))))),
% 0.44/0.61 inference(and_elim,[status(thm)],[31])).
% 0.44/0.61 tff(432,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.44/0.61 tff(433,plain,
% 0.44/0.61 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[432, 428])).
% 0.44/0.61 tff(434,plain,
% 0.44/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(435,plain,
% 0.44/0.61 (((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))) <=> ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))),
% 0.44/0.61 inference(rewrite,[status(thm)],[])).
% 0.44/0.61 tff(436,plain,
% 0.44/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))))),
% 0.44/0.61 inference(monotonicity,[status(thm)],[435])).
% 0.44/0.61 tff(437,plain,
% 0.44/0.61 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))),
% 0.44/0.61 inference(transitivity,[status(thm)],[436, 434])).
% 0.44/0.61 tff(438,plain,
% 0.44/0.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1)))))),
% 0.44/0.61 inference(quant_inst,[status(thm)],[])).
% 0.44/0.61 tff(439,plain,
% 0.44/0.61 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))),
% 0.44/0.61 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.44/0.61 tff(440,plain,
% 0.44/0.61 ((~m1_subset_1(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[439, 433])).
% 0.44/0.61 tff(441,plain,
% 0.44/0.61 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))),
% 0.44/0.61 inference(unit_resolution,[status(thm)],[440, 423])).
% 0.44/0.61 tff(442,plain,
% 0.44/0.61 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(443,plain,
% 0.44/0.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(quant_inst,[status(thm)],[])).
% 0.44/0.62 tff(444,plain,
% 0.44/0.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), D), B!1))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[443, 442])).
% 0.44/0.62 tff(445,plain,
% 0.44/0.62 (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[444, 57, 441])).
% 0.44/0.62 tff(446,plain,
% 0.44/0.62 (((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | ((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(447,plain,
% 0.44/0.62 ((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[446, 55])).
% 0.44/0.62 tff(448,plain,
% 0.44/0.62 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(449,plain,
% 0.44/0.62 (((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) <=> ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(450,plain,
% 0.44/0.62 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[449])).
% 0.44/0.62 tff(451,plain,
% 0.44/0.62 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))),
% 0.44/0.62 inference(transitivity,[status(thm)],[450, 448])).
% 0.44/0.62 tff(452,plain,
% 0.44/0.62 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | ((~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1)))))),
% 0.44/0.62 inference(quant_inst,[status(thm)],[])).
% 0.44/0.62 tff(453,plain,
% 0.44/0.62 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(C, B!1)) | (~r2_hidden(D, B!1))) <=> r2_hidden(k4_lattices(A!0, C, D), B!1)))))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[452, 451])).
% 0.44/0.62 tff(454,plain,
% 0.44/0.62 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[453, 433, 57])).
% 0.44/0.62 tff(455,plain,
% 0.44/0.62 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(456,plain,
% 0.44/0.62 (((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) <=> ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(rewrite,[status(thm)],[])).
% 0.44/0.62 tff(457,plain,
% 0.44/0.62 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))))),
% 0.44/0.62 inference(monotonicity,[status(thm)],[456])).
% 0.44/0.62 tff(458,plain,
% 0.44/0.62 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(transitivity,[status(thm)],[457, 455])).
% 0.44/0.62 tff(459,plain,
% 0.44/0.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | ((~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))))),
% 0.44/0.62 inference(quant_inst,[status(thm)],[])).
% 0.44/0.62 tff(460,plain,
% 0.44/0.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, B!1)) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), D), B!1))))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))),
% 0.44/0.62 inference(modus_ponens,[status(thm)],[459, 458])).
% 0.44/0.62 tff(461,plain,
% 0.44/0.62 (~(((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[460, 112, 454])).
% 0.44/0.62 tff(462,plain,
% 0.44/0.62 (((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~m1_subset_1(tptp_fun_C_2(B!1, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_3(B!1, A!0), u1_struct_0(A!0))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(463,plain,
% 0.44/0.62 (r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[462, 55])).
% 0.44/0.62 tff(464,plain,
% 0.44/0.62 ((~((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))) | (~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(465,plain,
% 0.44/0.62 (~((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1)))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[464, 402, 463])).
% 0.44/0.62 tff(466,plain,
% 0.44/0.62 ((((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | ((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) | r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(467,plain,
% 0.44/0.62 ((((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(tptp_fun_D_3(B!1, A!0), B!1))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[466, 465])).
% 0.44/0.62 tff(468,plain,
% 0.44/0.62 (r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[467, 461])).
% 0.44/0.62 tff(469,plain,
% 0.44/0.62 ((~((~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(470,plain,
% 0.44/0.62 (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[469, 468, 447])).
% 0.44/0.62 tff(471,plain,
% 0.44/0.62 (((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) | r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(472,plain,
% 0.44/0.62 ((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))),
% 0.44/0.62 inference(unit_resolution,[status(thm)],[471, 470])).
% 0.44/0.62 tff(473,plain,
% 0.44/0.62 ((((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)) | (~((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1)))) | (~r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))),
% 0.44/0.62 inference(tautology,[status(thm)],[])).
% 0.44/0.62 tff(474,plain,
% 0.44/0.62 ((((~r2_hidden(tptp_fun_C_2(B!1, A!0), B!1)) | (~r2_hidden(k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), B!1))) <=> r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)) | (~r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1))),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[473, 472])).
% 0.44/0.63 tff(475,plain,
% 0.44/0.63 (~r2_hidden(k4_lattices(A!0, k3_lattices(A!0, tptp_fun_C_2(B!1, A!0), tptp_fun_D_3(B!1, A!0)), tptp_fun_C_2(B!1, A!0)), B!1)),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[474, 445])).
% 0.44/0.63 tff(476,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[475, 403])).
% 0.44/0.63 % SZS output end Proof
% 0.44/0.63 % E exiting
%------------------------------------------------------------------------------