%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT308+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:14:16 AM UTC 2025
% Result : Theorem 0.52s 0.74s
% Output : Proof 0.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT308+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Jun 19 20:09:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.52/0.74 % SZS status Theorem
% 0.52/0.74 % SZS output start Proof
% 0.52/0.74 tff(tptp_fun_B_1_type, type, (
% 0.52/0.74 tptp_fun_B_1: $i)).
% 0.52/0.74 tff(k3_lattices_type, type, (
% 0.52/0.74 k3_lattices: ( $i * $i * $i ) > $i)).
% 0.52/0.74 tff(tptp_fun_C_2_type, type, (
% 0.52/0.74 tptp_fun_C_2: $i)).
% 0.52/0.74 tff(tptp_fun_A_0_type, type, (
% 0.52/0.74 tptp_fun_A_0: $i)).
% 0.52/0.74 tff(k4_lattices_type, type, (
% 0.52/0.74 k4_lattices: ( $i * $i * $i ) > $i)).
% 0.52/0.74 tff(g3_lattices_type, type, (
% 0.52/0.74 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.52/0.74 tff(u2_lattices_type, type, (
% 0.52/0.74 u2_lattices: $i > $i)).
% 0.52/0.74 tff(u1_lattices_type, type, (
% 0.52/0.74 u1_lattices: $i > $i)).
% 0.52/0.74 tff(u1_struct_0_type, type, (
% 0.52/0.74 u1_struct_0: $i > $i)).
% 0.52/0.74 tff(m1_subset_1_type, type, (
% 0.52/0.74 m1_subset_1: ( $i * $i ) > $o)).
% 0.52/0.74 tff(k2_filter_0_type, type, (
% 0.52/0.74 k2_filter_0: ( $i * $i ) > $i)).
% 0.52/0.74 tff(k2_filter_2_type, type, (
% 0.52/0.74 k2_filter_2: ( $i * $i ) > $i)).
% 0.52/0.74 tff(k5_filter_2_type, type, (
% 0.52/0.74 k5_filter_2: ( $i * $i ) > $i)).
% 0.52/0.74 tff(k1_lattice2_type, type, (
% 0.52/0.74 k1_lattice2: $i > $i)).
% 0.52/0.74 tff(v10_lattices_type, type, (
% 0.52/0.74 v10_lattices: $i > $o)).
% 0.52/0.74 tff(l3_lattices_type, type, (
% 0.52/0.74 l3_lattices: $i > $o)).
% 0.52/0.74 tff(v3_struct_0_type, type, (
% 0.52/0.74 v3_struct_0: $i > $o)).
% 0.52/0.74 tff(k18_filter_2_type, type, (
% 0.52/0.74 k18_filter_2: ( $i * $i ) > $i)).
% 0.52/0.74 tff(v3_lattices_type, type, (
% 0.52/0.74 v3_lattices: $i > $o)).
% 0.52/0.74 tff(m1_relset_1_type, type, (
% 0.52/0.74 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(k2_zfmisc_1_type, type, (
% 0.52/0.74 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.52/0.74 tff(m2_relset_1_type, type, (
% 0.52/0.74 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(v1_funct_2_type, type, (
% 0.52/0.74 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.52/0.74 tff(v1_funct_1_type, type, (
% 0.52/0.74 v1_funct_1: $i > $o)).
% 0.52/0.74 tff(l1_lattices_type, type, (
% 0.52/0.74 l1_lattices: $i > $o)).
% 0.52/0.74 tff(l2_lattices_type, type, (
% 0.52/0.74 l2_lattices: $i > $o)).
% 0.52/0.74 tff(v9_lattices_type, type, (
% 0.52/0.74 v9_lattices: $i > $o)).
% 0.52/0.74 tff(v8_lattices_type, type, (
% 0.52/0.74 v8_lattices: $i > $o)).
% 0.52/0.74 tff(v7_lattices_type, type, (
% 0.52/0.74 v7_lattices: $i > $o)).
% 0.52/0.74 tff(v6_lattices_type, type, (
% 0.52/0.74 v6_lattices: $i > $o)).
% 0.52/0.74 tff(v5_lattices_type, type, (
% 0.52/0.74 v5_lattices: $i > $o)).
% 0.52/0.74 tff(v4_lattices_type, type, (
% 0.52/0.74 v4_lattices: $i > $o)).
% 0.52/0.74 tff(k2_lattices_type, type, (
% 0.52/0.74 k2_lattices: ( $i * $i * $i ) > $i)).
% 0.52/0.74 tff(k2_binop_1_type, type, (
% 0.52/0.74 k2_binop_1: ( $i * $i * $i * $i * $i * $i ) > $i)).
% 0.52/0.74 tff(k1_lattices_type, type, (
% 0.52/0.74 k1_lattices: ( $i * $i * $i ) > $i)).
% 0.52/0.74 tff(1,plain,
% 0.52/0.74 ((k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) <=> (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.52/0.74 inference(commutativity,[status(thm)],[])).
% 0.52/0.74 tff(2,plain,
% 0.52/0.74 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(3,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[2])).
% 0.52/0.74 tff(4,plain,
% 0.52/0.74 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(5,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[4])).
% 0.52/0.74 tff(6,plain,
% 0.52/0.74 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(7,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[6])).
% 0.52/0.74 tff(8,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(transitivity,[status(thm)],[7, 5])).
% 0.52/0.74 tff(9,plain,
% 0.52/0.74 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(10,plain,
% 0.52/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[9])).
% 0.52/0.74 tff(11,plain,
% 0.52/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(12,plain,
% 0.52/0.74 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 0.52/0.74 inference(bind,[status(th)],[])).
% 0.52/0.74 tff(13,plain,
% 0.52/0.74 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(quant_intro,[status(thm)],[12])).
% 0.52/0.74 tff(14,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 0.52/0.74 tff(15,plain,
% 0.52/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.52/0.74 tff(16,plain,
% 0.52/0.74 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.52/0.74 tff(17,plain,(
% 0.52/0.74 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(skolemize,[status(sab)],[16])).
% 0.52/0.74 tff(18,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.52/0.74 tff(19,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[18, 8])).
% 0.52/0.74 tff(20,plain,
% 0.52/0.74 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[19, 3])).
% 0.52/0.74 tff(21,plain,
% 0.52/0.74 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(22,plain,
% 0.52/0.74 ((m1_subset_1(B!1, u1_struct_0(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(23,plain,
% 0.52/0.74 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0))))),
% 0.52/0.74 inference(monotonicity,[status(thm)],[22])).
% 0.52/0.74 tff(24,plain,
% 0.52/0.74 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)))),
% 0.52/0.74 inference(transitivity,[status(thm)],[23, 21])).
% 0.52/0.74 tff(25,plain,
% 0.52/0.74 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A)))))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(26,plain,
% 0.52/0.74 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A)))))))),
% 0.52/0.74 inference(rewrite,[status(thm)],[])).
% 0.52/0.74 tff(27,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t35_filter_2')).
% 0.52/0.74 tff(28,plain,
% 0.52/0.74 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.52/0.74 tff(29,plain,
% 0.52/0.74 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[28, 25])).
% 0.52/0.74 tff(30,plain,
% 0.52/0.74 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.52/0.74 tff(31,plain,
% 0.52/0.74 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k3_lattices(A, B, C) = B))) & (k18_filter_2(A, B) = u1_struct_0(A))))))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[30, 25])).
% 0.52/0.74 tff(32,plain,
% 0.52/0.74 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))) & (k18_filter_2(A!0, B!1) = u1_struct_0(A!0))),
% 0.52/0.74 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.52/0.74 tff(33,plain,
% 0.52/0.74 (l3_lattices(A!0)),
% 0.52/0.74 inference(and_elim,[status(thm)],[32])).
% 0.52/0.74 tff(34,plain,
% 0.52/0.74 (v10_lattices(A!0)),
% 0.52/0.74 inference(and_elim,[status(thm)],[32])).
% 0.52/0.74 tff(35,plain,
% 0.52/0.74 (~v3_struct_0(A!0)),
% 0.52/0.74 inference(and_elim,[status(thm)],[32])).
% 0.52/0.74 tff(36,plain,
% 0.52/0.74 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(37,plain,
% 0.52/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(38,plain,
% 0.52/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.52/0.75 tff(39,plain,
% 0.52/0.75 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[38, 35, 34, 33, 20])).
% 0.52/0.75 tff(40,plain,
% 0.52/0.75 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.52/0.75 inference(and_elim,[status(thm)],[32])).
% 0.52/0.75 tff(41,plain,
% 0.52/0.75 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(42,plain,
% 0.52/0.75 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(43,plain,
% 0.52/0.75 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[42, 41])).
% 0.52/0.75 tff(44,plain,
% 0.52/0.75 (k5_filter_2(A!0, B!1) = B!1),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[43, 40, 39])).
% 0.52/0.75 tff(45,plain,
% 0.52/0.75 (B!1 = k5_filter_2(A!0, B!1)),
% 0.52/0.75 inference(symmetry,[status(thm)],[44])).
% 0.52/0.75 tff(46,plain,
% 0.52/0.75 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(47,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[46])).
% 0.52/0.75 tff(48,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(49,plain,
% 0.52/0.75 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(50,plain,
% 0.52/0.75 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[49])).
% 0.52/0.75 tff(51,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 0.52/0.75 tff(52,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.52/0.75 tff(53,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.52/0.75 tff(54,plain,(
% 0.52/0.75 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(skolemize,[status(sab)],[53])).
% 0.52/0.75 tff(55,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.52/0.75 tff(56,plain,
% 0.52/0.75 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(57,plain,
% 0.52/0.75 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(58,plain,
% 0.52/0.75 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.52/0.75 tff(59,plain,
% 0.52/0.75 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[58, 33, 55])).
% 0.52/0.75 tff(60,plain,
% 0.52/0.75 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.52/0.75 inference(symmetry,[status(thm)],[59])).
% 0.52/0.75 tff(61,plain,
% 0.52/0.75 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.52/0.75 inference(monotonicity,[status(thm)],[60, 45])).
% 0.52/0.75 tff(62,plain,
% 0.52/0.75 (k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.52/0.75 inference(symmetry,[status(thm)],[61])).
% 0.52/0.75 tff(63,plain,
% 0.52/0.75 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(64,plain,
% 0.52/0.75 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[63])).
% 0.52/0.75 tff(65,plain,
% 0.52/0.75 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(66,plain,
% 0.52/0.75 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[65])).
% 0.52/0.75 tff(67,plain,
% 0.52/0.75 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(transitivity,[status(thm)],[66, 64])).
% 0.52/0.75 tff(68,plain,
% 0.52/0.75 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(69,plain,
% 0.52/0.75 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[68])).
% 0.52/0.75 tff(70,plain,
% 0.52/0.75 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(71,plain,
% 0.52/0.75 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(72,plain,
% 0.52/0.75 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[71])).
% 0.52/0.75 tff(73,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_filter_2')).
% 0.52/0.75 tff(74,plain,
% 0.52/0.75 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[73, 72])).
% 0.52/0.75 tff(75,plain,
% 0.52/0.75 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[74, 70])).
% 0.52/0.75 tff(76,plain,(
% 0.52/0.75 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.52/0.75 inference(skolemize,[status(sab)],[75])).
% 0.52/0.75 tff(77,plain,
% 0.52/0.75 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[76, 69])).
% 0.52/0.75 tff(78,plain,
% 0.52/0.75 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[77, 67])).
% 0.52/0.75 tff(79,plain,
% 0.52/0.75 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(80,plain,
% 0.52/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(81,plain,
% 0.52/0.75 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.52/0.75 tff(82,plain,
% 0.52/0.75 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[81, 35, 34, 33, 78])).
% 0.52/0.75 tff(83,plain,
% 0.52/0.75 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(84,plain,
% 0.52/0.75 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(85,plain,
% 0.52/0.75 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.52/0.75 tff(86,plain,
% 0.52/0.75 (~((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[85, 40, 82])).
% 0.52/0.75 tff(87,plain,
% 0.52/0.75 (((~(k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)) = k2_filter_2(A!0, B!1)))) | (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1)))),
% 0.52/0.75 inference(tautology,[status(thm)],[])).
% 0.52/0.75 tff(88,plain,
% 0.52/0.75 (k18_filter_2(A!0, B!1) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B!1))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[87, 86])).
% 0.52/0.75 tff(89,plain,
% 0.52/0.75 (k18_filter_2(A!0, B!1) = u1_struct_0(A!0)),
% 0.52/0.75 inference(and_elim,[status(thm)],[32])).
% 0.52/0.75 tff(90,plain,
% 0.52/0.75 (u1_struct_0(A!0) = k18_filter_2(A!0, B!1)),
% 0.52/0.75 inference(symmetry,[status(thm)],[89])).
% 0.52/0.75 tff(91,plain,
% 0.52/0.75 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(92,plain,
% 0.52/0.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[91])).
% 0.52/0.75 tff(93,plain,
% 0.52/0.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(94,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.52/0.75 tff(95,plain,
% 0.52/0.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.52/0.75 tff(96,plain,(
% 0.52/0.75 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.52/0.75 inference(skolemize,[status(sab)],[95])).
% 0.52/0.75 tff(97,plain,
% 0.52/0.75 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[96, 92])).
% 0.52/0.75 tff(98,plain,
% 0.52/0.75 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(99,plain,
% 0.52/0.75 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[98, 97])).
% 0.52/0.75 tff(100,plain,
% 0.52/0.75 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(101,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[100])).
% 0.52/0.75 tff(102,plain,
% 0.52/0.75 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(103,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[102])).
% 0.52/0.75 tff(104,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(105,plain,
% 0.52/0.75 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(106,plain,
% 0.52/0.75 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[105])).
% 0.52/0.75 tff(107,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.52/0.75 tff(108,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.52/0.75 tff(109,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[108, 104])).
% 0.52/0.75 tff(110,plain,(
% 0.52/0.75 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.52/0.75 inference(skolemize,[status(sab)],[109])).
% 0.52/0.75 tff(111,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[110, 103])).
% 0.52/0.75 tff(112,plain,
% 0.52/0.75 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[111, 101])).
% 0.52/0.75 tff(113,plain,
% 0.52/0.75 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(114,plain,
% 0.52/0.75 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(115,plain,
% 0.52/0.75 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[114, 113])).
% 0.52/0.75 tff(116,plain,
% 0.52/0.75 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[115, 33, 112])).
% 0.52/0.75 tff(117,plain,
% 0.52/0.75 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.52/0.75 inference(tautology,[status(thm)],[])).
% 0.52/0.75 tff(118,plain,
% 0.52/0.75 (l1_lattices(A!0)),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.52/0.75 tff(119,plain,
% 0.52/0.75 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(120,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[119])).
% 0.52/0.75 tff(121,plain,
% 0.52/0.75 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(122,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[121])).
% 0.52/0.75 tff(123,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(124,plain,
% 0.52/0.75 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.52/0.75 inference(bind,[status(th)],[])).
% 0.52/0.75 tff(125,plain,
% 0.52/0.75 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.52/0.75 inference(quant_intro,[status(thm)],[124])).
% 0.52/0.75 tff(126,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.52/0.75 tff(127,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[126, 125])).
% 0.52/0.75 tff(128,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[127, 123])).
% 0.52/0.75 tff(129,plain,(
% 0.52/0.75 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.52/0.75 inference(skolemize,[status(sab)],[128])).
% 0.52/0.75 tff(130,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[129, 122])).
% 0.52/0.75 tff(131,plain,
% 0.52/0.75 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[130, 120])).
% 0.52/0.75 tff(132,plain,
% 0.52/0.75 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.52/0.75 inference(rewrite,[status(thm)],[])).
% 0.52/0.75 tff(133,plain,
% 0.52/0.75 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.52/0.75 inference(quant_inst,[status(thm)],[])).
% 0.52/0.75 tff(134,plain,
% 0.52/0.75 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.52/0.75 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.52/0.75 tff(135,plain,
% 0.52/0.75 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[134, 131])).
% 0.52/0.75 tff(136,plain,
% 0.52/0.75 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[135, 118])).
% 0.52/0.75 tff(137,plain,
% 0.52/0.75 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.52/0.75 inference(tautology,[status(thm)],[])).
% 0.52/0.75 tff(138,plain,
% 0.52/0.75 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.52/0.75 inference(unit_resolution,[status(thm)],[137, 136])).
% 0.52/0.75 tff(139,plain,
% 0.52/0.75 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(140,plain,
% 0.59/0.76 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[139, 138])).
% 0.59/0.76 tff(141,plain,
% 0.59/0.76 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[140, 99])).
% 0.59/0.76 tff(142,plain,
% 0.59/0.76 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(143,plain,
% 0.59/0.76 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[142, 97])).
% 0.59/0.76 tff(144,plain,
% 0.59/0.76 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(145,plain,
% 0.59/0.76 (l2_lattices(A!0)),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[144, 116])).
% 0.59/0.76 tff(146,plain,
% 0.59/0.76 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(147,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[146])).
% 0.59/0.76 tff(148,plain,
% 0.59/0.76 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(149,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[148])).
% 0.59/0.76 tff(150,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(151,plain,
% 0.59/0.76 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(152,plain,
% 0.59/0.76 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[151])).
% 0.59/0.76 tff(153,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.59/0.76 tff(154,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[153, 152])).
% 0.59/0.76 tff(155,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[154, 150])).
% 0.59/0.76 tff(156,plain,(
% 0.59/0.76 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.59/0.76 inference(skolemize,[status(sab)],[155])).
% 0.59/0.76 tff(157,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[156, 149])).
% 0.59/0.76 tff(158,plain,
% 0.59/0.76 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[157, 147])).
% 0.59/0.76 tff(159,plain,
% 0.59/0.76 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(160,plain,
% 0.59/0.76 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.59/0.76 inference(quant_inst,[status(thm)],[])).
% 0.59/0.76 tff(161,plain,
% 0.59/0.76 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[160, 159])).
% 0.59/0.76 tff(162,plain,
% 0.59/0.76 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[161, 158])).
% 0.59/0.76 tff(163,plain,
% 0.59/0.76 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[162, 145])).
% 0.59/0.76 tff(164,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(165,plain,
% 0.59/0.76 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[164, 163])).
% 0.59/0.76 tff(166,plain,
% 0.59/0.76 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(167,plain,
% 0.59/0.76 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.59/0.76 tff(168,plain,
% 0.59/0.76 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[167, 143])).
% 0.59/0.76 tff(169,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(170,plain,
% 0.59/0.76 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[169, 163])).
% 0.59/0.76 tff(171,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(172,plain,
% 0.59/0.76 (v1_funct_1(u2_lattices(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[171, 163])).
% 0.59/0.76 tff(173,plain,
% 0.59/0.76 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(174,plain,
% 0.59/0.76 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[173, 136])).
% 0.59/0.76 tff(175,plain,
% 0.59/0.76 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 0.59/0.76 inference(tautology,[status(thm)],[])).
% 0.59/0.76 tff(176,plain,
% 0.59/0.76 (v1_funct_1(u1_lattices(A!0))),
% 0.59/0.76 inference(unit_resolution,[status(thm)],[175, 136])).
% 0.59/0.76 tff(177,plain,
% 0.59/0.76 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(178,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[177])).
% 0.59/0.76 tff(179,plain,
% 0.59/0.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(180,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[179])).
% 0.59/0.76 tff(181,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(182,plain,
% 0.59/0.76 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 0.59/0.76 inference(bind,[status(th)],[])).
% 0.59/0.76 tff(183,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.59/0.76 inference(quant_intro,[status(thm)],[182])).
% 0.59/0.76 tff(184,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 0.59/0.76 tff(185,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[184, 183])).
% 0.59/0.76 tff(186,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[185, 181])).
% 0.59/0.76 tff(187,plain,(
% 0.59/0.76 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.59/0.76 inference(skolemize,[status(sab)],[186])).
% 0.59/0.76 tff(188,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[187, 180])).
% 0.59/0.76 tff(189,plain,
% 0.59/0.76 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.59/0.76 inference(modus_ponens,[status(thm)],[188, 178])).
% 0.59/0.76 tff(190,plain,
% 0.59/0.76 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(191,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(192,plain,
% 0.59/0.76 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.59/0.76 inference(rewrite,[status(thm)],[])).
% 0.59/0.76 tff(193,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.76 inference(monotonicity,[status(thm)],[192])).
% 0.59/0.76 tff(194,plain,
% 0.59/0.76 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.76 inference(transitivity,[status(thm)],[193, 191])).
% 0.59/0.76 tff(195,plain,
% 0.59/0.76 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.59/0.77 inference(monotonicity,[status(thm)],[194])).
% 0.59/0.77 tff(196,plain,
% 0.59/0.77 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.77 inference(transitivity,[status(thm)],[195, 190])).
% 0.59/0.77 tff(197,plain,
% 0.59/0.77 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.59/0.77 inference(quant_inst,[status(thm)],[])).
% 0.59/0.77 tff(198,plain,
% 0.59/0.77 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[197, 196])).
% 0.59/0.77 tff(199,plain,
% 0.59/0.77 ((~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[198, 189, 176, 174, 172, 170])).
% 0.59/0.77 tff(200,plain,
% 0.59/0.77 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[199, 168, 141])).
% 0.59/0.77 tff(201,plain,
% 0.59/0.77 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.59/0.77 inference(tautology,[status(thm)],[])).
% 0.59/0.77 tff(202,plain,
% 0.59/0.77 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[201, 200])).
% 0.59/0.77 tff(203,plain,
% 0.59/0.77 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.59/0.77 inference(tautology,[status(thm)],[])).
% 0.59/0.77 tff(204,plain,
% 0.59/0.77 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.59/0.77 inference(unit_resolution,[status(thm)],[203, 200])).
% 0.59/0.77 tff(205,plain,
% 0.59/0.77 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(206,plain,
% 0.59/0.77 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[205])).
% 0.59/0.77 tff(207,plain,
% 0.59/0.77 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(208,plain,
% 0.59/0.77 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 0.59/0.77 inference(bind,[status(th)],[])).
% 0.59/0.77 tff(209,plain,
% 0.59/0.77 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(quant_intro,[status(thm)],[208])).
% 0.59/0.77 tff(210,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 0.59/0.77 tff(211,plain,
% 0.59/0.77 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.59/0.77 tff(212,plain,
% 0.59/0.77 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.59/0.77 tff(213,plain,(
% 0.59/0.77 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(skolemize,[status(sab)],[212])).
% 0.59/0.77 tff(214,plain,
% 0.59/0.77 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.59/0.77 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.59/0.77 tff(215,plain,
% 0.59/0.77 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.59/0.77 inference(rewrite,[status(thm)],[])).
% 0.59/0.77 tff(216,plain,
% 0.59/0.77 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(217,plain,
% 0.61/0.77 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.77 inference(monotonicity,[status(thm)],[216])).
% 0.61/0.77 tff(218,plain,
% 0.61/0.77 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[217, 215])).
% 0.61/0.77 tff(219,plain,
% 0.61/0.77 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.77 inference(quant_inst,[status(thm)],[])).
% 0.61/0.77 tff(220,plain,
% 0.61/0.77 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.61/0.77 tff(221,plain,
% 0.61/0.77 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[220, 214])).
% 0.61/0.77 tff(222,plain,
% 0.61/0.77 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.77 inference(unit_resolution,[status(thm)],[221, 204, 202])).
% 0.61/0.77 tff(223,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(224,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[223])).
% 0.61/0.77 tff(225,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(226,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[225])).
% 0.61/0.77 tff(227,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(transitivity,[status(thm)],[226, 224])).
% 0.61/0.77 tff(228,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(229,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[228])).
% 0.61/0.77 tff(230,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.77 inference(rewrite,[status(thm)],[])).
% 0.61/0.77 tff(231,plain,
% 0.61/0.77 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.61/0.77 inference(bind,[status(th)],[])).
% 0.61/0.77 tff(232,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.77 inference(quant_intro,[status(thm)],[231])).
% 0.61/0.77 tff(233,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.61/0.77 tff(234,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[233, 232])).
% 0.61/0.77 tff(235,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[234, 230])).
% 0.61/0.77 tff(236,plain,(
% 0.61/0.77 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.77 inference(skolemize,[status(sab)],[235])).
% 0.61/0.77 tff(237,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[236, 229])).
% 0.61/0.77 tff(238,plain,
% 0.61/0.77 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.77 inference(modus_ponens,[status(thm)],[237, 227])).
% 0.61/0.77 tff(239,plain,
% 0.61/0.77 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(240,plain,
% 0.61/0.78 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(241,plain,
% 0.61/0.78 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[240])).
% 0.61/0.78 tff(242,plain,
% 0.61/0.78 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.61/0.78 inference(transitivity,[status(thm)],[241, 239])).
% 0.61/0.78 tff(243,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(244,plain,
% 0.61/0.78 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.61/0.78 tff(245,plain,
% 0.61/0.78 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[244, 238, 176, 174, 172, 170])).
% 0.61/0.78 tff(246,plain,
% 0.61/0.78 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[245, 168, 141])).
% 0.61/0.78 tff(247,plain,
% 0.61/0.78 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(248,plain,
% 0.61/0.78 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.61/0.78 inference(quant_inst,[status(thm)],[])).
% 0.61/0.78 tff(249,plain,
% 0.61/0.78 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.61/0.78 tff(250,plain,
% 0.61/0.78 (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[249, 246, 222])).
% 0.61/0.78 tff(251,plain,
% 0.61/0.78 (((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.78 inference(tautology,[status(thm)],[])).
% 0.61/0.78 tff(252,plain,
% 0.61/0.78 (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.78 inference(unit_resolution,[status(thm)],[251, 250])).
% 0.61/0.78 tff(253,plain,
% 0.61/0.78 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 0.61/0.78 inference(symmetry,[status(thm)],[252])).
% 0.61/0.78 tff(254,plain,
% 0.61/0.78 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.61/0.78 inference(transitivity,[status(thm)],[253, 90, 88, 62])).
% 0.61/0.78 tff(255,plain,
% 0.61/0.78 ((k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[254])).
% 0.61/0.78 tff(256,plain,
% 0.61/0.78 ((k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.61/0.78 inference(transitivity,[status(thm)],[255, 1])).
% 0.61/0.78 tff(257,plain,
% 0.61/0.78 ((k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) <=> (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.78 inference(symmetry,[status(thm)],[256])).
% 0.61/0.78 tff(258,plain,
% 0.61/0.78 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(B!1, u1_struct_0(A!0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[253])).
% 0.61/0.78 tff(259,plain,
% 0.61/0.78 (m1_subset_1(B!1, u1_struct_0(A!0)) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.78 inference(symmetry,[status(thm)],[258])).
% 0.61/0.78 tff(260,plain,
% 0.61/0.78 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.78 inference(modus_ponens,[status(thm)],[40, 259])).
% 0.61/0.78 tff(261,plain,
% 0.61/0.78 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.61/0.78 inference(monotonicity,[status(thm)],[60])).
% 0.61/0.78 tff(262,plain,
% 0.61/0.78 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.78 inference(symmetry,[status(thm)],[261])).
% 0.61/0.78 tff(263,plain,
% 0.61/0.78 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(264,plain,
% 0.61/0.78 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[263])).
% 0.61/0.78 tff(265,plain,
% 0.61/0.78 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 0.61/0.78 inference(bind,[status(th)],[])).
% 0.61/0.78 tff(266,plain,
% 0.61/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.61/0.78 inference(quant_intro,[status(thm)],[265])).
% 0.61/0.78 tff(267,plain,
% 0.61/0.78 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.61/0.78 inference(rewrite,[status(thm)],[])).
% 0.61/0.78 tff(268,plain,
% 0.61/0.78 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(269,plain,
% 0.61/0.79 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[268])).
% 0.61/0.79 tff(270,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.61/0.79 tff(271,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.61/0.79 tff(272,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[271, 267])).
% 0.61/0.79 tff(273,plain,(
% 0.61/0.79 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[272])).
% 0.61/0.79 tff(274,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[273, 266])).
% 0.61/0.79 tff(275,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[274, 264])).
% 0.61/0.79 tff(276,plain,
% 0.61/0.79 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(277,plain,
% 0.61/0.79 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(278,plain,
% 0.61/0.79 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.61/0.79 tff(279,plain,
% 0.61/0.79 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[278, 35, 34, 33, 275])).
% 0.61/0.79 tff(280,plain,
% 0.61/0.79 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(281,plain,
% 0.61/0.79 (v10_lattices(k1_lattice2(A!0))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[280, 279])).
% 0.61/0.79 tff(282,plain,
% 0.61/0.79 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[281, 262])).
% 0.61/0.79 tff(283,plain,
% 0.61/0.79 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[60])).
% 0.61/0.79 tff(284,plain,
% 0.61/0.79 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.79 inference(symmetry,[status(thm)],[283])).
% 0.61/0.79 tff(285,plain,
% 0.61/0.79 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[284])).
% 0.61/0.79 tff(286,plain,
% 0.61/0.79 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 0.61/0.79 inference(tautology,[status(thm)],[])).
% 0.61/0.79 tff(287,plain,
% 0.61/0.79 (~v3_struct_0(k1_lattice2(A!0))),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[286, 279])).
% 0.61/0.79 tff(288,plain,
% 0.61/0.79 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[287, 285])).
% 0.61/0.79 tff(289,plain,
% 0.61/0.79 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(290,plain,
% 0.61/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[289])).
% 0.61/0.79 tff(291,plain,
% 0.61/0.79 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(292,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[291])).
% 0.61/0.79 tff(293,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(294,plain,
% 0.61/0.79 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(295,plain,
% 0.61/0.79 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[294])).
% 0.61/0.79 tff(296,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 0.61/0.79 tff(297,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.61/0.79 tff(298,plain,
% 0.61/0.79 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[297, 293])).
% 0.61/0.79 tff(299,plain,(
% 0.61/0.79 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.61/0.79 inference(skolemize,[status(sab)],[298])).
% 0.61/0.79 tff(300,plain,
% 0.61/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[299, 292])).
% 0.61/0.79 tff(301,plain,
% 0.61/0.79 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[300, 290])).
% 0.61/0.79 tff(302,plain,
% 0.61/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(303,plain,
% 0.61/0.79 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(304,plain,
% 0.61/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))))),
% 0.61/0.79 inference(monotonicity,[status(thm)],[303])).
% 0.61/0.79 tff(305,plain,
% 0.61/0.79 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[304, 302])).
% 0.61/0.79 tff(306,plain,
% 0.61/0.79 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.79 inference(quant_inst,[status(thm)],[])).
% 0.61/0.79 tff(307,plain,
% 0.61/0.79 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[306, 305])).
% 0.61/0.79 tff(308,plain,
% 0.61/0.79 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1)),
% 0.61/0.79 inference(unit_resolution,[status(thm)],[307, 301, 204, 288, 282, 260])).
% 0.61/0.79 tff(309,plain,
% 0.61/0.79 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[308, 257])).
% 0.61/0.79 tff(310,plain,
% 0.61/0.79 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))), ((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) | (~v10_lattices(A))))), rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))), ((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(311,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[310])).
% 0.61/0.79 tff(312,plain,
% 0.61/0.79 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(313,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[312])).
% 0.61/0.79 tff(314,plain,
% 0.61/0.79 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(315,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[314])).
% 0.61/0.79 tff(316,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(transitivity,[status(thm)],[315, 313])).
% 0.61/0.79 tff(317,plain,
% 0.61/0.79 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(318,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[317])).
% 0.61/0.79 tff(319,plain,
% 0.61/0.79 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(320,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[319])).
% 0.61/0.79 tff(321,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(rewrite,[status(thm)],[])).
% 0.61/0.79 tff(322,plain,
% 0.61/0.79 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))) <=> (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))) <=> (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))))),
% 0.61/0.79 inference(bind,[status(th)],[])).
% 0.61/0.79 tff(323,plain,
% 0.61/0.79 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(quant_intro,[status(thm)],[322])).
% 0.61/0.79 tff(324,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((~![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t23_filter_0')).
% 0.61/0.79 tff(325,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[324, 323])).
% 0.61/0.79 tff(326,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))) & (k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[325, 321])).
% 0.61/0.79 tff(327,plain,(
% 0.61/0.79 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A))))))),
% 0.61/0.79 inference(skolemize,[status(sab)],[326])).
% 0.61/0.79 tff(328,plain,
% 0.61/0.79 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[327, 320])).
% 0.61/0.79 tff(329,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[328, 318])).
% 0.61/0.79 tff(330,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B)) | (~(k2_filter_0(A, B) = u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[329, 316])).
% 0.61/0.79 tff(331,plain,
% 0.61/0.79 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))),
% 0.61/0.79 inference(modus_ponens,[status(thm)],[330, 311])).
% 0.61/0.79 tff(332,plain,
% 0.61/0.79 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(333,plain,
% 0.61/0.80 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)))) <=> (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(334,plain,
% 0.61/0.80 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[333])).
% 0.61/0.80 tff(335,plain,
% 0.61/0.80 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.80 inference(transitivity,[status(thm)],[334, 332])).
% 0.61/0.80 tff(336,plain,
% 0.61/0.80 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(337,plain,
% 0.61/0.80 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(k2_filter_0(A, B) = u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k4_lattices(A, B, C) = B))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[336, 335])).
% 0.61/0.80 tff(338,plain,
% 0.61/0.80 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[337, 331, 204, 288, 282])).
% 0.61/0.80 tff(339,plain,
% 0.61/0.80 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(340,plain,
% 0.61/0.80 (((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)))),
% 0.61/0.80 inference(rewrite,[status(thm)],[])).
% 0.61/0.80 tff(341,plain,
% 0.61/0.80 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[340])).
% 0.61/0.80 tff(342,plain,
% 0.61/0.80 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)))),
% 0.61/0.80 inference(transitivity,[status(thm)],[341, 339])).
% 0.61/0.80 tff(343,plain,
% 0.61/0.80 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.80 inference(quant_inst,[status(thm)],[])).
% 0.61/0.80 tff(344,plain,
% 0.61/0.80 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = B)) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[343, 342])).
% 0.61/0.80 tff(345,plain,
% 0.61/0.80 ((~(k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[344, 338, 260])).
% 0.61/0.80 tff(346,plain,
% 0.61/0.80 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))),
% 0.61/0.80 inference(unit_resolution,[status(thm)],[345, 309])).
% 0.61/0.80 tff(347,plain,
% 0.61/0.80 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.61/0.80 inference(monotonicity,[status(thm)],[253])).
% 0.61/0.80 tff(348,plain,
% 0.61/0.80 (m1_subset_1(C!2, u1_struct_0(A!0)) <=> m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.80 inference(symmetry,[status(thm)],[347])).
% 0.61/0.80 tff(349,plain,
% 0.61/0.80 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k3_lattices(A!0, B!1, C!2) = B!1))),
% 0.61/0.80 inference(and_elim,[status(thm)],[32])).
% 0.61/0.80 tff(350,plain,
% 0.61/0.80 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.61/0.80 inference(or_elim,[status(thm)],[349])).
% 0.61/0.80 tff(351,plain,
% 0.61/0.80 (m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.80 inference(modus_ponens,[status(thm)],[350, 348])).
% 0.61/0.80 tff(352,plain,
% 0.61/0.80 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = B!1))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = B!1))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(353,plain,
% 0.61/0.81 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = B!1))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(354,plain,
% 0.61/0.81 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = B!1))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = B!1)),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[353, 352])).
% 0.61/0.81 tff(355,plain,
% 0.61/0.81 (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = B!1),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[354, 351, 346])).
% 0.61/0.81 tff(356,plain,
% 0.61/0.81 (v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v6_lattices(k1_lattice2(A!0))),
% 0.61/0.81 inference(monotonicity,[status(thm)],[60])).
% 0.61/0.81 tff(357,plain,
% 0.61/0.81 (v6_lattices(k1_lattice2(A!0)) <=> v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.81 inference(symmetry,[status(thm)],[356])).
% 0.61/0.81 tff(358,plain,
% 0.61/0.81 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v6_lattices(k1_lattice2(A!0))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(359,plain,
% 0.61/0.81 (v6_lattices(k1_lattice2(A!0))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[358, 279])).
% 0.61/0.81 tff(360,plain,
% 0.61/0.81 (v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[359, 357])).
% 0.61/0.81 tff(361,plain,
% 0.61/0.81 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(362,plain,
% 0.61/0.81 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.81 inference(quant_inst,[status(thm)],[])).
% 0.61/0.81 tff(363,plain,
% 0.61/0.81 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.61/0.81 tff(364,plain,
% 0.61/0.81 (~((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[363, 112, 204])).
% 0.61/0.81 tff(365,plain,
% 0.61/0.81 (((~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.81 inference(tautology,[status(thm)],[])).
% 0.61/0.81 tff(366,plain,
% 0.61/0.81 (l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.81 inference(unit_resolution,[status(thm)],[365, 364])).
% 0.61/0.81 tff(367,plain,
% 0.61/0.81 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(368,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[367])).
% 0.61/0.81 tff(369,plain,
% 0.61/0.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(370,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[369])).
% 0.61/0.81 tff(371,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.61/0.81 inference(rewrite,[status(thm)],[])).
% 0.61/0.81 tff(372,plain,
% 0.61/0.81 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))))),
% 0.61/0.81 inference(bind,[status(th)],[])).
% 0.61/0.81 tff(373,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.61/0.81 inference(quant_intro,[status(thm)],[372])).
% 0.61/0.81 tff(374,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v6_lattices(A)) & l1_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k4_lattices(A, B, C) = k2_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k4_lattices')).
% 0.61/0.81 tff(375,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.61/0.81 tff(376,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[375, 371])).
% 0.61/0.81 tff(377,plain,(
% 0.61/0.81 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v6_lattices(A) & l1_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)))),
% 0.61/0.81 inference(skolemize,[status(sab)],[376])).
% 0.61/0.81 tff(378,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[377, 370])).
% 0.61/0.81 tff(379,plain,
% 0.61/0.81 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))),
% 0.61/0.81 inference(modus_ponens,[status(thm)],[378, 368])).
% 0.61/0.81 tff(380,plain,
% 0.61/0.81 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(381,plain,
% 0.65/0.81 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(382,plain,
% 0.65/0.81 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2))))),
% 0.65/0.81 inference(monotonicity,[status(thm)],[381])).
% 0.65/0.81 tff(383,plain,
% 0.65/0.81 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[382, 380])).
% 0.65/0.81 tff(384,plain,
% 0.65/0.81 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.65/0.81 inference(quant_inst,[status(thm)],[])).
% 0.65/0.81 tff(385,plain,
% 0.65/0.81 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k4_lattices(A, B, C) = k2_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v6_lattices(A)) | (~l1_lattices(A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[384, 383])).
% 0.65/0.81 tff(386,plain,
% 0.65/0.81 (k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)),
% 0.65/0.81 inference(unit_resolution,[status(thm)],[385, 379, 288, 366, 360, 260, 351])).
% 0.65/0.81 tff(387,plain,
% 0.65/0.81 (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k4_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)),
% 0.65/0.81 inference(symmetry,[status(thm)],[386])).
% 0.65/0.81 tff(388,plain,
% 0.65/0.81 (^[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))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(389,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[388])).
% 0.65/0.81 tff(390,plain,
% 0.65/0.81 (^[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))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(391,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[390])).
% 0.65/0.81 tff(392,plain,
% 0.65/0.81 (^[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))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(393,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[392])).
% 0.65/0.81 tff(394,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(transitivity,[status(thm)],[393, 391])).
% 0.65/0.81 tff(395,plain,
% 0.65/0.81 (^[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)))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(396,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[395])).
% 0.65/0.81 tff(397,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(398,plain,
% 0.65/0.81 (^[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)))))))),
% 0.65/0.81 inference(bind,[status(th)],[])).
% 0.65/0.81 tff(399,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(quant_intro,[status(thm)],[398])).
% 0.65/0.81 tff(400,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/sandbox2/benchmark/theBenchmark.p','d2_lattices')).
% 0.65/0.81 tff(401,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[400, 399])).
% 0.65/0.81 tff(402,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[401, 397])).
% 0.65/0.81 tff(403,plain,(
% 0.65/0.81 ![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)))))),
% 0.65/0.81 inference(skolemize,[status(sab)],[402])).
% 0.65/0.81 tff(404,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[403, 396])).
% 0.65/0.81 tff(405,plain,
% 0.65/0.81 (![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)))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[404, 394])).
% 0.65/0.81 tff(406,plain,
% 0.65/0.81 (![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)))))),
% 0.65/0.81 inference(modus_ponens,[status(thm)],[405, 389])).
% 0.65/0.81 tff(407,plain,
% 0.65/0.81 (((~![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(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), 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(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)))))),
% 0.65/0.81 inference(rewrite,[status(thm)],[])).
% 0.65/0.81 tff(408,plain,
% 0.65/0.81 ((~![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(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C)))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(409,plain,
% 0.65/0.82 ((~![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(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[408, 407])).
% 0.65/0.82 tff(410,plain,
% 0.65/0.82 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[409, 406])).
% 0.65/0.82 tff(411,plain,
% 0.65/0.82 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[410, 366, 288])).
% 0.65/0.82 tff(412,plain,
% 0.65/0.82 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(413,plain,
% 0.65/0.82 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(414,plain,
% 0.65/0.82 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B, C))))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.65/0.82 tff(415,plain,
% 0.65/0.82 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[414, 411, 260])).
% 0.65/0.82 tff(416,plain,
% 0.65/0.82 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2)))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(417,plain,
% 0.65/0.82 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2)))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(418,plain,
% 0.65/0.82 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.65/0.82 tff(419,plain,
% 0.65/0.82 (k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2)),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[418, 351, 415])).
% 0.65/0.82 tff(420,plain,
% 0.65/0.82 (k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2) = k2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), B!1, C!2)),
% 0.65/0.82 inference(symmetry,[status(thm)],[419])).
% 0.65/0.82 tff(421,plain,
% 0.65/0.82 (((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.82 inference(tautology,[status(thm)],[])).
% 0.65/0.82 tff(422,plain,
% 0.65/0.82 (u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.82 inference(unit_resolution,[status(thm)],[421, 250])).
% 0.65/0.82 tff(423,plain,
% 0.65/0.82 (u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u2_lattices(A!0)),
% 0.65/0.82 inference(symmetry,[status(thm)],[422])).
% 0.65/0.82 tff(424,plain,
% 0.65/0.82 (k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2)),
% 0.65/0.82 inference(monotonicity,[status(thm)],[253, 253, 253, 423])).
% 0.65/0.82 tff(425,plain,
% 0.65/0.82 (k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2) = k2_binop_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), B!1, C!2)),
% 0.65/0.82 inference(symmetry,[status(thm)],[424])).
% 0.65/0.82 tff(426,plain,
% 0.65/0.82 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(427,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[426])).
% 0.65/0.82 tff(428,plain,
% 0.65/0.82 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(429,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[428])).
% 0.65/0.82 tff(430,plain,
% 0.65/0.82 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(431,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[430])).
% 0.65/0.82 tff(432,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(transitivity,[status(thm)],[431, 429])).
% 0.65/0.82 tff(433,plain,
% 0.65/0.82 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(434,plain,
% 0.65/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[433])).
% 0.65/0.82 tff(435,plain,
% 0.65/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(436,plain,
% 0.65/0.82 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))), ((m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))))), rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), ((((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))))),
% 0.65/0.82 inference(bind,[status(th)],[])).
% 0.65/0.82 tff(437,plain,
% 0.65/0.82 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(quant_intro,[status(thm)],[436])).
% 0.65/0.82 tff(438,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d1_lattices')).
% 0.65/0.82 tff(439,plain,
% 0.65/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[438, 437])).
% 0.65/0.82 tff(440,plain,
% 0.65/0.82 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[439, 435])).
% 0.65/0.82 tff(441,plain,(
% 0.65/0.82 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(skolemize,[status(sab)],[440])).
% 0.65/0.82 tff(442,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[441, 434])).
% 0.65/0.82 tff(443,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))) | (~l2_lattices(A)))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[442, 432])).
% 0.65/0.82 tff(444,plain,
% 0.65/0.82 (![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[443, 427])).
% 0.65/0.82 tff(445,plain,
% 0.65/0.82 (((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))),
% 0.65/0.82 inference(rewrite,[status(thm)],[])).
% 0.65/0.82 tff(446,plain,
% 0.65/0.82 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C)))))),
% 0.65/0.82 inference(quant_inst,[status(thm)],[])).
% 0.65/0.82 tff(447,plain,
% 0.65/0.82 ((~![A: $i] : (v3_struct_0(A) | (~l2_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (k1_lattices(A, B, C) = k2_binop_1(u1_struct_0(A), u1_struct_0(A), u1_struct_0(A), u2_lattices(A), B, C)))))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.65/0.82 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.65/0.82 tff(448,plain,
% 0.65/0.82 ((~l2_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[447, 35, 444])).
% 0.65/0.83 tff(449,plain,
% 0.65/0.83 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[448, 145])).
% 0.65/0.83 tff(450,plain,
% 0.65/0.83 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), 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))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(451,plain,
% 0.65/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C))))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(452,plain,
% 0.65/0.83 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B, C))))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.65/0.83 tff(453,plain,
% 0.65/0.83 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[452, 40, 449])).
% 0.65/0.83 tff(454,plain,
% 0.65/0.83 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(455,plain,
% 0.65/0.83 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(456,plain,
% 0.65/0.83 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (k1_lattices(A!0, B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[455, 454])).
% 0.65/0.83 tff(457,plain,
% 0.65/0.83 (k1_lattices(A!0, B!1, C!2) = k2_binop_1(u1_struct_0(A!0), u1_struct_0(A!0), u1_struct_0(A!0), u2_lattices(A!0), B!1, C!2)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[456, 350, 453])).
% 0.65/0.83 tff(458,plain,
% 0.65/0.83 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(459,plain,
% 0.65/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[458])).
% 0.65/0.83 tff(460,plain,
% 0.65/0.83 (^[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)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(461,plain,
% 0.65/0.83 (![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)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[460])).
% 0.65/0.83 tff(462,plain,
% 0.65/0.83 (![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))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(463,plain,
% 0.65/0.83 (^[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))))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(464,plain,
% 0.65/0.83 (![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))))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[463])).
% 0.65/0.83 tff(465,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v10_lattices(A)) => (((((((~v3_struct_0(A)) & v4_lattices(A)) & v5_lattices(A)) & v6_lattices(A)) & v7_lattices(A)) & v8_lattices(A)) & v9_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc1_lattices')).
% 0.65/0.83 tff(466,plain,
% 0.65/0.83 (![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))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.65/0.83 tff(467,plain,
% 0.65/0.83 (![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))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[466, 462])).
% 0.65/0.83 tff(468,plain,(
% 0.65/0.83 ![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))))),
% 0.65/0.83 inference(skolemize,[status(sab)],[467])).
% 0.65/0.83 tff(469,plain,
% 0.65/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[468, 461])).
% 0.65/0.83 tff(470,plain,
% 0.65/0.83 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[469, 459])).
% 0.65/0.83 tff(471,plain,
% 0.65/0.83 (((~![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)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(472,plain,
% 0.65/0.83 ((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)))))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(473,plain,
% 0.65/0.83 (((~![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))))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[472])).
% 0.65/0.83 tff(474,plain,
% 0.65/0.83 (((~![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)))))),
% 0.65/0.83 inference(transitivity,[status(thm)],[473, 471])).
% 0.65/0.83 tff(475,plain,
% 0.65/0.83 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v4_lattices(A)) | (~v5_lattices(A)) | (~v6_lattices(A)) | (~v7_lattices(A)) | (~v8_lattices(A)) | (~v9_lattices(A)))) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))) | (~v10_lattices(A!0)))),
% 0.65/0.83 inference(quant_inst,[status(thm)],[])).
% 0.65/0.83 tff(476,plain,
% 0.65/0.83 ((~![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))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[475, 474])).
% 0.65/0.83 tff(477,plain,
% 0.65/0.83 (~(v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0)))),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[476, 35, 34, 33, 470])).
% 0.65/0.83 tff(478,plain,
% 0.65/0.83 ((v3_struct_0(A!0) | (~v4_lattices(A!0)) | (~v5_lattices(A!0)) | (~v6_lattices(A!0)) | (~v7_lattices(A!0)) | (~v8_lattices(A!0)) | (~v9_lattices(A!0))) | v4_lattices(A!0)),
% 0.65/0.83 inference(tautology,[status(thm)],[])).
% 0.65/0.83 tff(479,plain,
% 0.65/0.83 (v4_lattices(A!0)),
% 0.65/0.83 inference(unit_resolution,[status(thm)],[478, 477])).
% 0.65/0.83 tff(480,plain,
% 0.65/0.83 (^[A: $i, B: $i, C: $i] : refl((v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(481,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[480])).
% 0.65/0.83 tff(482,plain,
% 0.65/0.83 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), (((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(483,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[482])).
% 0.65/0.83 tff(484,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(485,plain,
% 0.65/0.83 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))), ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> (((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))))), rewrite((((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), (((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))))),
% 0.65/0.83 inference(bind,[status(th)],[])).
% 0.65/0.83 tff(486,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.65/0.83 inference(quant_intro,[status(thm)],[485])).
% 0.65/0.83 tff(487,axiom,(![A: $i, B: $i, C: $i] : ((((((~v3_struct_0(A)) & v4_lattices(A)) & l2_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) & m1_subset_1(C, u1_struct_0(A))) => (k3_lattices(A, B, C) = k1_lattices(A, B, C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k3_lattices')).
% 0.65/0.83 tff(488,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.65/0.83 tff(489,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[488, 484])).
% 0.65/0.83 tff(490,plain,(
% 0.65/0.83 ![A: $i, B: $i, C: $i] : ((~((~v3_struct_0(A)) & v4_lattices(A) & l2_lattices(A) & m1_subset_1(B, u1_struct_0(A)) & m1_subset_1(C, u1_struct_0(A)))) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)))),
% 0.65/0.83 inference(skolemize,[status(sab)],[489])).
% 0.65/0.83 tff(491,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[490, 483])).
% 0.65/0.83 tff(492,plain,
% 0.65/0.83 (![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))),
% 0.65/0.83 inference(modus_ponens,[status(thm)],[491, 481])).
% 0.65/0.83 tff(493,plain,
% 0.65/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(494,plain,
% 0.65/0.83 ((v3_struct_0(A!0) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)))),
% 0.65/0.83 inference(rewrite,[status(thm)],[])).
% 0.65/0.83 tff(495,plain,
% 0.65/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2))))),
% 0.65/0.83 inference(monotonicity,[status(thm)],[494])).
% 0.65/0.83 tff(496,plain,
% 0.65/0.83 (((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)))),
% 0.65/0.83 inference(transitivity,[status(thm)],[495, 493])).
% 0.65/0.83 tff(497,plain,
% 0.65/0.83 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | (v3_struct_0(A!0) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v4_lattices(A!0)) | (~l2_lattices(A!0)) | (~m1_subset_1(B!1, u1_struct_0(A!0))))),
% 0.67/0.84 inference(quant_inst,[status(thm)],[])).
% 0.67/0.84 tff(498,plain,
% 0.67/0.84 ((~![A: $i, B: $i, C: $i] : (v3_struct_0(A) | (k3_lattices(A, B, C) = k1_lattices(A, B, C)) | (~m1_subset_1(C, u1_struct_0(A))) | (~v4_lattices(A)) | (~l2_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))) | v3_struct_0(A!0) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2))),
% 0.67/0.84 inference(modus_ponens,[status(thm)],[497, 496])).
% 0.67/0.84 tff(499,plain,
% 0.67/0.84 ((~l2_lattices(A!0)) | (~v4_lattices(A!0)) | (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2))),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[498, 35, 40, 350, 492])).
% 0.67/0.84 tff(500,plain,
% 0.67/0.84 (k3_lattices(A!0, B!1, C!2) = k1_lattices(A!0, B!1, C!2)),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[499, 479, 145])).
% 0.67/0.84 tff(501,plain,
% 0.67/0.84 (k3_lattices(A!0, B!1, C!2) = B!1),
% 0.67/0.84 inference(transitivity,[status(thm)],[500, 457, 425, 420, 387, 355])).
% 0.67/0.84 tff(502,plain,
% 0.67/0.84 (~(k3_lattices(A!0, B!1, C!2) = B!1)),
% 0.67/0.84 inference(or_elim,[status(thm)],[349])).
% 0.67/0.84 tff(503,plain,
% 0.67/0.84 ($false),
% 0.67/0.84 inference(unit_resolution,[status(thm)],[502, 501])).
% 0.67/0.84 % SZS output end Proof
% 0.67/0.84 % E exiting
%------------------------------------------------------------------------------