%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : LAT296+1 : TPTP v9.0.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:14:13 AM UTC 2025
% Result : Theorem 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LAT296+1 : TPTP v9.0.0. Released v3.4.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n014.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Thu Jun 19 20:05:09 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.44 % SZS status Theorem
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 tff(r2_lattices_type, type, (
% 0.19/0.44 r2_lattices: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(tptp_fun_C_2_type, type, (
% 0.19/0.44 tptp_fun_C_2: $i)).
% 0.19/0.44 tff(k7_lattices_type, type, (
% 0.19/0.44 k7_lattices: ( $i * $i ) > $i)).
% 0.19/0.44 tff(tptp_fun_A_0_type, type, (
% 0.19/0.44 tptp_fun_A_0: $i)).
% 0.19/0.44 tff(tptp_fun_B_1_type, type, (
% 0.19/0.44 tptp_fun_B_1: $i)).
% 0.19/0.44 tff(m1_subset_1_type, type, (
% 0.19/0.44 m1_subset_1: ( $i * $i ) > $o)).
% 0.19/0.44 tff(u1_struct_0_type, type, (
% 0.19/0.44 u1_struct_0: $i > $i)).
% 0.19/0.44 tff(v16_lattices_type, type, (
% 0.19/0.44 v16_lattices: $i > $o)).
% 0.19/0.44 tff(v15_lattices_type, type, (
% 0.19/0.44 v15_lattices: $i > $o)).
% 0.19/0.44 tff(v14_lattices_type, type, (
% 0.19/0.44 v14_lattices: $i > $o)).
% 0.19/0.44 tff(v13_lattices_type, type, (
% 0.19/0.44 v13_lattices: $i > $o)).
% 0.19/0.44 tff(v11_lattices_type, type, (
% 0.19/0.44 v11_lattices: $i > $o)).
% 0.19/0.44 tff(v3_struct_0_type, type, (
% 0.19/0.44 v3_struct_0: $i > $o)).
% 0.19/0.44 tff(v17_lattices_type, type, (
% 0.19/0.44 v17_lattices: $i > $o)).
% 0.19/0.44 tff(l3_lattices_type, type, (
% 0.19/0.44 l3_lattices: $i > $o)).
% 0.19/0.44 tff(v10_lattices_type, type, (
% 0.19/0.44 v10_lattices: $i > $o)).
% 0.19/0.44 tff(g3_lattices_type, type, (
% 0.19/0.44 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.19/0.44 tff(u1_lattices_type, type, (
% 0.19/0.44 u1_lattices: $i > $i)).
% 0.19/0.44 tff(u2_lattices_type, type, (
% 0.19/0.44 u2_lattices: $i > $i)).
% 0.19/0.44 tff(m1_relset_1_type, type, (
% 0.19/0.44 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(k2_zfmisc_1_type, type, (
% 0.19/0.44 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.19/0.44 tff(m2_relset_1_type, type, (
% 0.19/0.44 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(v1_funct_2_type, type, (
% 0.19/0.44 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.19/0.44 tff(v1_funct_1_type, type, (
% 0.19/0.44 v1_funct_1: $i > $o)).
% 0.19/0.44 tff(l2_lattices_type, type, (
% 0.19/0.44 l2_lattices: $i > $o)).
% 0.19/0.44 tff(l1_lattices_type, type, (
% 0.19/0.44 l1_lattices: $i > $o)).
% 0.19/0.44 tff(1,plain,
% 0.19/0.44 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(2,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[1])).
% 0.19/0.44 tff(3,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(rewrite(((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) <=> (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v17_lattices(A)) <=> (~(v3_struct_0(A) | (~v17_lattices(A))))), ((~((~v3_struct_0(A)) & v17_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v17_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v17_lattices(A))))) <=> (v3_struct_0(A) | (~v17_lattices(A)))), ((~((~v3_struct_0(A)) & v17_lattices(A))) <=> (v3_struct_0(A) | (~v17_lattices(A))))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (v3_struct_0(A) | (~v17_lattices(A)))))), rewrite(((~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (v3_struct_0(A) | (~v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))), (((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(4,plain,
% 0.19/0.44 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[3])).
% 0.19/0.44 tff(5,plain,
% 0.19/0.44 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.19/0.44 inference(rewrite,[status(thm)],[])).
% 0.19/0.44 tff(6,plain,
% 0.19/0.44 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A)) & v14_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)) & v15_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A))), ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)))), (((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))) <=> (((~v3_struct_0(A)) & v17_lattices(A)) => ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))))), rewrite((((~v3_struct_0(A)) & v17_lattices(A)) => ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))) <=> ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))) <=> ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> (l3_lattices(A) => ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))))), rewrite((l3_lattices(A) => ((~((~v3_struct_0(A)) & v17_lattices(A))) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))), ((l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))))),
% 0.19/0.44 inference(bind,[status(th)],[])).
% 0.19/0.44 tff(7,plain,
% 0.19/0.44 (![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.19/0.44 inference(quant_intro,[status(thm)],[6])).
% 0.19/0.44 tff(8,axiom,(![A: $i] : (l3_lattices(A) => (((~v3_struct_0(A)) & v17_lattices(A)) => ((((((~v3_struct_0(A)) & v11_lattices(A)) & v13_lattices(A)) & v14_lattices(A)) & v15_lattices(A)) & v16_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cc5_lattices')).
% 0.19/0.44 tff(9,plain,
% 0.19/0.44 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[8, 7])).
% 0.19/0.44 tff(10,plain,
% 0.19/0.44 (![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[9, 5])).
% 0.19/0.44 tff(11,plain,(
% 0.19/0.44 ![A: $i] : ((~l3_lattices(A)) | ((~v3_struct_0(A)) & v11_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A)) | (~((~v3_struct_0(A)) & v17_lattices(A))))),
% 0.19/0.44 inference(skolemize,[status(sab)],[10])).
% 0.19/0.44 tff(12,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[11, 4])).
% 0.19/0.44 tff(13,plain,
% 0.19/0.44 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))),
% 0.19/0.44 inference(modus_ponens,[status(thm)],[12, 2])).
% 0.19/0.44 tff(14,plain,
% 0.19/0.44 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(15,plain,
% 0.19/0.45 (((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))) <=> ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(16,plain,
% 0.19/0.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))),
% 0.19/0.45 inference(monotonicity,[status(thm)],[15])).
% 0.19/0.45 tff(17,plain,
% 0.19/0.45 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)) & ((~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.19/0.45 inference(transitivity,[status(thm)],[16, 14])).
% 0.19/0.45 tff(18,plain,
% 0.19/0.45 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(19,plain,
% 0.19/0.45 ((~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => ((C = D) => (k7_lattices(A, C) = k7_lattices(B, D))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B))))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(20,axiom,(~![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v17_lattices(A)) & l3_lattices(A)) => ![B: $i] : (((((~v3_struct_0(B)) & v10_lattices(B)) & v17_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(B)) => ((C = D) => (k7_lattices(A, C) = k7_lattices(B, D))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t12_filter_2')).
% 0.19/0.45 tff(21,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.19/0.45 tff(22,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[21, 18])).
% 0.19/0.45 tff(23,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.19/0.45 tff(24,plain,
% 0.19/0.45 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A))) | ![B: $i] : (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | (k7_lattices(A, C) = k7_lattices(B, C))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[23, 18])).
% 0.19/0.45 tff(25,plain,
% 0.19/0.45 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0) & (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))) & (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.19/0.45 tff(26,plain,
% 0.19/0.45 (l3_lattices(B!1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(27,plain,
% 0.19/0.45 (v17_lattices(B!1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(28,plain,
% 0.19/0.45 (~v3_struct_0(B!1)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(29,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)))) | (~v17_lattices(B!1)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)))) | (~v17_lattices(B!1)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(30,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)))) | (~v17_lattices(B!1)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(31,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)))) | (~v17_lattices(B!1))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[30, 29])).
% 0.19/0.45 tff(32,plain,
% 0.19/0.45 (~(v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[31, 28, 27, 26, 13])).
% 0.19/0.45 tff(33,plain,
% 0.19/0.45 ((v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1))) | v16_lattices(B!1)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(34,plain,
% 0.19/0.45 (v16_lattices(B!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[33, 32])).
% 0.19/0.45 tff(35,plain,
% 0.19/0.45 ((v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1))) | v15_lattices(B!1)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(36,plain,
% 0.19/0.45 (v15_lattices(B!1)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[35, 32])).
% 0.19/0.45 tff(37,plain,
% 0.19/0.45 (l3_lattices(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(38,plain,
% 0.19/0.45 (v17_lattices(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(39,plain,
% 0.19/0.45 (~v3_struct_0(A!0)),
% 0.19/0.45 inference(and_elim,[status(thm)],[25])).
% 0.19/0.45 tff(40,plain,
% 0.19/0.45 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(41,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0)))),
% 0.19/0.45 inference(quant_inst,[status(thm)],[])).
% 0.19/0.45 tff(42,plain,
% 0.19/0.45 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~(v3_struct_0(A) | (~v11_lattices(A)) | (~v13_lattices(A)) | (~v14_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))) | (~v17_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))) | (~v17_lattices(A!0))),
% 0.19/0.45 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.19/0.45 tff(43,plain,
% 0.19/0.45 (~(v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)))),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[42, 39, 38, 37, 13])).
% 0.19/0.45 tff(44,plain,
% 0.19/0.45 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v15_lattices(A!0)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(45,plain,
% 0.19/0.45 (v15_lattices(A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[44, 43])).
% 0.19/0.45 tff(46,plain,
% 0.19/0.45 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v16_lattices(A!0)),
% 0.19/0.45 inference(tautology,[status(thm)],[])).
% 0.19/0.45 tff(47,plain,
% 0.19/0.45 (v16_lattices(A!0)),
% 0.19/0.45 inference(unit_resolution,[status(thm)],[46, 43])).
% 0.19/0.45 tff(48,plain,
% 0.19/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(49,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[48])).
% 0.19/0.45 tff(50,plain,
% 0.19/0.45 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(51,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[50])).
% 0.19/0.45 tff(52,plain,
% 0.19/0.45 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(53,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[52])).
% 0.19/0.45 tff(54,plain,
% 0.19/0.45 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.45 inference(transitivity,[status(thm)],[53, 51])).
% 0.19/0.45 tff(55,plain,
% 0.19/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)) <=> (~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))) <=> (~(~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))))), rewrite((~(~(v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))), ((~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))), (((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))) <=> ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))))), rewrite(((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))), (((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))) <=> (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))))), (![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))) <=> ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A))) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))))),
% 0.19/0.45 inference(bind,[status(th)],[])).
% 0.19/0.45 tff(56,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.45 inference(quant_intro,[status(thm)],[55])).
% 0.19/0.45 tff(57,plain,
% 0.19/0.45 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.19/0.45 inference(rewrite,[status(thm)],[])).
% 0.19/0.45 tff(58,plain,
% 0.19/0.45 (^[A: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B)) & v16_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B)) & v16_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B))), (((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B)))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B)) & l3_lattices(B)))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))), ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) <=> ((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))), trans(monotonicity(quant_intro(proof_bind(^[C: $i] : trans(monotonicity(quant_intro(proof_bind(^[D: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(trans(quant_intro(proof_bind(^[F: $i] : trans(monotonicity(trans(monotonicity(rewrite((((C = E) & (D = F)) & r2_lattices(A, C, D)) <=> ((C = E) & (D = F) & r2_lattices(A, C, D))), (((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)) <=> (((C = E) & (D = F) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))), rewrite((((C = E) & (D = F) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)) <=> ((~((C = E) & (D = F) & r2_lattices(A, C, D))) | r2_lattices(B, E, F))), (((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)) <=> ((~((C = E) & (D = F) & r2_lattices(A, C, D))) | r2_lattices(B, E, F)))), ((m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))) <=> (m1_subset_1(F, u1_struct_0(B)) => ((~((C = E) & (D = F) & r2_lattices(A, C, D))) | r2_lattices(B, E, F))))), rewrite((m1_subset_1(F, u1_struct_0(B)) => ((~((C = E) & (D = F) & r2_lattices(A, C, D))) | r2_lattices(B, E, F))) <=> (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))), ((m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))) <=> (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))) <=> ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B)))))), trans(der(![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B)))) <=> ![F: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)))), elim_unused(![F: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)))), (![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E))))), (![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E))))), ((m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))) <=> (m1_subset_1(E, u1_struct_0(B)) => ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)))))), rewrite((m1_subset_1(E, u1_struct_0(B)) => ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B))))), ((m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B))))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))) <=> ![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B)))))), trans(trans(der(![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B)))) <=> ![E: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))), elim_unused(![E: $i] : ((~m1_subset_1(C, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))), (![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B)))) <=> ((~m1_subset_1(C, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))), rewrite(((~m1_subset_1(C, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))), (![E: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | r2_lattices(B, E, D) | (~r2_lattices(A, C, D)) | (~(C = E)) | (~m1_subset_1(E, u1_struct_0(B)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))), (![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))) <=> (m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))), ((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))) <=> ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))), (![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))) <=> ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))) <=> (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))), rewrite((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))), ((m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))), (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))))) <=> ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))), rewrite(((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))) <=> ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))), (((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))))) <=> ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))))) <=> (((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)) => ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))))), rewrite((((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)) => ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))))) <=> ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))), (((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))))) <=> ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))))), (![B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))))) <=> ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(59,plain,
% 0.19/0.46 (![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F))))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[58])).
% 0.19/0.46 tff(60,axiom,(![A: $i] : ((((((~v3_struct_0(A)) & v10_lattices(A)) & v15_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![B: $i] : ((((((~v3_struct_0(B)) & v10_lattices(B)) & v15_lattices(B)) & v16_lattices(B)) & l3_lattices(B)) => ((g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B))) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ![D: $i] : (m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : (m1_subset_1(E, u1_struct_0(B)) => ![F: $i] : (m1_subset_1(F, u1_struct_0(B)) => ((((C = E) & (D = F)) & r2_lattices(A, C, D)) => r2_lattices(B, E, F)))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t11_filter_2')).
% 0.19/0.46 tff(61,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.19/0.46 tff(62,plain,
% 0.19/0.46 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.19/0.46 tff(63,plain,(
% 0.19/0.46 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.19/0.46 inference(skolemize,[status(sab)],[62])).
% 0.19/0.46 tff(64,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.19/0.46 tff(65,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.19/0.46 tff(66,plain,
% 0.19/0.46 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[65, 49])).
% 0.19/0.46 tff(67,plain,
% 0.19/0.46 (v10_lattices(A!0)),
% 0.19/0.46 inference(and_elim,[status(thm)],[25])).
% 0.19/0.46 tff(68,plain,
% 0.19/0.46 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(69,plain,
% 0.19/0.46 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A!0, C, D)))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(70,plain,
% 0.19/0.46 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A!0, C, D))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[69])).
% 0.19/0.46 tff(71,plain,
% 0.19/0.46 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A!0, C, D))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))))),
% 0.19/0.46 inference(transitivity,[status(thm)],[70, 68])).
% 0.19/0.46 tff(72,plain,
% 0.19/0.46 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A!0, C, D))))))),
% 0.19/0.46 inference(quant_inst,[status(thm)],[])).
% 0.19/0.46 tff(73,plain,
% 0.19/0.46 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v15_lattices(A)) | (~v16_lattices(A)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(D, u1_struct_0(A))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~r2_lattices(A, C, D))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))),
% 0.19/0.46 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.19/0.46 tff(74,plain,
% 0.19/0.46 ((~v15_lattices(A!0)) | (~v16_lattices(A!0)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[73, 39, 67, 37, 66])).
% 0.19/0.46 tff(75,plain,
% 0.19/0.46 (![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))),
% 0.19/0.46 inference(unit_resolution,[status(thm)],[74, 47, 45])).
% 0.19/0.46 tff(76,plain,
% 0.19/0.46 (v10_lattices(B!1)),
% 0.19/0.46 inference(and_elim,[status(thm)],[25])).
% 0.19/0.46 tff(77,plain,
% 0.19/0.46 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 0.19/0.46 inference(and_elim,[status(thm)],[25])).
% 0.19/0.46 tff(78,plain,
% 0.19/0.46 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | (v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(79,plain,
% 0.19/0.46 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) <=> (v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.46 inference(rewrite,[status(thm)],[])).
% 0.19/0.46 tff(80,plain,
% 0.19/0.46 (^[C: $i] : rewrite(((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))) <=> ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.46 inference(bind,[status(th)],[])).
% 0.19/0.46 tff(81,plain,
% 0.19/0.46 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))),
% 0.19/0.46 inference(quant_intro,[status(thm)],[80])).
% 0.19/0.46 tff(82,plain,
% 0.19/0.46 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.46 inference(monotonicity,[status(thm)],[81])).
% 0.19/0.46 tff(83,plain,
% 0.19/0.46 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D))))) <=> (v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[82, 79])).
% 0.19/0.47 tff(84,plain,
% 0.19/0.47 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | (v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[83])).
% 0.19/0.47 tff(85,plain,
% 0.19/0.47 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1))))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[84, 78])).
% 0.19/0.47 tff(86,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | (~m1_subset_1(C, u1_struct_0(B!1))) | r2_lattices(B!1, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(87,plain,
% 0.19/0.47 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B))) | (~m1_subset_1(C, u1_struct_0(B))) | r2_lattices(B, C, D) | (~m1_subset_1(D, u1_struct_0(A!0))) | (~r2_lattices(A!0, C, D)))))) | v3_struct_0(B!1) | (~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)))) | (~v16_lattices(B!1)) | (~v15_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.19/0.47 tff(88,plain,
% 0.19/0.47 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[87, 77, 28, 76, 26, 75, 36, 34])).
% 0.19/0.47 tff(89,plain,
% 0.19/0.47 (^[A: $i, B: $i] : refl((m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A))) <=> (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(90,plain,
% 0.19/0.47 (![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[89])).
% 0.19/0.47 tff(91,plain,
% 0.19/0.47 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))))), ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))))), (((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(92,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[91])).
% 0.19/0.47 tff(93,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(94,plain,
% 0.19/0.47 (^[A: $i, B: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> (((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))), (((((~v3_struct_0(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(95,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((((~v3_struct_0(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[94])).
% 0.19/0.47 tff(96,axiom,(![A: $i, B: $i] : ((((~v3_struct_0(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k7_lattices')).
% 0.19/0.47 tff(97,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.19/0.47 tff(98,plain,
% 0.19/0.47 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[97, 93])).
% 0.19/0.47 tff(99,plain,(
% 0.19/0.47 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k7_lattices(A, B), u1_struct_0(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[98])).
% 0.19/0.47 tff(100,plain,
% 0.19/0.47 (![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[99, 92])).
% 0.19/0.47 tff(101,plain,
% 0.19/0.47 (![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[100, 90])).
% 0.19/0.47 tff(102,plain,
% 0.19/0.47 (~((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)))),
% 0.19/0.47 inference(and_elim,[status(thm)],[25])).
% 0.19/0.47 tff(103,plain,
% 0.19/0.47 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.19/0.47 inference(or_elim,[status(thm)],[102])).
% 0.19/0.47 tff(104,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(105,plain,
% 0.19/0.47 ((m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(106,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[105])).
% 0.19/0.47 tff(107,plain,
% 0.19/0.47 (((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)))),
% 0.19/0.47 inference(transitivity,[status(thm)],[106, 104])).
% 0.19/0.47 tff(108,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(109,plain,
% 0.19/0.47 ((~![A: $i, B: $i] : (m1_subset_1(k7_lattices(A, B), u1_struct_0(A)) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~l3_lattices(A!0)) | m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.19/0.47 tff(110,plain,
% 0.19/0.47 (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[109, 39, 37, 103, 101])).
% 0.19/0.47 tff(111,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(112,plain,
% 0.19/0.47 (((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))))) <=> ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(113,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))))),
% 0.19/0.47 inference(monotonicity,[status(thm)],[112])).
% 0.19/0.47 tff(114,plain,
% 0.19/0.47 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1)))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D))))),
% 0.19/0.47 inference(transitivity,[status(thm)],[113, 111])).
% 0.19/0.47 tff(115,plain,
% 0.19/0.47 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(116,plain,
% 0.19/0.47 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | (~r2_lattices(A!0, C, D)) | r2_lattices(B!1, C, D) | (~m1_subset_1(C, u1_struct_0(B!1)))))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[115, 114])).
% 0.19/0.47 tff(117,plain,
% 0.19/0.47 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[116, 110, 88])).
% 0.19/0.47 tff(118,plain,
% 0.19/0.47 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 0.19/0.47 inference(symmetry,[status(thm)],[77])).
% 0.19/0.47 tff(119,plain,
% 0.19/0.47 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(120,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[119])).
% 0.19/0.47 tff(121,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(122,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.19/0.47 tff(123,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.19/0.47 tff(124,plain,(
% 0.19/0.47 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.47 inference(skolemize,[status(sab)],[123])).
% 0.19/0.47 tff(125,plain,
% 0.19/0.47 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.19/0.47 tff(126,plain,
% 0.19/0.47 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(127,plain,
% 0.19/0.47 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.19/0.47 tff(128,plain,
% 0.19/0.47 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(129,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[128])).
% 0.19/0.47 tff(130,plain,
% 0.19/0.47 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(131,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[130])).
% 0.19/0.47 tff(132,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(133,plain,
% 0.19/0.47 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(134,plain,
% 0.19/0.47 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[133])).
% 0.19/0.47 tff(135,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.19/0.47 tff(136,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.19/0.47 tff(137,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.19/0.47 tff(138,plain,(
% 0.19/0.47 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.19/0.47 inference(skolemize,[status(sab)],[137])).
% 0.19/0.47 tff(139,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.19/0.47 tff(140,plain,
% 0.19/0.47 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[139, 129])).
% 0.19/0.47 tff(141,plain,
% 0.19/0.47 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(142,plain,
% 0.19/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.19/0.47 inference(quant_inst,[status(thm)],[])).
% 0.19/0.47 tff(143,plain,
% 0.19/0.47 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 0.19/0.47 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.19/0.47 tff(144,plain,
% 0.19/0.47 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[143, 26, 140])).
% 0.19/0.47 tff(145,plain,
% 0.19/0.47 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 0.19/0.47 inference(tautology,[status(thm)],[])).
% 0.19/0.47 tff(146,plain,
% 0.19/0.47 (l2_lattices(B!1)),
% 0.19/0.47 inference(unit_resolution,[status(thm)],[145, 144])).
% 0.19/0.47 tff(147,plain,
% 0.19/0.47 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(148,plain,
% 0.19/0.47 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[147])).
% 0.19/0.47 tff(149,plain,
% 0.19/0.47 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(150,plain,
% 0.19/0.47 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[149])).
% 0.19/0.47 tff(151,plain,
% 0.19/0.47 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.47 inference(rewrite,[status(thm)],[])).
% 0.19/0.47 tff(152,plain,
% 0.19/0.47 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.47 inference(bind,[status(th)],[])).
% 0.19/0.47 tff(153,plain,
% 0.19/0.47 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.47 inference(quant_intro,[status(thm)],[152])).
% 0.19/0.47 tff(154,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.19/0.48 tff(155,plain,
% 0.19/0.48 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.19/0.48 tff(156,plain,
% 0.19/0.48 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.19/0.48 tff(157,plain,(
% 0.19/0.48 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[156])).
% 0.19/0.48 tff(158,plain,
% 0.19/0.48 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.19/0.48 tff(159,plain,
% 0.19/0.48 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.19/0.48 tff(160,plain,
% 0.19/0.48 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(161,plain,
% 0.19/0.48 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(162,plain,
% 0.19/0.48 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[161, 160])).
% 0.19/0.48 tff(163,plain,
% 0.19/0.48 ((~l2_lattices(B!1)) | (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.19/0.48 tff(164,plain,
% 0.19/0.48 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[163, 146])).
% 0.19/0.48 tff(165,plain,
% 0.19/0.48 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(166,plain,
% 0.19/0.48 (m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[165, 164])).
% 0.19/0.48 tff(167,plain,
% 0.19/0.48 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(168,plain,
% 0.19/0.48 ((~(m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[167, 166])).
% 0.19/0.48 tff(169,plain,
% 0.19/0.48 (m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[168, 127])).
% 0.19/0.48 tff(170,plain,
% 0.19/0.48 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(171,plain,
% 0.19/0.48 (l1_lattices(B!1)),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[170, 144])).
% 0.19/0.48 tff(172,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(173,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[172])).
% 0.19/0.48 tff(174,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(175,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[174])).
% 0.19/0.48 tff(176,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(177,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(178,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[177])).
% 0.19/0.48 tff(179,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')).
% 0.19/0.48 tff(180,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[179, 178])).
% 0.19/0.48 tff(181,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[180, 176])).
% 0.19/0.48 tff(182,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[181])).
% 0.19/0.48 tff(183,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[182, 175])).
% 0.19/0.48 tff(184,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[183, 173])).
% 0.19/0.48 tff(185,plain,
% 0.19/0.48 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(186,plain,
% 0.19/0.48 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(187,plain,
% 0.19/0.48 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.19/0.48 tff(188,plain,
% 0.19/0.48 ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[187, 184])).
% 0.19/0.48 tff(189,plain,
% 0.19/0.48 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[188, 171])).
% 0.19/0.48 tff(190,plain,
% 0.19/0.48 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(191,plain,
% 0.19/0.48 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.19/0.48 tff(192,plain,
% 0.19/0.48 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(193,plain,
% 0.19/0.48 (v1_funct_1(u1_lattices(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[192, 189])).
% 0.19/0.48 tff(194,plain,
% 0.19/0.48 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(195,plain,
% 0.19/0.48 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[194, 164])).
% 0.19/0.48 tff(196,plain,
% 0.19/0.48 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(197,plain,
% 0.19/0.48 (v1_funct_1(u2_lattices(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[196, 164])).
% 0.19/0.48 tff(198,plain,
% 0.19/0.48 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.19/0.48 inference(quant_inst,[status(thm)],[])).
% 0.19/0.48 tff(199,plain,
% 0.19/0.48 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[198, 125])).
% 0.19/0.48 tff(200,plain,
% 0.19/0.48 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(201,plain,
% 0.19/0.48 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[200, 189])).
% 0.19/0.48 tff(202,plain,
% 0.19/0.48 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(tautology,[status(thm)],[])).
% 0.19/0.48 tff(203,plain,
% 0.19/0.48 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[202, 201])).
% 0.19/0.48 tff(204,plain,
% 0.19/0.48 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.19/0.48 inference(unit_resolution,[status(thm)],[203, 199])).
% 0.19/0.48 tff(205,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(206,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[205])).
% 0.19/0.48 tff(207,plain,
% 0.19/0.48 (^[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)))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(208,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[207])).
% 0.19/0.48 tff(209,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(transitivity,[status(thm)],[208, 206])).
% 0.19/0.48 tff(210,plain,
% 0.19/0.48 (^[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))))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(211,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[210])).
% 0.19/0.48 tff(212,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(rewrite,[status(thm)],[])).
% 0.19/0.48 tff(213,plain,
% 0.19/0.48 (^[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))))))),
% 0.19/0.48 inference(bind,[status(th)],[])).
% 0.19/0.48 tff(214,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(quant_intro,[status(thm)],[213])).
% 0.19/0.48 tff(215,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')).
% 0.19/0.48 tff(216,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.19/0.48 tff(217,plain,
% 0.19/0.48 (![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))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[216, 212])).
% 0.19/0.48 tff(218,plain,(
% 0.19/0.48 ![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))))),
% 0.19/0.48 inference(skolemize,[status(sab)],[217])).
% 0.19/0.48 tff(219,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[218, 211])).
% 0.19/0.48 tff(220,plain,
% 0.19/0.48 (![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))))))),
% 0.19/0.48 inference(modus_ponens,[status(thm)],[219, 209])).
% 0.19/0.48 tff(221,plain,
% 0.19/0.48 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(222,plain,
% 0.19/0.49 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(223,plain,
% 0.19/0.49 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[222])).
% 0.19/0.49 tff(224,plain,
% 0.19/0.49 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[223, 221])).
% 0.19/0.49 tff(225,plain,
% 0.19/0.49 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(226,plain,
% 0.19/0.49 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.19/0.49 tff(227,plain,
% 0.19/0.49 ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F))))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[226, 220])).
% 0.19/0.49 tff(228,plain,
% 0.19/0.49 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[227, 204, 197, 195, 193, 191, 169])).
% 0.19/0.49 tff(229,plain,
% 0.19/0.49 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(230,plain,
% 0.19/0.49 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))))),
% 0.19/0.49 inference(quant_inst,[status(thm)],[])).
% 0.19/0.49 tff(231,plain,
% 0.19/0.49 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)))) | (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[230, 229])).
% 0.19/0.49 tff(232,plain,
% 0.19/0.49 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))))),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[231, 228, 118])).
% 0.19/0.49 tff(233,plain,
% 0.19/0.49 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0)))) | (u1_struct_0(B!1) = u1_struct_0(A!0))),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(234,plain,
% 0.19/0.49 (u1_struct_0(B!1) = u1_struct_0(A!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.19/0.49 tff(235,plain,
% 0.19/0.49 (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1)) <=> m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))),
% 0.19/0.49 inference(monotonicity,[status(thm)],[234])).
% 0.19/0.49 tff(236,plain,
% 0.19/0.49 (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0)) <=> m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))),
% 0.19/0.49 inference(symmetry,[status(thm)],[235])).
% 0.19/0.49 tff(237,plain,
% 0.19/0.49 (m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))),
% 0.19/0.49 inference(modus_ponens,[status(thm)],[110, 236])).
% 0.19/0.49 tff(238,plain,
% 0.19/0.49 ((v3_struct_0(A!0) | (~v11_lattices(A!0)) | (~v13_lattices(A!0)) | (~v14_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0))) | v11_lattices(A!0)),
% 0.19/0.49 inference(tautology,[status(thm)],[])).
% 0.19/0.49 tff(239,plain,
% 0.19/0.49 (v11_lattices(A!0)),
% 0.19/0.49 inference(unit_resolution,[status(thm)],[238, 43])).
% 0.19/0.49 tff(240,plain,
% 0.19/0.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(241,plain,
% 0.19/0.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[240])).
% 0.19/0.49 tff(242,plain,
% 0.19/0.49 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(243,plain,
% 0.19/0.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[242])).
% 0.19/0.49 tff(244,plain,
% 0.19/0.49 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(245,plain,
% 0.19/0.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[244])).
% 0.19/0.49 tff(246,plain,
% 0.19/0.49 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.49 inference(transitivity,[status(thm)],[245, 243])).
% 0.19/0.49 tff(247,plain,
% 0.19/0.49 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))), (((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))), rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (v3_struct_0(A) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))), (((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))) <=> ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(248,plain,
% 0.19/0.49 (![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[247])).
% 0.19/0.49 tff(249,plain,
% 0.19/0.49 (![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))),
% 0.19/0.49 inference(rewrite,[status(thm)],[])).
% 0.19/0.49 tff(250,plain,
% 0.19/0.49 (^[A: $i] : trans(monotonicity(quant_intro(proof_bind(^[B: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)) & v16_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))), quant_intro(proof_bind(^[C: $i] : rewrite((m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) <=> ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))), (![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) <=> ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)) => ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))), (((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))), ((m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))) <=> (m1_subset_1(B, u1_struct_0(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))), ((m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, 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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A))))))), 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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))), ((((~v3_struct_0(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, 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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))))),
% 0.19/0.49 inference(bind,[status(th)],[])).
% 0.19/0.49 tff(251,plain,
% 0.19/0.49 (![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) <=> ![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))),
% 0.19/0.49 inference(quant_intro,[status(thm)],[250])).
% 0.19/0.49 tff(252,axiom,(![A: $i] : (((~v3_struct_0(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((((((~v3_struct_0(A)) & v10_lattices(A)) & v11_lattices(A)) & v16_lattices(A)) & l3_lattices(A)) => ![C: $i] : (m1_subset_1(C, u1_struct_0(A)) => ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d21_lattices')).
% 0.19/0.49 tff(253,plain,
% 0.19/0.49 (![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.19/0.50 tff(254,plain,
% 0.19/0.50 (![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[253, 249])).
% 0.19/0.50 tff(255,plain,(
% 0.19/0.50 ![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))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v11_lattices(A) & v16_lattices(A) & l3_lattices(A)))))),
% 0.19/0.50 inference(skolemize,[status(sab)],[254])).
% 0.19/0.50 tff(256,plain,
% 0.19/0.50 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[255, 248])).
% 0.19/0.50 tff(257,plain,
% 0.19/0.50 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[256, 246])).
% 0.19/0.50 tff(258,plain,
% 0.19/0.50 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[257, 241])).
% 0.19/0.50 tff(259,plain,
% 0.19/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(260,plain,
% 0.19/0.50 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : (v3_struct_0(A!0) | (~m1_subset_1(B, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(261,plain,
% 0.19/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : (v3_struct_0(A!0) | (~m1_subset_1(B, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[260])).
% 0.19/0.50 tff(262,plain,
% 0.19/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : (v3_struct_0(A!0) | (~m1_subset_1(B, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[261, 259])).
% 0.19/0.50 tff(263,plain,
% 0.19/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : (v3_struct_0(A!0) | (~m1_subset_1(B, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~v11_lattices(A!0)) | (~v16_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B)))))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(264,plain,
% 0.19/0.50 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[263, 262])).
% 0.19/0.50 tff(265,plain,
% 0.19/0.50 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[264, 39, 37, 258])).
% 0.19/0.50 tff(266,plain,
% 0.19/0.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(267,plain,
% 0.19/0.50 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))) | (~v11_lattices(A!0))) <=> (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(268,plain,
% 0.19/0.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))) | (~v11_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | (v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[267])).
% 0.19/0.50 tff(269,plain,
% 0.19/0.50 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))) | (~v11_lattices(A!0)))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))))),
% 0.19/0.50 inference(transitivity,[status(thm)],[268, 266])).
% 0.19/0.50 tff(270,plain,
% 0.19/0.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2))) | (~v11_lattices(A!0)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(271,plain,
% 0.19/0.50 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, B)) <=> r2_lattices(A!0, C, B))) | (~v11_lattices(A!0)))) | v3_struct_0(A!0) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~v16_lattices(A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[270, 269])).
% 0.19/0.50 tff(272,plain,
% 0.19/0.50 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[271, 39, 67, 37, 103, 47, 265, 239])).
% 0.19/0.50 tff(273,plain,
% 0.19/0.50 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(274,plain,
% 0.19/0.50 (((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ((k7_lattices(A!0, C!2) = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))) <=> ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(275,plain,
% 0.19/0.50 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ((k7_lattices(A!0, C!2) = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[274])).
% 0.19/0.50 tff(276,plain,
% 0.19/0.50 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ((k7_lattices(A!0, C!2) = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(transitivity,[status(thm)],[275, 273])).
% 0.19/0.50 tff(277,plain,
% 0.19/0.50 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | ((k7_lattices(A!0, C!2) = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(278,plain,
% 0.19/0.50 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, C!2)) <=> r2_lattices(A!0, C, C!2)))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.19/0.50 tff(279,plain,
% 0.19/0.50 (r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[278, 110, 272])).
% 0.19/0.50 tff(280,plain,
% 0.19/0.50 (m1_subset_1(C!2, u1_struct_0(B!1))),
% 0.19/0.50 inference(or_elim,[status(thm)],[102])).
% 0.19/0.50 tff(281,plain,
% 0.19/0.50 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(282,plain,
% 0.19/0.50 (((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))) <=> ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(283,plain,
% 0.19/0.50 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))))),
% 0.19/0.50 inference(monotonicity,[status(thm)],[282])).
% 0.19/0.50 tff(284,plain,
% 0.19/0.50 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(transitivity,[status(thm)],[283, 281])).
% 0.19/0.50 tff(285,plain,
% 0.19/0.50 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | ((~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.50 inference(quant_inst,[status(thm)],[])).
% 0.19/0.50 tff(286,plain,
% 0.19/0.50 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(A!0))) | (~m1_subset_1(D, u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), D) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), D)))) | (~m1_subset_1(C!2, u1_struct_0(A!0))) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(A!0, C!2), C!2) | (~r2_lattices(A!0, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.19/0.50 tff(287,plain,
% 0.19/0.50 (r2_lattices(B!1, k7_lattices(A!0, C!2), C!2)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[286, 103, 280, 279, 237, 117])).
% 0.19/0.50 tff(288,plain,
% 0.19/0.50 (~(k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2))),
% 0.19/0.50 inference(or_elim,[status(thm)],[102])).
% 0.19/0.50 tff(289,plain,
% 0.19/0.50 ((~((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2))) | (k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) | (~r2_lattices(B!1, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(290,plain,
% 0.19/0.50 (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[289, 288, 287])).
% 0.19/0.50 tff(291,plain,
% 0.19/0.50 ((v3_struct_0(B!1) | (~v11_lattices(B!1)) | (~v13_lattices(B!1)) | (~v14_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1))) | v11_lattices(B!1)),
% 0.19/0.50 inference(tautology,[status(thm)],[])).
% 0.19/0.50 tff(292,plain,
% 0.19/0.50 (v11_lattices(B!1)),
% 0.19/0.50 inference(unit_resolution,[status(thm)],[291, 32])).
% 0.19/0.50 tff(293,plain,
% 0.19/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(294,plain,
% 0.19/0.50 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v10_lattices(B!1)) | (~v11_lattices(B!1)) | (~v16_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1))))),
% 0.19/0.50 inference(rewrite,[status(thm)],[])).
% 0.19/0.50 tff(295,plain,
% 0.19/0.50 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v10_lattices(B!1)) | (~v11_lattices(B!1)) | (~v16_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[294])).
% 0.19/0.51 tff(296,plain,
% 0.19/0.51 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v10_lattices(B!1)) | (~v11_lattices(B!1)) | (~v16_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[295, 293])).
% 0.19/0.51 tff(297,plain,
% 0.19/0.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v10_lattices(B!1)) | (~v11_lattices(B!1)) | (~v16_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B)))))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(298,plain,
% 0.19/0.51 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A))) | ((C = k7_lattices(A, B)) <=> r2_lattices(A, C, B)))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | ![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.19/0.51 tff(299,plain,
% 0.19/0.51 (![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[298, 28, 26, 258])).
% 0.19/0.51 tff(300,plain,
% 0.19/0.51 (((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))))) <=> ((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(301,plain,
% 0.19/0.51 ((v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))) | (~v11_lattices(B!1))) <=> (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(302,plain,
% 0.19/0.51 (((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))) | (~v11_lattices(B!1)))) <=> ((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))))),
% 0.19/0.51 inference(monotonicity,[status(thm)],[301])).
% 0.19/0.51 tff(303,plain,
% 0.19/0.51 (((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))) | (~v11_lattices(B!1)))) <=> ((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))))),
% 0.19/0.51 inference(transitivity,[status(thm)],[302, 300])).
% 0.19/0.51 tff(304,plain,
% 0.19/0.51 ((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | (v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2))) | (~v11_lattices(B!1)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(305,plain,
% 0.19/0.51 ((~![B: $i] : (v3_struct_0(B!1) | (~m1_subset_1(B, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, B)) <=> r2_lattices(B!1, C, B))) | (~v11_lattices(B!1)))) | v3_struct_0(B!1) | (~m1_subset_1(C!2, u1_struct_0(B!1))) | (~v16_lattices(B!1)) | (~v10_lattices(B!1)) | (~l3_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.19/0.51 tff(306,plain,
% 0.19/0.51 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[305, 280, 28, 76, 26, 34, 299, 292])).
% 0.19/0.51 tff(307,plain,
% 0.19/0.51 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | ((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | ((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.51 inference(rewrite,[status(thm)],[])).
% 0.19/0.51 tff(308,plain,
% 0.19/0.51 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))) | ((~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | ((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2)))),
% 0.19/0.51 inference(quant_inst,[status(thm)],[])).
% 0.19/0.51 tff(309,plain,
% 0.19/0.51 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, C, C!2)))) | (~m1_subset_1(k7_lattices(A!0, C!2), u1_struct_0(B!1))) | ((k7_lattices(A!0, C!2) = k7_lattices(B!1, C!2)) <=> r2_lattices(B!1, k7_lattices(A!0, C!2), C!2))),
% 0.19/0.51 inference(modus_ponens,[status(thm)],[308, 307])).
% 0.19/0.51 tff(310,plain,
% 0.19/0.51 ($false),
% 0.19/0.51 inference(unit_resolution,[status(thm)],[309, 306, 237, 290])).
% 0.19/0.51 % SZS output end Proof
% 0.19/0.51 % E exiting
%------------------------------------------------------------------------------