%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT298+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:14:14 AM UTC 2025
% Result : Theorem 53.33s 53.53s
% Output : Proof 53.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : LAT298+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 20:09:49 EDT 2025
% 0.12/0.35 % CPUTime :
% 53.33/53.53 % SZS status Theorem
% 53.33/53.53 % SZS output start Proof
% 53.33/53.53 tff(r2_hidden_type, type, (
% 53.33/53.53 r2_hidden: ( $i * $i ) > $o)).
% 53.33/53.53 tff(tptp_fun_C_2_type, type, (
% 53.33/53.53 tptp_fun_C_2: $i)).
% 53.33/53.53 tff(k4_lattices_type, type, (
% 53.33/53.53 k4_lattices: ( $i * $i * $i ) > $i)).
% 53.33/53.53 tff(tptp_fun_C_3_type, type, (
% 53.33/53.53 tptp_fun_C_3: ( $i * $i ) > $i)).
% 53.33/53.53 tff(tptp_fun_B_1_type, type, (
% 53.33/53.53 tptp_fun_B_1: $i)).
% 53.33/53.53 tff(tptp_fun_D_4_type, type, (
% 53.33/53.53 tptp_fun_D_4: ( $i * $i ) > $i)).
% 53.33/53.53 tff(tptp_fun_A_0_type, type, (
% 53.33/53.53 tptp_fun_A_0: $i)).
% 53.33/53.53 tff(m1_subset_1_type, type, (
% 53.33/53.53 m1_subset_1: ( $i * $i ) > $o)).
% 53.33/53.53 tff(u1_struct_0_type, type, (
% 53.33/53.53 u1_struct_0: $i > $i)).
% 53.33/53.53 tff(m1_filter_0_type, type, (
% 53.33/53.53 m1_filter_0: ( $i * $i ) > $o)).
% 53.33/53.53 tff(k1_zfmisc_1_type, type, (
% 53.33/53.53 k1_zfmisc_1: $i > $i)).
% 53.33/53.53 tff(u1_lattices_type, type, (
% 53.33/53.53 u1_lattices: $i > $i)).
% 53.33/53.53 tff(u2_lattices_type, type, (
% 53.33/53.53 u2_lattices: $i > $i)).
% 53.33/53.53 tff(g3_lattices_type, type, (
% 53.33/53.53 g3_lattices: ( $i * $i * $i ) > $i)).
% 53.33/53.53 tff(l3_lattices_type, type, (
% 53.33/53.53 l3_lattices: $i > $o)).
% 53.33/53.53 tff(v10_lattices_type, type, (
% 53.33/53.53 v10_lattices: $i > $o)).
% 53.33/53.53 tff(v3_struct_0_type, type, (
% 53.33/53.53 v3_struct_0: $i > $o)).
% 53.33/53.53 tff(m1_filter_2_type, type, (
% 53.33/53.53 m1_filter_2: ( $i * $i ) > $o)).
% 53.33/53.53 tff(m1_relset_1_type, type, (
% 53.33/53.53 m1_relset_1: ( $i * $i * $i ) > $o)).
% 53.33/53.53 tff(k2_zfmisc_1_type, type, (
% 53.33/53.53 k2_zfmisc_1: ( $i * $i ) > $i)).
% 53.33/53.53 tff(m2_relset_1_type, type, (
% 53.33/53.53 m2_relset_1: ( $i * $i * $i ) > $o)).
% 53.33/53.53 tff(v1_funct_2_type, type, (
% 53.33/53.53 v1_funct_2: ( $i * $i * $i ) > $o)).
% 53.33/53.53 tff(v1_funct_1_type, type, (
% 53.33/53.53 v1_funct_1: $i > $o)).
% 53.33/53.53 tff(l2_lattices_type, type, (
% 53.33/53.53 l2_lattices: $i > $o)).
% 53.33/53.53 tff(l1_lattices_type, type, (
% 53.33/53.53 l1_lattices: $i > $o)).
% 53.33/53.53 tff(m2_lattice4_type, type, (
% 53.33/53.53 m2_lattice4: ( $i * $i ) > $o)).
% 53.33/53.53 tff(v1_xboole_0_type, type, (
% 53.33/53.53 v1_xboole_0: $i > $o)).
% 53.33/53.53 tff(v6_lattices_type, type, (
% 53.33/53.53 v6_lattices: $i > $o)).
% 53.33/53.53 tff(v9_lattices_type, type, (
% 53.33/53.53 v9_lattices: $i > $o)).
% 53.33/53.53 tff(v8_lattices_type, type, (
% 53.33/53.53 v8_lattices: $i > $o)).
% 53.33/53.53 tff(v7_lattices_type, type, (
% 53.33/53.53 v7_lattices: $i > $o)).
% 53.33/53.53 tff(v5_lattices_type, type, (
% 53.33/53.53 v5_lattices: $i > $o)).
% 53.33/53.53 tff(v4_lattices_type, type, (
% 53.33/53.53 v4_lattices: $i > $o)).
% 53.33/53.53 tff(k2_lattices_type, type, (
% 53.33/53.53 k2_lattices: ( $i * $i * $i ) > $i)).
% 53.33/53.53 tff(k2_binop_1_type, type, (
% 53.33/53.53 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 53.33/53.53 tff(1,plain,
% 53.33/53.53 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(2,plain,
% 53.33/53.53 (((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))) <=> ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(3,plain,
% 53.33/53.53 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))),
% 53.33/53.53 inference(monotonicity,[status(thm)],[2])).
% 53.33/53.53 tff(4,plain,
% 53.33/53.53 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1))),
% 53.33/53.53 inference(transitivity,[status(thm)],[3, 1])).
% 53.33/53.53 tff(5,plain,
% 53.33/53.53 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(6,plain,
% 53.33/53.53 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_filter_2(C, A) => m1_filter_2(C, B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B))))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(7,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((~v3_struct_0(B)) & v10_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_filter_2(C, A) => m1_filter_2(C, B)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t16_filter_2')).
% 53.33/53.53 tff(8,plain,
% 53.33/53.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[7, 6])).
% 53.33/53.53 tff(9,plain,
% 53.33/53.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[8, 5])).
% 53.33/53.53 tff(10,plain,
% 53.33/53.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[9, 5])).
% 53.33/53.53 tff(11,plain,
% 53.33/53.53 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_filter_2(C, A)) | m1_filter_2(C, B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & l3_lattices(B)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[10, 5])).
% 53.33/53.53 tff(12,plain,
% 53.33/53.53 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & l3_lattices(B!1)),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[11, 4])).
% 53.33/53.53 tff(13,plain,
% 53.33/53.53 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 53.33/53.53 inference(and_elim,[status(thm)],[12])).
% 53.33/53.53 tff(14,plain,
% 53.33/53.53 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 53.33/53.53 inference(symmetry,[status(thm)],[13])).
% 53.33/53.53 tff(15,plain,
% 53.33/53.53 (^[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)))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(16,plain,
% 53.33/53.53 (![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))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[15])).
% 53.33/53.53 tff(17,plain,
% 53.33/53.53 (![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))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(18,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 53.33/53.53 tff(19,plain,
% 53.33/53.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[18, 17])).
% 53.33/53.53 tff(20,plain,(
% 53.33/53.53 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.33/53.53 inference(skolemize,[status(sab)],[19])).
% 53.33/53.53 tff(21,plain,
% 53.33/53.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[20, 16])).
% 53.33/53.53 tff(22,plain,
% 53.33/53.53 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 53.33/53.53 inference(quant_inst,[status(thm)],[])).
% 53.33/53.53 tff(23,plain,
% 53.33/53.53 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[22, 21])).
% 53.33/53.53 tff(24,plain,
% 53.33/53.53 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(25,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[24])).
% 53.33/53.53 tff(26,plain,
% 53.33/53.53 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(27,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[26])).
% 53.33/53.53 tff(28,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(29,plain,
% 53.33/53.53 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(30,plain,
% 53.33/53.53 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[29])).
% 53.33/53.53 tff(31,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 53.33/53.53 tff(32,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[31, 30])).
% 53.33/53.53 tff(33,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[32, 28])).
% 53.33/53.53 tff(34,plain,(
% 53.33/53.53 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 53.33/53.53 inference(skolemize,[status(sab)],[33])).
% 53.33/53.53 tff(35,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[34, 27])).
% 53.33/53.53 tff(36,plain,
% 53.33/53.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[35, 25])).
% 53.33/53.53 tff(37,plain,
% 53.33/53.53 (l3_lattices(B!1)),
% 53.33/53.53 inference(and_elim,[status(thm)],[12])).
% 53.33/53.53 tff(38,plain,
% 53.33/53.53 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(39,plain,
% 53.33/53.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 53.33/53.53 inference(quant_inst,[status(thm)],[])).
% 53.33/53.53 tff(40,plain,
% 53.33/53.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[39, 38])).
% 53.33/53.53 tff(41,plain,
% 53.33/53.53 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[40, 37, 36])).
% 53.33/53.53 tff(42,plain,
% 53.33/53.53 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 53.33/53.53 inference(tautology,[status(thm)],[])).
% 53.33/53.53 tff(43,plain,
% 53.33/53.53 (l2_lattices(B!1)),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[42, 41])).
% 53.33/53.53 tff(44,plain,
% 53.33/53.53 (^[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)))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(45,plain,
% 53.33/53.53 (![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))))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[44])).
% 53.33/53.53 tff(46,plain,
% 53.33/53.53 (^[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)))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(47,plain,
% 53.33/53.53 (![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))))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[46])).
% 53.33/53.53 tff(48,plain,
% 53.33/53.53 (![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))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(49,plain,
% 53.33/53.53 (^[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))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(50,plain,
% 53.33/53.53 (![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))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[49])).
% 53.33/53.53 tff(51,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 53.33/53.53 tff(52,plain,
% 53.33/53.53 (![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))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[51, 50])).
% 53.33/53.53 tff(53,plain,
% 53.33/53.53 (![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))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[52, 48])).
% 53.33/53.53 tff(54,plain,(
% 53.33/53.53 ![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))))),
% 53.33/53.53 inference(skolemize,[status(sab)],[53])).
% 53.33/53.53 tff(55,plain,
% 53.33/53.53 (![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))))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[54, 47])).
% 53.33/53.53 tff(56,plain,
% 53.33/53.53 (![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))))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[55, 45])).
% 53.33/53.53 tff(57,plain,
% 53.33/53.53 (((~![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(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![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(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(58,plain,
% 53.33/53.53 ((~![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(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 53.33/53.53 inference(quant_inst,[status(thm)],[])).
% 53.33/53.53 tff(59,plain,
% 53.33/53.53 ((~![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(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[58, 57])).
% 53.33/53.53 tff(60,plain,
% 53.33/53.53 ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[59, 56])).
% 53.33/53.53 tff(61,plain,
% 53.33/53.53 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[60, 43])).
% 53.33/53.53 tff(62,plain,
% 53.33/53.53 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(tautology,[status(thm)],[])).
% 53.33/53.53 tff(63,plain,
% 53.33/53.53 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[62, 61])).
% 53.33/53.53 tff(64,plain,
% 53.33/53.53 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(tautology,[status(thm)],[])).
% 53.33/53.53 tff(65,plain,
% 53.33/53.53 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[64, 63])).
% 53.33/53.53 tff(66,plain,
% 53.33/53.53 (m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[65, 23])).
% 53.33/53.53 tff(67,plain,
% 53.33/53.53 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 53.33/53.53 inference(tautology,[status(thm)],[])).
% 53.33/53.53 tff(68,plain,
% 53.33/53.53 (l1_lattices(B!1)),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[67, 41])).
% 53.33/53.53 tff(69,plain,
% 53.33/53.53 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(70,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[69])).
% 53.33/53.53 tff(71,plain,
% 53.33/53.53 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(72,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[71])).
% 53.33/53.53 tff(73,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(74,plain,
% 53.33/53.53 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.33/53.53 inference(bind,[status(th)],[])).
% 53.33/53.53 tff(75,plain,
% 53.33/53.53 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.33/53.53 inference(quant_intro,[status(thm)],[74])).
% 53.33/53.53 tff(76,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 53.33/53.53 tff(77,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[76, 75])).
% 53.33/53.53 tff(78,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[77, 73])).
% 53.33/53.53 tff(79,plain,(
% 53.33/53.53 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 53.33/53.53 inference(skolemize,[status(sab)],[78])).
% 53.33/53.53 tff(80,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[79, 72])).
% 53.33/53.53 tff(81,plain,
% 53.33/53.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[80, 70])).
% 53.33/53.53 tff(82,plain,
% 53.33/53.53 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 53.33/53.53 inference(rewrite,[status(thm)],[])).
% 53.33/53.53 tff(83,plain,
% 53.33/53.53 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 53.33/53.53 inference(quant_inst,[status(thm)],[])).
% 53.33/53.53 tff(84,plain,
% 53.33/53.53 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 53.33/53.53 inference(modus_ponens,[status(thm)],[83, 82])).
% 53.33/53.53 tff(85,plain,
% 53.33/53.53 ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[84, 81])).
% 53.33/53.53 tff(86,plain,
% 53.33/53.53 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 53.33/53.53 inference(unit_resolution,[status(thm)],[85, 68])).
% 53.33/53.54 tff(87,plain,
% 53.33/53.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(88,plain,
% 53.33/53.54 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[87, 86])).
% 53.33/53.54 tff(89,plain,
% 53.33/53.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(90,plain,
% 53.33/53.54 (v1_funct_1(u1_lattices(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[89, 86])).
% 53.33/53.54 tff(91,plain,
% 53.33/53.54 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(92,plain,
% 53.33/53.54 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[91, 61])).
% 53.33/53.54 tff(93,plain,
% 53.33/53.54 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(94,plain,
% 53.33/53.54 (v1_funct_1(u2_lattices(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[93, 61])).
% 53.33/53.54 tff(95,plain,
% 53.33/53.54 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 53.33/53.54 inference(quant_inst,[status(thm)],[])).
% 53.33/53.54 tff(96,plain,
% 53.33/53.54 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[95, 21])).
% 53.33/53.54 tff(97,plain,
% 53.33/53.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(98,plain,
% 53.33/53.54 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[97, 86])).
% 53.33/53.54 tff(99,plain,
% 53.33/53.54 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(100,plain,
% 53.33/53.54 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[99, 98])).
% 53.33/53.54 tff(101,plain,
% 53.33/53.54 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[100, 96])).
% 53.33/53.54 tff(102,plain,
% 53.33/53.54 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 53.33/53.54 inference(bind,[status(th)],[])).
% 53.33/53.54 tff(103,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(quant_intro,[status(thm)],[102])).
% 53.33/53.54 tff(104,plain,
% 53.33/53.54 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 53.33/53.54 inference(bind,[status(th)],[])).
% 53.33/53.54 tff(105,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(quant_intro,[status(thm)],[104])).
% 53.33/53.54 tff(106,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(transitivity,[status(thm)],[105, 103])).
% 53.33/53.54 tff(107,plain,
% 53.33/53.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 53.33/53.54 inference(bind,[status(th)],[])).
% 53.33/53.54 tff(108,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(quant_intro,[status(thm)],[107])).
% 53.33/53.54 tff(109,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.33/53.54 inference(rewrite,[status(thm)],[])).
% 53.33/53.54 tff(110,plain,
% 53.33/53.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 53.33/53.54 inference(bind,[status(th)],[])).
% 53.33/53.54 tff(111,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.33/53.54 inference(quant_intro,[status(thm)],[110])).
% 53.33/53.54 tff(112,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 53.33/53.54 tff(113,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[112, 111])).
% 53.33/53.54 tff(114,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[113, 109])).
% 53.33/53.54 tff(115,plain,(
% 53.33/53.54 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 53.33/53.54 inference(skolemize,[status(sab)],[114])).
% 53.33/53.54 tff(116,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[115, 108])).
% 53.33/53.54 tff(117,plain,
% 53.33/53.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[116, 106])).
% 53.33/53.54 tff(118,plain,
% 53.33/53.54 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 53.33/53.54 inference(rewrite,[status(thm)],[])).
% 53.33/53.54 tff(119,plain,
% 53.33/53.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 53.33/53.54 inference(rewrite,[status(thm)],[])).
% 53.33/53.54 tff(120,plain,
% 53.33/53.54 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 53.33/53.54 inference(monotonicity,[status(thm)],[119])).
% 53.33/53.54 tff(121,plain,
% 53.33/53.54 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 53.33/53.54 inference(transitivity,[status(thm)],[120, 118])).
% 53.33/53.54 tff(122,plain,
% 53.33/53.54 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 53.33/53.54 inference(quant_inst,[status(thm)],[])).
% 53.33/53.54 tff(123,plain,
% 53.33/53.54 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[122, 121])).
% 53.33/53.54 tff(124,plain,
% 53.33/53.54 ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[123, 117])).
% 53.33/53.54 tff(125,plain,
% 53.33/53.54 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[124, 101, 94, 92, 90, 88, 66])).
% 53.33/53.54 tff(126,plain,
% 53.33/53.54 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 53.33/53.54 inference(rewrite,[status(thm)],[])).
% 53.33/53.54 tff(127,plain,
% 53.33/53.54 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 53.33/53.54 inference(quant_inst,[status(thm)],[])).
% 53.33/53.54 tff(128,plain,
% 53.33/53.54 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))))),
% 53.33/53.54 inference(modus_ponens,[status(thm)],[127, 126])).
% 53.33/53.54 tff(129,plain,
% 53.33/53.54 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[128, 125, 14])).
% 53.33/53.54 tff(130,plain,
% 53.33/53.54 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_struct_0(B!1) = u1_struct_0(A!0))),
% 53.33/53.54 inference(tautology,[status(thm)],[])).
% 53.33/53.54 tff(131,plain,
% 53.33/53.54 (u1_struct_0(B!1) = u1_struct_0(A!0)),
% 53.33/53.54 inference(unit_resolution,[status(thm)],[130, 129])).
% 53.33/53.54 tff(132,plain,
% 53.33/53.54 (k1_zfmisc_1(u1_struct_0(B!1)) = k1_zfmisc_1(u1_struct_0(A!0))),
% 53.33/53.55 inference(monotonicity,[status(thm)],[131])).
% 53.33/53.55 tff(133,plain,
% 53.33/53.55 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 53.33/53.55 inference(monotonicity,[status(thm)],[132])).
% 53.33/53.55 tff(134,plain,
% 53.33/53.55 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 53.33/53.55 inference(symmetry,[status(thm)],[133])).
% 53.33/53.55 tff(135,plain,
% 53.33/53.55 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(136,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[135])).
% 53.33/53.55 tff(137,plain,
% 53.33/53.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(138,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[137])).
% 53.33/53.55 tff(139,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(transitivity,[status(thm)],[138, 136])).
% 53.33/53.55 tff(140,plain,
% 53.33/53.55 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(141,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[140])).
% 53.33/53.55 tff(142,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(143,plain,
% 53.33/53.55 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(144,plain,
% 53.33/53.55 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[143])).
% 53.33/53.55 tff(145,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m1_filter_2')).
% 53.33/53.55 tff(146,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[145, 144])).
% 53.33/53.55 tff(147,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[146, 142])).
% 53.33/53.55 tff(148,plain,(
% 53.33/53.55 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 53.33/53.55 inference(skolemize,[status(sab)],[147])).
% 53.33/53.55 tff(149,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[148, 141])).
% 53.33/53.55 tff(150,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[149, 139])).
% 53.33/53.55 tff(151,plain,
% 53.33/53.55 (l3_lattices(A!0)),
% 53.33/53.55 inference(and_elim,[status(thm)],[12])).
% 53.33/53.55 tff(152,plain,
% 53.33/53.55 (v10_lattices(A!0)),
% 53.33/53.55 inference(and_elim,[status(thm)],[12])).
% 53.33/53.55 tff(153,plain,
% 53.33/53.55 (~v3_struct_0(A!0)),
% 53.33/53.55 inference(and_elim,[status(thm)],[12])).
% 53.33/53.55 tff(154,plain,
% 53.33/53.55 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(155,plain,
% 53.33/53.55 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 53.33/53.55 inference(quant_inst,[status(thm)],[])).
% 53.33/53.55 tff(156,plain,
% 53.33/53.55 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[155, 154])).
% 53.33/53.55 tff(157,plain,
% 53.33/53.55 (![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[156, 153, 152, 151, 150])).
% 53.33/53.55 tff(158,plain,
% 53.33/53.55 (~((~m1_filter_2(C!2, A!0)) | m1_filter_2(C!2, B!1))),
% 53.33/53.55 inference(and_elim,[status(thm)],[12])).
% 53.33/53.55 tff(159,plain,
% 53.33/53.55 (m1_filter_2(C!2, A!0)),
% 53.33/53.55 inference(or_elim,[status(thm)],[158])).
% 53.33/53.55 tff(160,plain,
% 53.33/53.55 (((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))) <=> ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(161,plain,
% 53.33/53.55 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))))),
% 53.33/53.55 inference(quant_inst,[status(thm)],[])).
% 53.33/53.55 tff(162,plain,
% 53.33/53.55 ((~![B: $i] : ((~m1_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m1_filter_2(C!2, A!0)) | (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[161, 160])).
% 53.33/53.55 tff(163,plain,
% 53.33/53.55 (~(v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0)))),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[162, 159, 157])).
% 53.33/53.55 tff(164,plain,
% 53.33/53.55 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | m2_lattice4(C!2, A!0)),
% 53.33/53.55 inference(tautology,[status(thm)],[])).
% 53.33/53.55 tff(165,plain,
% 53.33/53.55 (m2_lattice4(C!2, A!0)),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[164, 163])).
% 53.33/53.55 tff(166,plain,
% 53.33/53.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(167,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[166])).
% 53.33/53.55 tff(168,plain,
% 53.33/53.55 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(169,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[168])).
% 53.33/53.55 tff(170,plain,
% 53.33/53.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(171,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[170])).
% 53.33/53.55 tff(172,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(transitivity,[status(thm)],[171, 169])).
% 53.33/53.55 tff(173,plain,
% 53.33/53.55 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(174,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[173])).
% 53.33/53.55 tff(175,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(176,plain,
% 53.33/53.55 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(177,plain,
% 53.33/53.55 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[176])).
% 53.33/53.55 tff(178,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 53.33/53.55 tff(179,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[178, 177])).
% 53.33/53.55 tff(180,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[179, 175])).
% 53.33/53.55 tff(181,plain,(
% 53.33/53.55 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(skolemize,[status(sab)],[180])).
% 53.33/53.55 tff(182,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[181, 174])).
% 53.33/53.55 tff(183,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[182, 172])).
% 53.33/53.55 tff(184,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[183, 167])).
% 53.33/53.55 tff(185,plain,
% 53.33/53.55 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(186,plain,
% 53.33/53.55 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 53.33/53.55 inference(quant_inst,[status(thm)],[])).
% 53.33/53.55 tff(187,plain,
% 53.33/53.55 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[186, 185])).
% 53.33/53.55 tff(188,plain,
% 53.33/53.55 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[187, 153, 152, 151, 184])).
% 53.33/53.55 tff(189,plain,
% 53.33/53.55 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(190,plain,
% 53.33/53.55 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0))))),
% 53.33/53.55 inference(quant_inst,[status(thm)],[])).
% 53.33/53.55 tff(191,plain,
% 53.33/53.55 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(C!2, A!0)) | m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[190, 189])).
% 53.33/53.55 tff(192,plain,
% 53.33/53.55 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[191, 188, 165])).
% 53.33/53.55 tff(193,plain,
% 53.33/53.55 (m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))),
% 53.33/53.55 inference(modus_ponens,[status(thm)],[192, 134])).
% 53.33/53.55 tff(194,plain,
% 53.33/53.55 ((v1_xboole_0(C!2) | (~m2_lattice4(C!2, A!0))) | (~v1_xboole_0(C!2))),
% 53.33/53.55 inference(tautology,[status(thm)],[])).
% 53.33/53.55 tff(195,plain,
% 53.33/53.55 (~v1_xboole_0(C!2)),
% 53.33/53.55 inference(unit_resolution,[status(thm)],[194, 163])).
% 53.33/53.55 tff(196,plain,
% 53.33/53.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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))))))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(197,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[196])).
% 53.33/53.55 tff(198,plain,
% 53.33/53.55 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(199,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[198])).
% 53.33/53.55 tff(200,plain,
% 53.33/53.55 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(201,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[200])).
% 53.33/53.55 tff(202,plain,
% 53.33/53.55 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.55 inference(transitivity,[status(thm)],[201, 199])).
% 53.33/53.55 tff(203,plain,
% 53.33/53.55 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), rewrite((~(~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), trans(monotonicity(rewrite(((~m1_filter_0(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_filter_0(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))))))), trans(monotonicity(trans(monotonicity(rewrite((~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))) <=> (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))), ((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))), rewrite((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))), ((m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))) <=> (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))), ((m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))), rewrite((m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))), ((m1_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))) <=> (m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))), ((((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) <=> (((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))), rewrite((((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) <=> (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))), ((((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) <=> (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> ((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))), rewrite(((v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))), (((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))))), (![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))) <=> ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(204,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[203])).
% 53.33/53.55 tff(205,plain,
% 53.33/53.55 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))),
% 53.33/53.55 inference(rewrite,[status(thm)],[])).
% 53.33/53.55 tff(206,plain,
% 53.33/53.55 (^[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((m1_filter_0(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_filter_0(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)))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))) <=> (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))))), rewrite((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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))))))), ((((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))) <=> ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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))))))))), (![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))) <=> ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))))),
% 53.33/53.55 inference(bind,[status(th)],[])).
% 53.33/53.55 tff(207,plain,
% 53.33/53.55 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))),
% 53.33/53.55 inference(quant_intro,[status(thm)],[206])).
% 53.33/53.55 tff(208,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) => (m1_filter_0(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)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d1_filter_0')).
% 53.33/53.56 tff(209,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[208, 207])).
% 53.33/53.56 tff(210,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (m1_filter_0(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)))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[209, 205])).
% 53.33/53.56 tff(211,plain,(
% 53.33/53.56 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) | (((~m1_filter_0(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_filter_0(B, A) | (m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A)) & (~((~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | ((r2_hidden(tptp_fun_C_3(B, A), B) & r2_hidden(tptp_fun_D_4(B, A), B)) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))),
% 53.33/53.56 inference(skolemize,[status(sab)],[210])).
% 53.33/53.56 tff(212,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[211, 204])).
% 53.33/53.56 tff(213,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~((~m1_filter_0(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_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B)))))))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[212, 202])).
% 53.33/53.56 tff(214,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[213, 197])).
% 53.33/53.56 tff(215,plain,
% 53.33/53.56 (v10_lattices(B!1)),
% 53.33/53.56 inference(and_elim,[status(thm)],[12])).
% 53.33/53.56 tff(216,plain,
% 53.33/53.56 (~v3_struct_0(B!1)),
% 53.33/53.56 inference(and_elim,[status(thm)],[12])).
% 53.33/53.56 tff(217,plain,
% 53.33/53.56 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))))),
% 53.33/53.56 inference(rewrite,[status(thm)],[])).
% 53.33/53.56 tff(218,plain,
% 53.33/53.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B)))))))))))),
% 53.33/53.56 inference(quant_inst,[status(thm)],[])).
% 53.33/53.56 tff(219,plain,
% 53.33/53.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[218, 217])).
% 53.33/53.56 tff(220,plain,
% 53.33/53.56 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[219, 216, 215, 37, 214])).
% 53.33/53.56 tff(221,plain,
% 53.33/53.56 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))))),
% 53.33/53.56 inference(rewrite,[status(thm)],[])).
% 53.33/53.56 tff(222,plain,
% 53.33/53.56 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))))),
% 53.33/53.56 inference(quant_inst,[status(thm)],[])).
% 53.33/53.56 tff(223,plain,
% 53.33/53.56 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(B, B!1) | (~((~m1_subset_1(tptp_fun_C_3(B, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(B, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(B, B!1), B)) | (~r2_hidden(tptp_fun_D_4(B, B!1), B))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(B, B!1), tptp_fun_D_4(B, B!1)), B))))))) | (~((~m1_filter_0(B, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, B)) | (~r2_hidden(D, B))) <=> r2_hidden(k4_lattices(B!1, C, D), B))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[222, 221])).
% 53.33/53.56 tff(224,plain,
% 53.33/53.56 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(B!1)))) | (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[223, 220, 195])).
% 53.33/53.56 tff(225,plain,
% 53.33/53.56 (~((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2))))))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[224, 193])).
% 53.33/53.56 tff(226,plain,
% 53.33/53.56 (((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_filter_0(C!2, B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~(((~r2_hidden(C, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(B!1, C, D), C!2)))))))) | (m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))),
% 53.33/53.56 inference(tautology,[status(thm)],[])).
% 53.33/53.56 tff(227,plain,
% 53.33/53.56 (m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[226, 225])).
% 53.33/53.56 tff(228,plain,
% 53.33/53.56 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(229,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[228])).
% 53.33/53.56 tff(230,plain,
% 53.33/53.56 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(231,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[230])).
% 53.33/53.56 tff(232,plain,
% 53.33/53.56 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(233,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[232])).
% 53.33/53.56 tff(234,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(transitivity,[status(thm)],[233, 231])).
% 53.33/53.56 tff(235,plain,
% 53.33/53.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(236,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[235])).
% 53.33/53.56 tff(237,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(rewrite,[status(thm)],[])).
% 53.33/53.56 tff(238,plain,
% 53.33/53.56 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(239,plain,
% 53.33/53.56 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[238])).
% 53.33/53.56 tff(240,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 53.33/53.56 tff(241,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[240, 239])).
% 53.33/53.56 tff(242,plain,
% 53.33/53.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[241, 237])).
% 53.33/53.56 tff(243,plain,(
% 53.33/53.56 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(skolemize,[status(sab)],[242])).
% 53.33/53.56 tff(244,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[243, 236])).
% 53.33/53.56 tff(245,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[244, 234])).
% 53.33/53.56 tff(246,plain,
% 53.33/53.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[245, 229])).
% 53.33/53.56 tff(247,plain,
% 53.33/53.56 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 53.33/53.56 inference(rewrite,[status(thm)],[])).
% 53.33/53.56 tff(248,plain,
% 53.33/53.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1)))),
% 53.33/53.56 inference(quant_inst,[status(thm)],[])).
% 53.33/53.56 tff(249,plain,
% 53.33/53.56 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | ![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 53.33/53.56 inference(modus_ponens,[status(thm)],[248, 247])).
% 53.33/53.56 tff(250,plain,
% 53.33/53.56 (![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[249, 216, 215, 37, 246])).
% 53.33/53.56 tff(251,plain,
% 53.33/53.56 ((~![B: $i] : (m1_filter_2(B, B!1) <=> m1_filter_0(B, B!1))) | (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))),
% 53.33/53.56 inference(quant_inst,[status(thm)],[])).
% 53.33/53.56 tff(252,plain,
% 53.33/53.56 (m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1)),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[251, 250])).
% 53.33/53.56 tff(253,plain,
% 53.33/53.56 (~m1_filter_2(C!2, B!1)),
% 53.33/53.56 inference(or_elim,[status(thm)],[158])).
% 53.33/53.56 tff(254,plain,
% 53.33/53.56 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | m1_filter_2(C!2, B!1) | (~m1_filter_0(C!2, B!1))),
% 53.33/53.56 inference(tautology,[status(thm)],[])).
% 53.33/53.56 tff(255,plain,
% 53.33/53.56 ((~(m1_filter_2(C!2, B!1) <=> m1_filter_0(C!2, B!1))) | (~m1_filter_0(C!2, B!1))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[254, 253])).
% 53.33/53.56 tff(256,plain,
% 53.33/53.56 (~m1_filter_0(C!2, B!1)),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[255, 252])).
% 53.33/53.56 tff(257,plain,
% 53.33/53.56 ((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))),
% 53.33/53.56 inference(tautology,[status(thm)],[])).
% 53.33/53.56 tff(258,plain,
% 53.33/53.56 ((~(m1_filter_0(C!2, B!1) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))))) | (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[257, 256])).
% 53.33/53.56 tff(259,plain,
% 53.33/53.56 (~((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[258, 227])).
% 53.33/53.56 tff(260,plain,
% 53.33/53.56 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))) | m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 53.33/53.56 inference(tautology,[status(thm)],[])).
% 53.33/53.56 tff(261,plain,
% 53.33/53.56 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[260, 259])).
% 53.33/53.56 tff(262,plain,
% 53.33/53.56 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))) | m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 53.33/53.56 inference(tautology,[status(thm)],[])).
% 53.33/53.56 tff(263,plain,
% 53.33/53.56 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 53.33/53.56 inference(unit_resolution,[status(thm)],[262, 259])).
% 53.33/53.56 tff(264,plain,
% 53.33/53.56 (^[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))))),
% 53.33/53.56 inference(bind,[status(th)],[])).
% 53.33/53.56 tff(265,plain,
% 53.33/53.56 (![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)))),
% 53.33/53.56 inference(quant_intro,[status(thm)],[264])).
% 53.33/53.56 tff(266,plain,
% 53.33/53.56 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) <=> (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (v3_struct_0(A) | (~v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))))),
% 53.38/53.56 inference(bind,[status(th)],[])).
% 53.38/53.56 tff(267,plain,
% 53.38/53.56 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 53.38/53.56 inference(quant_intro,[status(thm)],[266])).
% 53.38/53.56 tff(268,plain,
% 53.38/53.56 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 53.38/53.56 inference(rewrite,[status(thm)],[])).
% 53.38/53.56 tff(269,plain,
% 53.38/53.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> (((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))), ((((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A)) => ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))), ((((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v10_lattices(A))) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))))),
% 53.38/53.56 inference(bind,[status(th)],[])).
% 53.38/53.56 tff(270,plain,
% 53.38/53.56 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 53.38/53.56 inference(quant_intro,[status(thm)],[269])).
% 53.38/53.56 tff(271,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/sandbox/benchmark/theBenchmark.p','cc1_lattices')).
% 53.38/53.56 tff(272,plain,
% 53.38/53.56 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 53.38/53.56 inference(modus_ponens,[status(thm)],[271, 270])).
% 53.38/53.56 tff(273,plain,
% 53.38/53.56 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 53.38/53.56 inference(modus_ponens,[status(thm)],[272, 268])).
% 53.38/53.56 tff(274,plain,(
% 53.38/53.56 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A))))),
% 53.38/53.57 inference(skolemize,[status(sab)],[273])).
% 53.38/53.57 tff(275,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[274, 267])).
% 53.38/53.57 tff(276,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[275, 265])).
% 53.38/53.57 tff(277,plain,
% 53.38/53.57 (((~![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(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))) <=> ((~![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(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(278,plain,
% 53.38/53.57 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1))) <=> (v3_struct_0(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(279,plain,
% 53.38/53.57 (((~![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(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))) <=> ((~![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(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))))))),
% 53.38/53.57 inference(monotonicity,[status(thm)],[278])).
% 53.38/53.57 tff(280,plain,
% 53.38/53.57 (((~![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(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))) <=> ((~![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(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))))),
% 53.38/53.57 inference(transitivity,[status(thm)],[279, 277])).
% 53.38/53.57 tff(281,plain,
% 53.38/53.57 ((~![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(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))) | (~v10_lattices(B!1)))),
% 53.38/53.57 inference(quant_inst,[status(thm)],[])).
% 53.38/53.57 tff(282,plain,
% 53.38/53.57 ((~![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(B!1) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[281, 280])).
% 53.38/53.57 tff(283,plain,
% 53.38/53.57 (~(v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1)))),
% 53.38/53.57 inference(unit_resolution,[status(thm)],[282, 216, 215, 37, 276])).
% 53.38/53.57 tff(284,plain,
% 53.38/53.57 ((v3_struct_0(B!1) | (~v4_lattices(B!1)) | (~v5_lattices(B!1)) | (~v6_lattices(B!1)) | (~v7_lattices(B!1)) | (~v8_lattices(B!1)) | (~v9_lattices(B!1))) | v6_lattices(B!1)),
% 53.38/53.57 inference(tautology,[status(thm)],[])).
% 53.38/53.57 tff(285,plain,
% 53.38/53.57 (v6_lattices(B!1)),
% 53.38/53.57 inference(unit_resolution,[status(thm)],[284, 283])).
% 53.38/53.57 tff(286,plain,
% 53.38/53.57 (^[A: $i, B: $i, C: $i] : refl(((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, 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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(287,plain,
% 53.38/53.57 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[286])).
% 53.38/53.57 tff(288,plain,
% 53.38/53.57 (^[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))) | (~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) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_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) | (~m1_subset_1(C, u1_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)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_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)))) | (k4_lattices(A, B, C) = k4_lattices(A, C, B))) <=> ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(289,plain,
% 53.38/53.57 (![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) = k4_lattices(A, C, B))) <=> ![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[288])).
% 53.38/53.57 tff(290,plain,
% 53.38/53.57 (![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) = 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)))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(291,plain,
% 53.38/53.57 (^[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) = 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)))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(292,plain,
% 53.38/53.57 (![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) = 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)))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[291])).
% 53.38/53.57 tff(293,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/sandbox/benchmark/theBenchmark.p','commutativity_k4_lattices')).
% 53.38/53.57 tff(294,plain,
% 53.38/53.57 (![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) = k4_lattices(A, C, B)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[293, 292])).
% 53.38/53.57 tff(295,plain,
% 53.38/53.57 (![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) = k4_lattices(A, C, B)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[294, 290])).
% 53.38/53.57 tff(296,plain,(
% 53.38/53.57 ![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) = k4_lattices(A, C, B)))),
% 53.38/53.57 inference(skolemize,[status(sab)],[295])).
% 53.38/53.57 tff(297,plain,
% 53.38/53.57 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[296, 289])).
% 53.38/53.57 tff(298,plain,
% 53.38/53.57 (![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[297, 287])).
% 53.38/53.57 tff(299,plain,
% 53.38/53.57 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(300,plain,
% 53.38/53.57 (((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(301,plain,
% 53.38/53.57 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 53.38/53.57 inference(monotonicity,[status(thm)],[300])).
% 53.38/53.57 tff(302,plain,
% 53.38/53.57 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(transitivity,[status(thm)],[301, 299])).
% 53.38/53.57 tff(303,plain,
% 53.38/53.57 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | v3_struct_0(B!1) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))),
% 53.38/53.57 inference(quant_inst,[status(thm)],[])).
% 53.38/53.57 tff(304,plain,
% 53.38/53.57 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[303, 302])).
% 53.38/53.57 tff(305,plain,
% 53.38/53.57 (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.57 inference(unit_resolution,[status(thm)],[304, 216, 298, 68, 285, 263, 261])).
% 53.38/53.57 tff(306,plain,
% 53.38/53.57 (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 53.38/53.57 inference(symmetry,[status(thm)],[305])).
% 53.38/53.57 tff(307,plain,
% 53.38/53.57 (^[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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(308,plain,
% 53.38/53.57 (![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[307])).
% 53.38/53.57 tff(309,plain,
% 53.38/53.57 (^[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))) | (~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) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_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) | (~m1_subset_1(C, u1_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)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, 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))) | (~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)))) | (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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(310,plain,
% 53.38/53.57 (![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[309])).
% 53.38/53.57 tff(311,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(312,plain,
% 53.38/53.57 (^[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)))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(313,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[312])).
% 53.38/53.57 tff(314,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/sandbox/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 53.38/53.57 tff(315,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[314, 313])).
% 53.38/53.57 tff(316,plain,
% 53.38/53.57 (![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)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[315, 311])).
% 53.38/53.57 tff(317,plain,(
% 53.38/53.57 ![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)))),
% 53.38/53.57 inference(skolemize,[status(sab)],[316])).
% 53.38/53.57 tff(318,plain,
% 53.38/53.57 (![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[317, 310])).
% 53.38/53.57 tff(319,plain,
% 53.38/53.57 (![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[318, 308])).
% 53.38/53.57 tff(320,plain,
% 53.38/53.57 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(321,plain,
% 53.38/53.57 ((v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(rewrite,[status(thm)],[])).
% 53.38/53.57 tff(322,plain,
% 53.38/53.57 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 53.38/53.57 inference(monotonicity,[status(thm)],[321])).
% 53.38/53.57 tff(323,plain,
% 53.38/53.57 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.57 inference(transitivity,[status(thm)],[322, 320])).
% 53.38/53.57 tff(324,plain,
% 53.38/53.57 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))))),
% 53.38/53.57 inference(quant_inst,[status(thm)],[])).
% 53.38/53.57 tff(325,plain,
% 53.38/53.57 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 53.38/53.57 inference(modus_ponens,[status(thm)],[324, 323])).
% 53.38/53.57 tff(326,plain,
% 53.38/53.57 (k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.57 inference(unit_resolution,[status(thm)],[325, 216, 319, 68, 285, 263, 261])).
% 53.38/53.57 tff(327,plain,
% 53.38/53.57 (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.57 inference(symmetry,[status(thm)],[326])).
% 53.38/53.57 tff(328,plain,
% 53.38/53.57 (^[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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(329,plain,
% 53.38/53.57 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[328])).
% 53.38/53.57 tff(330,plain,
% 53.38/53.57 (^[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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(331,plain,
% 53.38/53.57 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[330])).
% 53.38/53.57 tff(332,plain,
% 53.38/53.57 (^[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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(333,plain,
% 53.38/53.57 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[332])).
% 53.38/53.57 tff(334,plain,
% 53.38/53.57 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.57 inference(transitivity,[status(thm)],[333, 331])).
% 53.38/53.57 tff(335,plain,
% 53.38/53.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))))),
% 53.38/53.57 inference(bind,[status(th)],[])).
% 53.38/53.57 tff(336,plain,
% 53.38/53.57 (![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.57 inference(quant_intro,[status(thm)],[335])).
% 53.38/53.57 tff(337,plain,
% 53.38/53.57 (![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(338,plain,
% 53.38/53.58 (^[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)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))))),
% 53.38/53.58 inference(bind,[status(th)],[])).
% 53.38/53.58 tff(339,plain,
% 53.38/53.58 (![A: $i] : (((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(quant_intro,[status(thm)],[338])).
% 53.38/53.58 tff(340,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattices')).
% 53.38/53.58 tff(341,plain,
% 53.38/53.58 (![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[340, 339])).
% 53.38/53.58 tff(342,plain,
% 53.38/53.58 (![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[341, 337])).
% 53.38/53.58 tff(343,plain,(
% 53.38/53.58 ![A: $i] : ((~((~v3_struct_0(A)) & l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(skolemize,[status(sab)],[342])).
% 53.38/53.58 tff(344,plain,
% 53.38/53.58 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[343, 336])).
% 53.38/53.58 tff(345,plain,
% 53.38/53.58 (![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))) | (k2_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))) | (~l1_lattices(A)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[344, 334])).
% 53.38/53.58 tff(346,plain,
% 53.38/53.58 (![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[345, 329])).
% 53.38/53.58 tff(347,plain,
% 53.38/53.58 (((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(348,plain,
% 53.38/53.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C)))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(349,plain,
% 53.38/53.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[348, 347])).
% 53.38/53.58 tff(350,plain,
% 53.38/53.58 ((~l1_lattices(B!1)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[349, 216, 346])).
% 53.38/53.58 tff(351,plain,
% 53.38/53.58 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[350, 68])).
% 53.38/53.58 tff(352,plain,
% 53.38/53.58 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(353,plain,
% 53.38/53.58 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(354,plain,
% 53.38/53.58 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, B, C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[353, 352])).
% 53.38/53.58 tff(355,plain,
% 53.38/53.58 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[354, 351, 261])).
% 53.38/53.58 tff(356,plain,
% 53.38/53.58 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(357,plain,
% 53.38/53.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(358,plain,
% 53.38/53.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[357, 356])).
% 53.38/53.58 tff(359,plain,
% 53.38/53.58 (k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[358, 263, 355])).
% 53.38/53.58 tff(360,plain,
% 53.38/53.58 (k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(B!1, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.58 inference(symmetry,[status(thm)],[359])).
% 53.38/53.58 tff(361,plain,
% 53.38/53.58 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_lattices(B!1) = u1_lattices(A!0))),
% 53.38/53.58 inference(tautology,[status(thm)],[])).
% 53.38/53.58 tff(362,plain,
% 53.38/53.58 (u1_lattices(B!1) = u1_lattices(A!0)),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[361, 129])).
% 53.38/53.58 tff(363,plain,
% 53.38/53.58 (u1_lattices(A!0) = u1_lattices(B!1)),
% 53.38/53.58 inference(symmetry,[status(thm)],[362])).
% 53.38/53.58 tff(364,plain,
% 53.38/53.58 (u1_struct_0(A!0) = u1_struct_0(B!1)),
% 53.38/53.58 inference(symmetry,[status(thm)],[131])).
% 53.38/53.58 tff(365,plain,
% 53.38/53.58 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.58 inference(monotonicity,[status(thm)],[364, 364, 364, 363])).
% 53.38/53.58 tff(366,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0)) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))),
% 53.38/53.58 inference(monotonicity,[status(thm)],[364])).
% 53.38/53.58 tff(367,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)) <=> m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))),
% 53.38/53.58 inference(symmetry,[status(thm)],[366])).
% 53.38/53.58 tff(368,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[263, 367])).
% 53.38/53.58 tff(369,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0)) <=> m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))),
% 53.38/53.58 inference(monotonicity,[status(thm)],[364])).
% 53.38/53.58 tff(370,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1)) <=> m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))),
% 53.38/53.58 inference(symmetry,[status(thm)],[369])).
% 53.38/53.58 tff(371,plain,
% 53.38/53.58 (m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[261, 370])).
% 53.38/53.58 tff(372,plain,
% 53.38/53.58 (((~![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)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(373,plain,
% 53.38/53.58 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(374,plain,
% 53.38/53.58 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[373, 372])).
% 53.38/53.58 tff(375,plain,
% 53.38/53.58 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[374, 151, 36])).
% 53.38/53.58 tff(376,plain,
% 53.38/53.58 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 53.38/53.58 inference(tautology,[status(thm)],[])).
% 53.38/53.58 tff(377,plain,
% 53.38/53.58 (l1_lattices(A!0)),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[376, 375])).
% 53.38/53.58 tff(378,plain,
% 53.38/53.58 (((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(379,plain,
% 53.38/53.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l1_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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C)))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(380,plain,
% 53.38/53.58 ((~![A: $i] : (v3_struct_0(A) | (~l1_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, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u1_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l1_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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[379, 378])).
% 53.38/53.58 tff(381,plain,
% 53.38/53.58 ((~l1_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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[380, 153, 346])).
% 53.38/53.58 tff(382,plain,
% 53.38/53.58 (![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[381, 377])).
% 53.38/53.58 tff(383,plain,
% 53.38/53.58 (((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))) <=> ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(384,plain,
% 53.38/53.58 ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(385,plain,
% 53.38/53.58 ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[384, 383])).
% 53.38/53.58 tff(386,plain,
% 53.38/53.58 ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[385, 382])).
% 53.38/53.58 tff(387,plain,
% 53.38/53.58 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[386, 371])).
% 53.38/53.58 tff(388,plain,
% 53.38/53.58 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(389,plain,
% 53.38/53.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(390,plain,
% 53.38/53.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), C)))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[389, 388])).
% 53.38/53.58 tff(391,plain,
% 53.38/53.58 (k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[390, 387, 368])).
% 53.38/53.58 tff(392,plain,
% 53.38/53.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(393,plain,
% 53.38/53.58 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 53.38/53.58 inference(rewrite,[status(thm)],[])).
% 53.38/53.58 tff(394,plain,
% 53.38/53.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))))),
% 53.38/53.58 inference(monotonicity,[status(thm)],[393])).
% 53.38/53.58 tff(395,plain,
% 53.38/53.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))))),
% 53.38/53.58 inference(transitivity,[status(thm)],[394, 392])).
% 53.38/53.58 tff(396,plain,
% 53.38/53.58 ((~![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)))),
% 53.38/53.58 inference(quant_inst,[status(thm)],[])).
% 53.38/53.58 tff(397,plain,
% 53.38/53.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))))),
% 53.38/53.58 inference(modus_ponens,[status(thm)],[396, 395])).
% 53.38/53.58 tff(398,plain,
% 53.38/53.58 (~(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)))),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[397, 153, 152, 151, 276])).
% 53.38/53.58 tff(399,plain,
% 53.38/53.58 ((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))) | v6_lattices(A!0)),
% 53.38/53.58 inference(tautology,[status(thm)],[])).
% 53.38/53.58 tff(400,plain,
% 53.38/53.58 (v6_lattices(A!0)),
% 53.38/53.58 inference(unit_resolution,[status(thm)],[399, 398])).
% 53.38/53.58 tff(401,plain,
% 53.38/53.58 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(402,plain,
% 53.38/53.59 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(403,plain,
% 53.38/53.59 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[402])).
% 53.38/53.59 tff(404,plain,
% 53.38/53.59 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))))),
% 53.38/53.59 inference(transitivity,[status(thm)],[403, 401])).
% 53.38/53.59 tff(405,plain,
% 53.38/53.59 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))),
% 53.38/53.59 inference(quant_inst,[status(thm)],[])).
% 53.38/53.59 tff(406,plain,
% 53.38/53.59 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[405, 404])).
% 53.38/53.59 tff(407,plain,
% 53.38/53.59 (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k2_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.59 inference(unit_resolution,[status(thm)],[406, 153, 319, 377, 400, 371, 368])).
% 53.38/53.59 tff(408,plain,
% 53.38/53.59 (k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)) = k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 53.38/53.59 inference(transitivity,[status(thm)],[407, 391, 365, 360, 327, 306])).
% 53.38/53.59 tff(409,plain,
% 53.38/53.59 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.38/53.59 inference(monotonicity,[status(thm)],[408])).
% 53.38/53.59 tff(410,plain,
% 53.38/53.59 (r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.59 inference(symmetry,[status(thm)],[409])).
% 53.38/53.59 tff(411,plain,
% 53.38/53.59 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(412,plain,
% 53.38/53.59 ((v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(413,plain,
% 53.38/53.59 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[412])).
% 53.38/53.59 tff(414,plain,
% 53.38/53.59 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.59 inference(transitivity,[status(thm)],[413, 411])).
% 53.38/53.59 tff(415,plain,
% 53.38/53.59 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))),
% 53.38/53.59 inference(quant_inst,[status(thm)],[])).
% 53.38/53.59 tff(416,plain,
% 53.38/53.59 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[415, 414])).
% 53.38/53.59 tff(417,plain,
% 53.38/53.59 (k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 53.38/53.59 inference(unit_resolution,[status(thm)],[416, 216, 319, 68, 285, 263, 261])).
% 53.38/53.59 tff(418,plain,
% 53.38/53.59 (k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)) = k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))),
% 53.38/53.59 inference(symmetry,[status(thm)],[417])).
% 53.38/53.59 tff(419,plain,
% 53.38/53.59 (m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0)) <=> m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[418])).
% 53.38/53.59 tff(420,plain,
% 53.38/53.59 (m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0)) <=> m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.59 inference(symmetry,[status(thm)],[419])).
% 53.38/53.59 tff(421,plain,
% 53.38/53.59 (m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)) <=> m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[131])).
% 53.38/53.59 tff(422,plain,
% 53.38/53.59 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 53.38/53.59 inference(bind,[status(th)],[])).
% 53.38/53.59 tff(423,plain,
% 53.38/53.59 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.59 inference(quant_intro,[status(thm)],[422])).
% 53.38/53.59 tff(424,plain,
% 53.38/53.59 (^[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))) | (~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) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_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) | (~m1_subset_1(C, u1_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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 53.38/53.59 inference(bind,[status(th)],[])).
% 53.38/53.59 tff(425,plain,
% 53.38/53.59 (![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.59 inference(quant_intro,[status(thm)],[424])).
% 53.38/53.59 tff(426,plain,
% 53.38/53.59 (![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(427,plain,
% 53.38/53.59 (^[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))) => m1_subset_1(k4_lattices(A, B, 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))) => m1_subset_1(k4_lattices(A, B, 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))) => m1_subset_1(k4_lattices(A, B, 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)))) | m1_subset_1(k4_lattices(A, B, 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))) => m1_subset_1(k4_lattices(A, B, 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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))))),
% 53.38/53.59 inference(bind,[status(th)],[])).
% 53.38/53.59 tff(428,plain,
% 53.38/53.59 (![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))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A))) <=> ![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 53.38/53.59 inference(quant_intro,[status(thm)],[427])).
% 53.38/53.59 tff(429,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))) => m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k4_lattices')).
% 53.38/53.59 tff(430,plain,
% 53.38/53.59 (![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[429, 428])).
% 53.38/53.59 tff(431,plain,
% 53.38/53.59 (![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[430, 426])).
% 53.38/53.59 tff(432,plain,(
% 53.38/53.59 ![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)))) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)))),
% 53.38/53.59 inference(skolemize,[status(sab)],[431])).
% 53.38/53.59 tff(433,plain,
% 53.38/53.59 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[432, 425])).
% 53.38/53.59 tff(434,plain,
% 53.38/53.59 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[433, 423])).
% 53.38/53.59 tff(435,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(436,plain,
% 53.38/53.59 ((v3_struct_0(B!1) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1)))) <=> (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(437,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1))))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[436])).
% 53.38/53.59 tff(438,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)))),
% 53.38/53.59 inference(transitivity,[status(thm)],[437, 435])).
% 53.38/53.59 tff(439,plain,
% 53.38/53.59 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(B!1) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~v6_lattices(B!1)) | (~l1_lattices(B!1)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))))),
% 53.38/53.59 inference(quant_inst,[status(thm)],[])).
% 53.38/53.59 tff(440,plain,
% 53.38/53.59 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(B!1) | (~l1_lattices(B!1)) | (~v6_lattices(B!1)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[439, 438])).
% 53.38/53.59 tff(441,plain,
% 53.38/53.59 (m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(B!1))),
% 53.38/53.59 inference(unit_resolution,[status(thm)],[440, 216, 434, 68, 285, 263, 261])).
% 53.38/53.59 tff(442,plain,
% 53.38/53.59 (m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[441, 421])).
% 53.38/53.59 tff(443,plain,
% 53.38/53.59 (m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.59 inference(modus_ponens,[status(thm)],[442, 420])).
% 53.38/53.59 tff(444,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(445,plain,
% 53.38/53.59 (((k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.59 inference(rewrite,[status(thm)],[])).
% 53.38/53.59 tff(446,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))))),
% 53.38/53.59 inference(monotonicity,[status(thm)],[445])).
% 53.38/53.59 tff(447,plain,
% 53.38/53.59 (((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.59 inference(transitivity,[status(thm)],[446, 444])).
% 53.38/53.59 tff(448,plain,
% 53.38/53.59 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | ((k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | v3_struct_0(A!0) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))))),
% 53.38/53.59 inference(quant_inst,[status(thm)],[])).
% 53.38/53.59 tff(449,plain,
% 53.38/53.59 ((~![A: $i, B: $i, C: $i] : ((k4_lattices(A, B, C) = k4_lattices(A, C, B)) | v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[448, 447])).
% 53.38/53.60 tff(450,plain,
% 53.38/53.60 (k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[449, 153, 298, 377, 400, 368, 443])).
% 53.38/53.60 tff(451,plain,
% 53.38/53.60 (k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[417])).
% 53.38/53.60 tff(452,plain,
% 53.38/53.60 (k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[408])).
% 53.38/53.60 tff(453,plain,
% 53.38/53.60 (k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(transitivity,[status(thm)],[452, 451, 450])).
% 53.38/53.60 tff(454,plain,
% 53.38/53.60 (r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)),
% 53.38/53.60 inference(monotonicity,[status(thm)],[453])).
% 53.38/53.60 tff(455,plain,
% 53.38/53.60 (r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.60 inference(symmetry,[status(thm)],[454])).
% 53.38/53.60 tff(456,plain,
% 53.38/53.60 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))) <=> ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(457,plain,
% 53.38/53.60 ((v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(458,plain,
% 53.38/53.60 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[457])).
% 53.38/53.60 tff(459,plain,
% 53.38/53.60 (((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.60 inference(transitivity,[status(thm)],[458, 456])).
% 53.38/53.60 tff(460,plain,
% 53.38/53.60 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))))),
% 53.38/53.60 inference(quant_inst,[status(thm)],[])).
% 53.38/53.60 tff(461,plain,
% 53.38/53.60 ((~![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))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[460, 459])).
% 53.38/53.60 tff(462,plain,
% 53.38/53.60 (k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[461, 153, 319, 377, 400, 368, 443])).
% 53.38/53.60 tff(463,plain,
% 53.38/53.60 (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(symmetry,[status(thm)],[462])).
% 53.38/53.60 tff(464,plain,
% 53.38/53.60 (((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C))))) <=> ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C))))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(465,plain,
% 53.38/53.60 ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C))))),
% 53.38/53.60 inference(quant_inst,[status(thm)],[])).
% 53.38/53.60 tff(466,plain,
% 53.38/53.60 ((~![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, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), B, C))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[465, 464])).
% 53.38/53.60 tff(467,plain,
% 53.38/53.60 ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[466, 382])).
% 53.38/53.60 tff(468,plain,
% 53.38/53.60 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[467, 368])).
% 53.38/53.60 tff(469,plain,
% 53.38/53.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))) | ((~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(470,plain,
% 53.38/53.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))) | ((~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))))),
% 53.38/53.60 inference(quant_inst,[status(thm)],[])).
% 53.38/53.60 tff(471,plain,
% 53.38/53.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), C)))) | (~m1_subset_1(k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))))),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[470, 469])).
% 53.38/53.60 tff(472,plain,
% 53.38/53.60 (k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[471, 468, 443])).
% 53.38/53.60 tff(473,plain,
% 53.38/53.60 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(symmetry,[status(thm)],[472])).
% 53.38/53.60 tff(474,plain,
% 53.38/53.60 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[364, 364, 364, 363])).
% 53.38/53.60 tff(475,plain,
% 53.38/53.60 (k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u1_lattices(A!0), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(symmetry,[status(thm)],[474])).
% 53.38/53.60 tff(476,plain,
% 53.38/53.60 (k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.60 inference(transitivity,[status(thm)],[475, 473, 463])).
% 53.38/53.60 tff(477,plain,
% 53.38/53.60 (r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)),
% 53.38/53.60 inference(monotonicity,[status(thm)],[476])).
% 53.38/53.60 tff(478,plain,
% 53.38/53.60 (r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.60 inference(transitivity,[status(thm)],[477, 455])).
% 53.38/53.60 tff(479,plain,
% 53.38/53.60 ((~r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)) <=> (~r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[478])).
% 53.38/53.60 tff(480,assumption,(r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)), introduced(assumption)).
% 53.38/53.60 tff(481,plain,
% 53.38/53.60 (r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[480, 478])).
% 53.38/53.60 tff(482,plain,
% 53.38/53.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(483,plain,
% 53.38/53.60 ((v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(484,plain,
% 53.38/53.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))))),
% 53.38/53.60 inference(monotonicity,[status(thm)],[483])).
% 53.38/53.60 tff(485,plain,
% 53.38/53.60 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)))),
% 53.38/53.60 inference(transitivity,[status(thm)],[484, 482])).
% 53.38/53.60 tff(486,plain,
% 53.38/53.60 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0)) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~v6_lattices(A!0)) | (~l1_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))))),
% 53.38/53.60 inference(quant_inst,[status(thm)],[])).
% 53.38/53.60 tff(487,plain,
% 53.38/53.60 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | m1_subset_1(k4_lattices(A, B, C), u1_struct_0(A)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | (~v6_lattices(A!0)) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.60 inference(modus_ponens,[status(thm)],[486, 485])).
% 53.38/53.60 tff(488,plain,
% 53.38/53.60 (m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))),
% 53.38/53.60 inference(unit_resolution,[status(thm)],[487, 153, 434, 377, 400, 371, 368])).
% 53.38/53.60 tff(489,plain,
% 53.38/53.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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)))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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)))))))))))),
% 53.38/53.60 inference(rewrite,[status(thm)],[])).
% 53.38/53.60 tff(490,plain,
% 53.38/53.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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)))))))))))),
% 53.38/53.60 inference(quant_inst,[status(thm)],[])).
% 53.38/53.60 tff(491,plain,
% 53.38/53.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~((~(m1_filter_0(B, A) | (~((~m1_subset_1(tptp_fun_C_3(B, A), u1_struct_0(A))) | (~m1_subset_1(tptp_fun_D_4(B, A), u1_struct_0(A))) | (~(((~r2_hidden(tptp_fun_C_3(B, A), B)) | (~r2_hidden(tptp_fun_D_4(B, A), B))) <=> r2_hidden(k4_lattices(A, tptp_fun_C_3(B, A), tptp_fun_D_4(B, A)), B))))))) | (~((~m1_filter_0(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)))))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))),
% 53.38/53.61 inference(modus_ponens,[status(thm)],[490, 489])).
% 53.38/53.61 tff(492,plain,
% 53.38/53.61 (![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[491, 153, 152, 151, 214])).
% 53.38/53.61 tff(493,plain,
% 53.38/53.61 (((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))))) <=> ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))))),
% 53.38/53.61 inference(rewrite,[status(thm)],[])).
% 53.38/53.61 tff(494,plain,
% 53.38/53.61 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))) | (v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))))),
% 53.38/53.61 inference(quant_inst,[status(thm)],[])).
% 53.38/53.61 tff(495,plain,
% 53.38/53.61 ((~![B: $i] : (v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(B, A!0) | (~((~m1_subset_1(tptp_fun_C_3(B, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(B, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(B, A!0), B)) | (~r2_hidden(tptp_fun_D_4(B, A!0), B))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(B, A!0), tptp_fun_D_4(B, A!0)), B))))))) | (~((~m1_filter_0(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))))))))))) | v1_xboole_0(C!2) | (~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))))),
% 53.38/53.61 inference(modus_ponens,[status(thm)],[494, 493])).
% 53.38/53.61 tff(496,plain,
% 53.38/53.61 ((~m1_subset_1(C!2, k1_zfmisc_1(u1_struct_0(A!0)))) | (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[495, 492, 195])).
% 53.38/53.61 tff(497,plain,
% 53.38/53.61 (~((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[496, 192])).
% 53.38/53.61 tff(498,plain,
% 53.38/53.61 (((~(m1_filter_0(C!2, A!0) | (~((~m1_subset_1(tptp_fun_C_3(C!2, A!0), u1_struct_0(A!0))) | (~m1_subset_1(tptp_fun_D_4(C!2, A!0), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, A!0), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, A!0), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, A!0), tptp_fun_D_4(C!2, A!0)), C!2))))))) | (~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))))) | ((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))),
% 53.38/53.61 inference(tautology,[status(thm)],[])).
% 53.38/53.61 tff(499,plain,
% 53.38/53.61 ((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[498, 497])).
% 53.38/53.61 tff(500,plain,
% 53.38/53.61 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 53.38/53.61 inference(rewrite,[status(thm)],[])).
% 53.38/53.61 tff(501,plain,
% 53.38/53.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0)))),
% 53.38/53.61 inference(quant_inst,[status(thm)],[])).
% 53.38/53.61 tff(502,plain,
% 53.38/53.61 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 53.38/53.61 inference(modus_ponens,[status(thm)],[501, 500])).
% 53.38/53.61 tff(503,plain,
% 53.38/53.61 (![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[502, 153, 152, 151, 246])).
% 53.38/53.61 tff(504,plain,
% 53.38/53.61 ((~![B: $i] : (m1_filter_2(B, A!0) <=> m1_filter_0(B, A!0))) | (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))),
% 53.38/53.61 inference(quant_inst,[status(thm)],[])).
% 53.38/53.61 tff(505,plain,
% 53.38/53.61 (m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0)),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[504, 503])).
% 53.38/53.61 tff(506,plain,
% 53.38/53.61 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | (~m1_filter_2(C!2, A!0)) | m1_filter_0(C!2, A!0)),
% 53.38/53.61 inference(tautology,[status(thm)],[])).
% 53.38/53.61 tff(507,plain,
% 53.38/53.61 ((~(m1_filter_2(C!2, A!0) <=> m1_filter_0(C!2, A!0))) | m1_filter_0(C!2, A!0)),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[506, 159])).
% 53.38/53.61 tff(508,plain,
% 53.38/53.61 (m1_filter_0(C!2, A!0)),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[507, 505])).
% 53.38/53.61 tff(509,plain,
% 53.38/53.61 ((~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))) | (~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))),
% 53.38/53.61 inference(tautology,[status(thm)],[])).
% 53.38/53.61 tff(510,plain,
% 53.38/53.61 ((~((~m1_filter_0(C!2, 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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2))))))) | ![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[509, 508])).
% 53.38/53.61 tff(511,plain,
% 53.38/53.61 (![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[510, 499])).
% 53.38/53.61 tff(512,plain,
% 53.38/53.61 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))),
% 53.38/53.61 inference(rewrite,[status(thm)],[])).
% 53.38/53.61 tff(513,plain,
% 53.38/53.61 (((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))) <=> ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))),
% 53.38/53.61 inference(rewrite,[status(thm)],[])).
% 53.38/53.61 tff(514,plain,
% 53.38/53.61 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))))),
% 53.38/53.61 inference(monotonicity,[status(thm)],[513])).
% 53.38/53.61 tff(515,plain,
% 53.38/53.61 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))),
% 53.38/53.61 inference(transitivity,[status(thm)],[514, 512])).
% 53.38/53.61 tff(516,plain,
% 53.38/53.61 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2)))))),
% 53.38/53.61 inference(quant_inst,[status(thm)],[])).
% 53.38/53.61 tff(517,plain,
% 53.38/53.61 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))),
% 53.38/53.61 inference(modus_ponens,[status(thm)],[516, 515])).
% 53.38/53.61 tff(518,plain,
% 53.38/53.61 ((~m1_subset_1(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[517, 511])).
% 53.38/53.61 tff(519,plain,
% 53.38/53.61 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[518, 488])).
% 53.38/53.61 tff(520,plain,
% 53.38/53.61 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.61 inference(rewrite,[status(thm)],[])).
% 53.38/53.61 tff(521,plain,
% 53.38/53.61 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.61 inference(quant_inst,[status(thm)],[])).
% 53.38/53.61 tff(522,plain,
% 53.38/53.61 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 53.38/53.61 inference(modus_ponens,[status(thm)],[521, 520])).
% 53.38/53.61 tff(523,plain,
% 53.38/53.61 (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[522, 368, 519])).
% 53.38/53.61 tff(524,plain,
% 53.38/53.61 ((((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))) | (~r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.61 inference(tautology,[status(thm)],[])).
% 53.38/53.61 tff(525,plain,
% 53.38/53.61 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))) | (~r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[524, 523])).
% 53.38/53.61 tff(526,plain,
% 53.38/53.61 (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[525, 481])).
% 53.38/53.61 tff(527,plain,
% 53.38/53.61 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) | r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.61 inference(tautology,[status(thm)],[])).
% 53.38/53.61 tff(528,plain,
% 53.38/53.61 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.61 inference(unit_resolution,[status(thm)],[527, 526])).
% 53.38/53.61 tff(529,plain,
% 53.38/53.61 (k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)) = k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)))),
% 53.38/53.61 inference(transitivity,[status(thm)],[451, 450])).
% 53.38/53.61 tff(530,plain,
% 53.38/53.61 (r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2) <=> r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)),
% 53.38/53.61 inference(monotonicity,[status(thm)],[529])).
% 53.38/53.61 tff(531,plain,
% 53.38/53.61 (r2_hidden(k4_lattices(A!0, tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.61 inference(symmetry,[status(thm)],[530])).
% 53.38/53.61 tff(532,plain,
% 53.38/53.61 (r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.62 inference(transitivity,[status(thm)],[477, 531])).
% 53.38/53.62 tff(533,plain,
% 53.38/53.62 (r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[480, 532])).
% 53.38/53.62 tff(534,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(535,plain,
% 53.38/53.62 (((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))) <=> ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(536,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))))),
% 53.38/53.62 inference(monotonicity,[status(thm)],[535])).
% 53.38/53.62 tff(537,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))),
% 53.38/53.62 inference(transitivity,[status(thm)],[536, 534])).
% 53.38/53.62 tff(538,plain,
% 53.38/53.62 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2)))))),
% 53.38/53.62 inference(quant_inst,[status(thm)],[])).
% 53.38/53.62 tff(539,plain,
% 53.38/53.62 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[538, 537])).
% 53.38/53.62 tff(540,plain,
% 53.38/53.62 ((~m1_subset_1(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[539, 511])).
% 53.38/53.62 tff(541,plain,
% 53.38/53.62 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[540, 442])).
% 53.38/53.62 tff(542,plain,
% 53.38/53.62 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(543,plain,
% 53.38/53.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.62 inference(quant_inst,[status(thm)],[])).
% 53.38/53.62 tff(544,plain,
% 53.38/53.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[543, 542])).
% 53.38/53.62 tff(545,plain,
% 53.38/53.62 (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[544, 368, 541])).
% 53.38/53.62 tff(546,plain,
% 53.38/53.62 ((((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))) | (~r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(547,plain,
% 53.38/53.62 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))) | (~r2_hidden(k4_lattices(A!0, k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[546, 545])).
% 53.38/53.62 tff(548,plain,
% 53.38/53.62 (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[547, 533])).
% 53.38/53.62 tff(549,plain,
% 53.38/53.62 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(550,plain,
% 53.38/53.62 (r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[549, 548])).
% 53.38/53.62 tff(551,plain,
% 53.38/53.62 (((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(B!1))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(B!1))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)))) | (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(552,plain,
% 53.38/53.62 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[551, 259])).
% 53.38/53.62 tff(553,plain,
% 53.38/53.62 ((~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(554,plain,
% 53.38/53.62 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | (~r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[553, 552])).
% 53.38/53.62 tff(555,plain,
% 53.38/53.62 ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[554, 550])).
% 53.38/53.62 tff(556,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(557,plain,
% 53.38/53.62 (((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) <=> ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(558,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))))),
% 53.38/53.62 inference(monotonicity,[status(thm)],[557])).
% 53.38/53.62 tff(559,plain,
% 53.38/53.62 (((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))) <=> ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))),
% 53.38/53.62 inference(transitivity,[status(thm)],[558, 556])).
% 53.38/53.62 tff(560,plain,
% 53.38/53.62 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2)))))),
% 53.38/53.62 inference(quant_inst,[status(thm)],[])).
% 53.38/53.62 tff(561,plain,
% 53.38/53.62 ((~![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, C!2)) | (~r2_hidden(D, C!2))) <=> r2_hidden(k4_lattices(A!0, C, D), C!2)))))) | (~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[560, 559])).
% 53.38/53.62 tff(562,plain,
% 53.38/53.62 ((~m1_subset_1(tptp_fun_D_4(C!2, B!1), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[561, 511])).
% 53.38/53.62 tff(563,plain,
% 53.38/53.62 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[562, 371])).
% 53.38/53.62 tff(564,plain,
% 53.38/53.62 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.62 inference(rewrite,[status(thm)],[])).
% 53.38/53.62 tff(565,plain,
% 53.38/53.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) | ((~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))))),
% 53.38/53.62 inference(quant_inst,[status(thm)],[])).
% 53.38/53.62 tff(566,plain,
% 53.38/53.62 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~(((~r2_hidden(D, C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), D), C!2))))) | (~m1_subset_1(tptp_fun_C_3(C!2, B!1), u1_struct_0(A!0))) | (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[565, 564])).
% 53.38/53.62 tff(567,plain,
% 53.38/53.62 (~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[566, 563, 368])).
% 53.38/53.62 tff(568,plain,
% 53.38/53.62 ((((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(569,plain,
% 53.38/53.62 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[568, 567])).
% 53.38/53.62 tff(570,plain,
% 53.38/53.62 ($false),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[569, 555, 528])).
% 53.38/53.62 tff(571,plain,(~r2_hidden(k2_binop_1(u1_struct_0(B!1), u1_struct_0(B!1), u1_struct_0(B!1), u1_lattices(B!1), tptp_fun_C_3(C!2, B!1), k2_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1))), C!2)), inference(lemma,lemma(discharge,[]))).
% 53.38/53.62 tff(572,plain,
% 53.38/53.62 (~r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.62 inference(modus_ponens,[status(thm)],[571, 479])).
% 53.38/53.62 tff(573,plain,
% 53.38/53.62 ((((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) <=> r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)) | ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) | r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(574,plain,
% 53.38/53.62 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))) | r2_hidden(k4_lattices(A!0, k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[573, 523])).
% 53.38/53.62 tff(575,plain,
% 53.38/53.62 ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[574, 572])).
% 53.38/53.62 tff(576,assumption,(~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))), introduced(assumption)).
% 53.38/53.62 tff(577,plain,
% 53.38/53.62 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)),
% 53.38/53.62 inference(tautology,[status(thm)],[])).
% 53.38/53.62 tff(578,plain,
% 53.38/53.62 (r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)),
% 53.38/53.62 inference(unit_resolution,[status(thm)],[577, 576])).
% 53.38/53.62 tff(579,plain,
% 53.38/53.62 ((((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)) | ((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.63 inference(tautology,[status(thm)],[])).
% 53.38/53.63 tff(580,plain,
% 53.38/53.63 (((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) | r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.63 inference(unit_resolution,[status(thm)],[579, 567])).
% 53.38/53.63 tff(581,plain,
% 53.38/53.63 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.38/53.63 inference(unit_resolution,[status(thm)],[580, 576])).
% 53.38/53.63 tff(582,plain,
% 53.38/53.63 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)))) | (~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2))),
% 53.38/53.63 inference(tautology,[status(thm)],[])).
% 53.38/53.63 tff(583,plain,
% 53.38/53.63 ($false),
% 53.38/53.63 inference(unit_resolution,[status(thm)],[582, 581, 578, 575])).
% 53.63/53.87 tff(584,plain,((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))), inference(lemma,lemma(discharge,[]))).
% 53.63/53.87 tff(585,plain,
% 53.63/53.87 ((~(((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2))) <=> r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2))) | (~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.63/53.87 inference(tautology,[status(thm)],[])).
% 53.63/53.87 tff(586,plain,
% 53.63/53.87 ((~((~r2_hidden(tptp_fun_C_3(C!2, B!1), C!2)) | (~r2_hidden(tptp_fun_D_4(C!2, B!1), C!2)))) | r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.63/53.87 inference(unit_resolution,[status(thm)],[585, 552])).
% 53.63/53.87 tff(587,plain,
% 53.63/53.87 (r2_hidden(k4_lattices(B!1, tptp_fun_C_3(C!2, B!1), tptp_fun_D_4(C!2, B!1)), C!2)),
% 53.63/53.87 inference(unit_resolution,[status(thm)],[586, 584])).
% 53.63/53.87 tff(588,plain,
% 53.63/53.87 (r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.63/53.87 inference(modus_ponens,[status(thm)],[587, 410])).
% 53.63/53.87 tff(589,plain,
% 53.63/53.87 (~r2_hidden(k4_lattices(A!0, tptp_fun_D_4(C!2, B!1), tptp_fun_C_3(C!2, B!1)), C!2)),
% 53.63/53.87 inference(unit_resolution,[status(thm)],[569, 584])).
% 53.63/53.87 tff(590,plain,
% 53.63/53.87 ($false),
% 53.63/53.87 inference(unit_resolution,[status(thm)],[589, 588])).
% 53.63/53.87 % SZS output end Proof
% 53.63/53.87 % E exiting
%------------------------------------------------------------------------------