TSTP Solution File: LAT296+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT296+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 18:32:48 EDT 2022
% Result : Theorem 0.20s 0.53s
% Output : Proof 0.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT296+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 13:22:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.53 % SZS status Theorem
% 0.20/0.53 % SZS output start Proof
% 0.20/0.53 tff(r2_lattices_type, type, (
% 0.20/0.53 r2_lattices: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(k7_lattices_type, type, (
% 0.20/0.53 k7_lattices: ( $i * $i ) > $i)).
% 0.20/0.53 tff(tptp_fun_D_3_type, type, (
% 0.20/0.53 tptp_fun_D_3: $i)).
% 0.20/0.53 tff(tptp_fun_B_1_type, type, (
% 0.20/0.53 tptp_fun_B_1: $i)).
% 0.20/0.53 tff(tptp_fun_A_0_type, type, (
% 0.20/0.53 tptp_fun_A_0: $i)).
% 0.20/0.53 tff(m1_subset_1_type, type, (
% 0.20/0.53 m1_subset_1: ( $i * $i ) > $o)).
% 0.20/0.53 tff(u1_struct_0_type, type, (
% 0.20/0.53 u1_struct_0: $i > $i)).
% 0.20/0.53 tff(u2_lattices_type, type, (
% 0.20/0.53 u2_lattices: $i > $i)).
% 0.20/0.53 tff(u1_lattices_type, type, (
% 0.20/0.53 u1_lattices: $i > $i)).
% 0.20/0.53 tff(g3_lattices_type, type, (
% 0.20/0.53 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.20/0.53 tff(l3_lattices_type, type, (
% 0.20/0.53 l3_lattices: $i > $o)).
% 0.20/0.53 tff(v17_lattices_type, type, (
% 0.20/0.53 v17_lattices: $i > $o)).
% 0.20/0.53 tff(v10_lattices_type, type, (
% 0.20/0.53 v10_lattices: $i > $o)).
% 0.20/0.53 tff(v3_struct_0_type, type, (
% 0.20/0.53 v3_struct_0: $i > $o)).
% 0.20/0.53 tff(tptp_fun_C_2_type, type, (
% 0.20/0.53 tptp_fun_C_2: $i)).
% 0.20/0.53 tff(m1_relset_1_type, type, (
% 0.20/0.53 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(k2_zfmisc_1_type, type, (
% 0.20/0.53 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.20/0.53 tff(m2_relset_1_type, type, (
% 0.20/0.53 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(v1_funct_2_type, type, (
% 0.20/0.53 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.20/0.53 tff(v1_funct_1_type, type, (
% 0.20/0.53 v1_funct_1: $i > $o)).
% 0.20/0.53 tff(l1_lattices_type, type, (
% 0.20/0.53 l1_lattices: $i > $o)).
% 0.20/0.53 tff(l2_lattices_type, type, (
% 0.20/0.53 l2_lattices: $i > $o)).
% 0.20/0.53 tff(v16_lattices_type, type, (
% 0.20/0.53 v16_lattices: $i > $o)).
% 0.20/0.53 tff(v15_lattices_type, type, (
% 0.20/0.53 v15_lattices: $i > $o)).
% 0.20/0.53 tff(v14_lattices_type, type, (
% 0.20/0.53 v14_lattices: $i > $o)).
% 0.20/0.53 tff(v13_lattices_type, type, (
% 0.20/0.53 v13_lattices: $i > $o)).
% 0.20/0.53 tff(v11_lattices_type, type, (
% 0.20/0.53 v11_lattices: $i > $o)).
% 0.20/0.53 tff(1,plain,
% 0.20/0.53 ((((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(2,plain,
% 0.20/0.53 (((m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & ((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(3,plain,
% 0.20/0.53 ((~(~((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))) <=> ((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(4,plain,
% 0.20/0.53 ((~(~(g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))))) <=> (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)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(5,plain,
% 0.20/0.53 (((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1)))))) <=> (m1_subset_1(C!2, u1_struct_0(A!0)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(6,plain,
% 0.20/0.53 ((((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))))) & (~(~((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & ((~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[5, 4, 3])).
% 0.20/0.53 tff(7,plain,
% 0.20/0.53 ((((~(~m1_subset_1(C!2, u1_struct_0(A!0)))) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))))) & (~(~((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.20/0.53 inference(transitivity,[status(thm)],[6, 2])).
% 0.20/0.53 tff(8,plain,
% 0.20/0.53 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & v17_lattices(A!0) & l3_lattices(A!0))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(9,plain,
% 0.20/0.53 (((~(~((~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)))) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))))) & (~(~((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[8, 7])).
% 0.20/0.53 tff(10,plain,
% 0.20/0.53 (((~(~((~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)))) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))))) & (~(~((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1))),
% 0.20/0.53 inference(transitivity,[status(thm)],[9, 1])).
% 0.20/0.53 tff(11,plain,
% 0.20/0.53 ((~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & 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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(12,plain,
% 0.20/0.53 ((~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B))))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(13,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/sandbox/benchmark/theBenchmark.p','t12_filter_2')).
% 0.20/0.53 tff(14,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.20/0.53 tff(15,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[14, 11])).
% 0.20/0.53 tff(16,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.20/0.53 tff(17,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[16, 11])).
% 0.20/0.53 tff(18,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[17, 11])).
% 0.20/0.53 tff(19,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.53 tff(20,plain,
% 0.20/0.53 (~![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))) | ![D: $i] : ((k7_lattices(A, C) = k7_lattices(B, D)) | (~(C = D)) | (~m1_subset_1(D, u1_struct_0(B))))) | (~(g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[19, 11])).
% 0.20/0.53 tff(21,plain,
% 0.20/0.53 ((~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)) & (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_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))) & (~v3_struct_0(B!1)) & v10_lattices(B!1) & v17_lattices(B!1) & l3_lattices(B!1)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[20, 10])).
% 0.20/0.53 tff(22,plain,
% 0.20/0.53 (g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0)) = g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1))),
% 0.20/0.53 inference(and_elim,[status(thm)],[21])).
% 0.20/0.53 tff(23,plain,
% 0.20/0.53 (g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(A!0), u2_lattices(A!0), u1_lattices(A!0))),
% 0.20/0.53 inference(symmetry,[status(thm)],[22])).
% 0.20/0.53 tff(24,plain,
% 0.20/0.53 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(25,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.53 tff(26,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(27,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.20/0.53 tff(28,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.20/0.53 tff(29,plain,(
% 0.20/0.53 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.53 inference(skolemize,[status(sab)],[28])).
% 0.20/0.53 tff(30,plain,
% 0.20/0.53 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.20/0.53 tff(31,plain,
% 0.20/0.53 ((~![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)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(32,plain,
% 0.20/0.53 (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))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[31, 30])).
% 0.20/0.53 tff(33,plain,
% 0.20/0.53 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(34,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[33])).
% 0.20/0.53 tff(35,plain,
% 0.20/0.53 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(36,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[35])).
% 0.20/0.53 tff(37,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(38,plain,
% 0.20/0.53 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(39,plain,
% 0.20/0.53 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[38])).
% 0.20/0.53 tff(40,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.20/0.53 tff(41,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[40, 39])).
% 0.20/0.53 tff(42,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[41, 37])).
% 0.20/0.53 tff(43,plain,(
% 0.20/0.53 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.20/0.53 inference(skolemize,[status(sab)],[42])).
% 0.20/0.53 tff(44,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[43, 36])).
% 0.20/0.53 tff(45,plain,
% 0.20/0.53 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[44, 34])).
% 0.20/0.53 tff(46,plain,
% 0.20/0.53 (l3_lattices(B!1)),
% 0.20/0.53 inference(and_elim,[status(thm)],[21])).
% 0.20/0.53 tff(47,plain,
% 0.20/0.53 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(48,plain,
% 0.20/0.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(49,plain,
% 0.20/0.53 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(B!1)) | (~((~l1_lattices(B!1)) | (~l2_lattices(B!1))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[48, 47])).
% 0.20/0.53 tff(50,plain,
% 0.20/0.53 (~((~l1_lattices(B!1)) | (~l2_lattices(B!1)))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[49, 46, 45])).
% 0.20/0.53 tff(51,plain,
% 0.20/0.53 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l1_lattices(B!1)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(52,plain,
% 0.20/0.53 (l1_lattices(B!1)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[51, 50])).
% 0.20/0.53 tff(53,plain,
% 0.20/0.53 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(54,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[53])).
% 0.20/0.53 tff(55,plain,
% 0.20/0.53 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(56,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[55])).
% 0.20/0.53 tff(57,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(58,plain,
% 0.20/0.53 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(59,plain,
% 0.20/0.53 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[58])).
% 0.20/0.53 tff(60,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.20/0.53 tff(61,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.53 tff(62,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.20/0.53 tff(63,plain,(
% 0.20/0.53 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.20/0.53 inference(skolemize,[status(sab)],[62])).
% 0.20/0.53 tff(64,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[63, 56])).
% 0.20/0.53 tff(65,plain,
% 0.20/0.53 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[64, 54])).
% 0.20/0.53 tff(66,plain,
% 0.20/0.53 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(B!1)) | (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(67,plain,
% 0.20/0.54 ((~![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))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(68,plain,
% 0.20/0.54 ((~![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)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[67, 66])).
% 0.20/0.54 tff(69,plain,
% 0.20/0.54 ((~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)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[68, 65])).
% 0.20/0.54 tff(70,plain,
% 0.20/0.54 (~((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[69, 52])).
% 0.20/0.54 tff(71,plain,
% 0.20/0.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(72,plain,
% 0.20/0.54 (m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[71, 70])).
% 0.20/0.54 tff(73,plain,
% 0.20/0.54 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(74,plain,
% 0.20/0.54 ((~(m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)) <=> m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[73, 72])).
% 0.20/0.54 tff(75,plain,
% 0.20/0.54 (m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[74, 32])).
% 0.20/0.54 tff(76,plain,
% 0.20/0.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(77,plain,
% 0.20/0.54 (v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[76, 70])).
% 0.20/0.54 tff(78,plain,
% 0.20/0.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u1_lattices(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(79,plain,
% 0.20/0.54 (v1_funct_1(u1_lattices(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[78, 70])).
% 0.20/0.54 tff(80,plain,
% 0.20/0.54 (((~l1_lattices(B!1)) | (~l2_lattices(B!1))) | l2_lattices(B!1)),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(81,plain,
% 0.20/0.54 (l2_lattices(B!1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[80, 50])).
% 0.20/0.54 tff(82,plain,
% 0.20/0.54 (^[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)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(83,plain,
% 0.20/0.54 (![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))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.54 tff(84,plain,
% 0.20/0.54 (^[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)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(85,plain,
% 0.20/0.54 (![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))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.54 tff(86,plain,
% 0.20/0.54 (![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))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(87,plain,
% 0.20/0.54 (^[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))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(88,plain,
% 0.20/0.54 (![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))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[87])).
% 0.20/0.54 tff(89,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.20/0.54 tff(90,plain,
% 0.20/0.54 (![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))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[89, 88])).
% 0.20/0.54 tff(91,plain,
% 0.20/0.54 (![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))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[90, 86])).
% 0.20/0.54 tff(92,plain,(
% 0.20/0.54 ![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))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[91])).
% 0.20/0.54 tff(93,plain,
% 0.20/0.54 (![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))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[92, 85])).
% 0.20/0.54 tff(94,plain,
% 0.20/0.54 (![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))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[93, 83])).
% 0.20/0.54 tff(95,plain,
% 0.20/0.54 (((~![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))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(96,plain,
% 0.20/0.54 ((~![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))))))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(97,plain,
% 0.20/0.54 ((~![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)))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[96, 95])).
% 0.20/0.54 tff(98,plain,
% 0.20/0.54 ((~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)))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[97, 94])).
% 0.20/0.54 tff(99,plain,
% 0.20/0.54 (~((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[98, 81])).
% 0.20/0.54 tff(100,plain,
% 0.20/0.54 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(101,plain,
% 0.20/0.54 (v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[100, 99])).
% 0.20/0.54 tff(102,plain,
% 0.20/0.54 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | v1_funct_1(u2_lattices(B!1))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(103,plain,
% 0.20/0.54 (v1_funct_1(u2_lattices(B!1))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[102, 99])).
% 0.20/0.54 tff(104,plain,
% 0.20/0.54 ((~![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)))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(105,plain,
% 0.20/0.54 (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))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[104, 30])).
% 0.20/0.54 tff(106,plain,
% 0.20/0.54 (((~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m2_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1)))) | 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))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(107,plain,
% 0.20/0.54 (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))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[106, 99])).
% 0.20/0.54 tff(108,plain,
% 0.20/0.54 ((~(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))),
% 0.20/0.54 inference(tautology,[status(thm)],[])).
% 0.20/0.54 tff(109,plain,
% 0.20/0.54 ((~(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))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[108, 107])).
% 0.20/0.54 tff(110,plain,
% 0.20/0.54 (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))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[109, 105])).
% 0.20/0.54 tff(111,plain,
% 0.20/0.54 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(112,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[111])).
% 0.20/0.54 tff(113,plain,
% 0.20/0.54 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(114,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[113])).
% 0.20/0.54 tff(115,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[114, 112])).
% 0.20/0.54 tff(116,plain,
% 0.20/0.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(117,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[116])).
% 0.20/0.54 tff(118,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(119,plain,
% 0.20/0.54 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(120,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[119])).
% 0.20/0.54 tff(121,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.20/0.54 tff(122,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[121, 120])).
% 0.20/0.54 tff(123,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[122, 118])).
% 0.20/0.54 tff(124,plain,(
% 0.20/0.54 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.20/0.54 inference(skolemize,[status(sab)],[123])).
% 0.20/0.54 tff(125,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[124, 117])).
% 0.20/0.54 tff(126,plain,
% 0.20/0.54 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[125, 115])).
% 0.20/0.54 tff(127,plain,
% 0.20/0.54 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~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(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))) | (~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(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))))))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(128,plain,
% 0.20/0.54 (((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~m1_relset_1(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(B!1) = D)) | (~(u2_lattices(B!1) = E)) | (~(u1_lattices(B!1) = F)))))) <=> ((~v1_funct_1(u1_lattices(B!1))) | (~v1_funct_2(u1_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~v1_funct_1(u2_lattices(B!1))) | (~v1_funct_2(u2_lattices(B!1), k2_zfmisc_1(u1_struct_0(B!1), u1_struct_0(B!1)), u1_struct_0(B!1))) | (~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(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))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(129,plain,
% 0.20/0.55 (((~![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))) | (~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(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)))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[128])).
% 0.20/0.55 tff(130,plain,
% 0.20/0.55 (((~![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))) | (~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(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))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[129, 127])).
% 0.20/0.55 tff(131,plain,
% 0.20/0.55 ((~![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))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(132,plain,
% 0.20/0.55 ((~![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))) | (~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(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)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[131, 130])).
% 0.20/0.55 tff(133,plain,
% 0.20/0.55 ((~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))) | (~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(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)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[132, 126])).
% 0.20/0.55 tff(134,plain,
% 0.20/0.55 (![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)))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[133, 110, 103, 101, 79, 77, 75])).
% 0.20/0.55 tff(135,plain,
% 0.20/0.55 (((~![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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(136,plain,
% 0.20/0.55 (((~(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)))))) <=> ((~(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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(137,plain,
% 0.20/0.55 (((~![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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0)))))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[136])).
% 0.20/0.55 tff(138,plain,
% 0.20/0.55 (((~![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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))))))),
% 0.20/0.55 inference(transitivity,[status(thm)],[137, 135])).
% 0.20/0.55 tff(139,plain,
% 0.20/0.55 ((~![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))))))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(140,plain,
% 0.20/0.55 ((~![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))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0)))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[139, 138])).
% 0.20/0.55 tff(141,plain,
% 0.20/0.55 (~((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0))))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[140, 134, 23])).
% 0.20/0.55 tff(142,plain,
% 0.20/0.55 (((~(u1_struct_0(B!1) = u1_struct_0(A!0))) | (~(u1_lattices(B!1) = u1_lattices(A!0))) | (~(u2_lattices(B!1) = u2_lattices(A!0)))) | (u1_struct_0(B!1) = u1_struct_0(A!0))),
% 0.20/0.55 inference(tautology,[status(thm)],[])).
% 0.20/0.55 tff(143,plain,
% 0.20/0.55 (u1_struct_0(B!1) = u1_struct_0(A!0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[142, 141])).
% 0.20/0.55 tff(144,plain,
% 0.20/0.55 (u1_struct_0(A!0) = u1_struct_0(B!1)),
% 0.20/0.55 inference(symmetry,[status(thm)],[143])).
% 0.20/0.55 tff(145,plain,
% 0.20/0.55 (m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0)) <=> m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[144])).
% 0.20/0.55 tff(146,plain,
% 0.20/0.55 (m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)) <=> m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))),
% 0.20/0.55 inference(symmetry,[status(thm)],[145])).
% 0.20/0.55 tff(147,plain,
% 0.20/0.55 (^[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))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(148,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[147])).
% 0.20/0.55 tff(149,plain,
% 0.20/0.55 (^[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)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(150,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[149])).
% 0.20/0.55 tff(151,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(152,plain,
% 0.20/0.55 (^[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)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(153,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[152])).
% 0.20/0.55 tff(154,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/sandbox/benchmark/theBenchmark.p','dt_k7_lattices')).
% 0.20/0.55 tff(155,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[154, 153])).
% 0.20/0.55 tff(156,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[155, 151])).
% 0.20/0.55 tff(157,plain,(
% 0.20/0.55 ![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)))),
% 0.20/0.55 inference(skolemize,[status(sab)],[156])).
% 0.20/0.55 tff(158,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[157, 150])).
% 0.20/0.55 tff(159,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[158, 148])).
% 0.20/0.55 tff(160,plain,
% 0.20/0.55 (~v3_struct_0(B!1)),
% 0.20/0.55 inference(and_elim,[status(thm)],[21])).
% 0.20/0.55 tff(161,plain,
% 0.20/0.55 (~((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) | (~(C!2 = D!3)) | (~m1_subset_1(D!3, u1_struct_0(B!1))))),
% 0.20/0.55 inference(and_elim,[status(thm)],[21])).
% 0.20/0.55 tff(162,plain,
% 0.20/0.55 (m1_subset_1(D!3, u1_struct_0(B!1))),
% 0.20/0.55 inference(or_elim,[status(thm)],[161])).
% 0.20/0.55 tff(163,plain,
% 0.20/0.55 (((~![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(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)))) <=> ((~![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(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(164,plain,
% 0.20/0.55 ((m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1))) <=> (v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(165,plain,
% 0.20/0.55 (((~![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(B!1, D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)))) <=> ((~![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(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))))),
% 0.20/0.55 inference(monotonicity,[status(thm)],[164])).
% 0.20/0.55 tff(166,plain,
% 0.20/0.55 (((~![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(B!1, D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)))) <=> ((~![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(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1)))),
% 0.20/0.55 inference(transitivity,[status(thm)],[165, 163])).
% 0.20/0.55 tff(167,plain,
% 0.20/0.55 ((~![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(B!1, D!3), u1_struct_0(B!1)) | v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)))),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(168,plain,
% 0.20/0.55 ((~![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(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[167, 166])).
% 0.20/0.55 tff(169,plain,
% 0.20/0.55 (m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[168, 162, 160, 46, 159])).
% 0.20/0.55 tff(170,plain,
% 0.20/0.55 (m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[169, 146])).
% 0.20/0.55 tff(171,plain,
% 0.20/0.55 (^[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))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(172,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[171])).
% 0.20/0.55 tff(173,plain,
% 0.20/0.55 (^[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)))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(174,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[173])).
% 0.20/0.55 tff(175,plain,
% 0.20/0.55 (![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))))),
% 0.20/0.55 inference(rewrite,[status(thm)],[])).
% 0.20/0.55 tff(176,plain,
% 0.20/0.55 (^[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))))))),
% 0.20/0.55 inference(bind,[status(th)],[])).
% 0.20/0.55 tff(177,plain,
% 0.20/0.55 (![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))))),
% 0.20/0.55 inference(quant_intro,[status(thm)],[176])).
% 0.20/0.55 tff(178,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/sandbox/benchmark/theBenchmark.p','cc5_lattices')).
% 0.20/0.55 tff(179,plain,
% 0.20/0.55 (![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))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[178, 177])).
% 0.20/0.55 tff(180,plain,
% 0.20/0.55 (![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))))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[179, 175])).
% 0.20/0.55 tff(181,plain,(
% 0.20/0.55 ![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))))),
% 0.20/0.55 inference(skolemize,[status(sab)],[180])).
% 0.20/0.55 tff(182,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[181, 174])).
% 0.20/0.55 tff(183,plain,
% 0.20/0.55 (![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)))),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[182, 172])).
% 0.20/0.55 tff(184,plain,
% 0.20/0.55 (v17_lattices(B!1)),
% 0.20/0.56 inference(and_elim,[status(thm)],[21])).
% 0.20/0.56 tff(185,plain,
% 0.20/0.56 (((~![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)))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(186,plain,
% 0.20/0.56 ((~![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)))),
% 0.20/0.56 inference(quant_inst,[status(thm)],[])).
% 0.20/0.56 tff(187,plain,
% 0.20/0.56 ((~![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))),
% 0.20/0.56 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.20/0.56 tff(188,plain,
% 0.20/0.56 (~(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)))),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[187, 160, 184, 46, 183])).
% 0.20/0.56 tff(189,plain,
% 0.20/0.56 ((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)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(190,plain,
% 0.20/0.56 (v15_lattices(B!1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[189, 188])).
% 0.20/0.56 tff(191,plain,
% 0.20/0.56 ((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)),
% 0.20/0.56 inference(tautology,[status(thm)],[])).
% 0.20/0.56 tff(192,plain,
% 0.20/0.56 (v16_lattices(B!1)),
% 0.20/0.56 inference(unit_resolution,[status(thm)],[191, 188])).
% 0.20/0.56 tff(193,plain,
% 0.20/0.56 (^[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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))) <=> (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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(194,plain,
% 0.20/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[193])).
% 0.20/0.56 tff(195,plain,
% 0.20/0.56 (^[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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))) <=> (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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(196,plain,
% 0.20/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[195])).
% 0.20/0.56 tff(197,plain,
% 0.20/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.20/0.56 inference(transitivity,[status(thm)],[196, 194])).
% 0.20/0.56 tff(198,plain,
% 0.20/0.56 (^[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(quant_intro(proof_bind(^[C: $i] : rewrite(((~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] : (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(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] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))), 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))))), (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))), (((~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))))), 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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D)))))))) <=> (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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))), (((~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))))),
% 0.20/0.56 inference(bind,[status(th)],[])).
% 0.20/0.56 tff(199,plain,
% 0.20/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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)))) | (~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.20/0.56 inference(quant_intro,[status(thm)],[198])).
% 0.20/0.56 tff(200,plain,
% 0.20/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.20/0.56 inference(rewrite,[status(thm)],[])).
% 0.20/0.56 tff(201,plain,
% 0.20/0.56 (^[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(quant_intro(proof_bind(^[E: $i] : trans(monotonicity(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)))))), ((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)) => ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))), rewrite((m1_subset_1(E, u1_struct_0(B)) => ![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(E, u1_struct_0(B))) | ![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(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))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, 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(E, u1_struct_0(B))) | ![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(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)) => ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B)))))))), rewrite((m1_subset_1(D, u1_struct_0(A)) => ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![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(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))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))))), (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![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(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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))))), rewrite((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] : (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(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] : (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(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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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)))))) <=> ![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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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)))))))) <=> (((~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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))))))), 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(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)) => ((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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))))),
% 0.50/0.56 inference(bind,[status(th)],[])).
% 0.50/0.56 tff(202,plain,
% 0.50/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.50/0.56 inference(quant_intro,[status(thm)],[201])).
% 0.50/0.56 tff(203,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/sandbox/benchmark/theBenchmark.p','t11_filter_2')).
% 0.50/0.56 tff(204,plain,
% 0.50/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.50/0.56 inference(modus_ponens,[status(thm)],[203, 202])).
% 0.50/0.56 tff(205,plain,
% 0.50/0.56 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[204, 200])).
% 0.50/0.57 tff(206,plain,(
% 0.50/0.57 ![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~((C = E) & (D = F) & r2_lattices(A, C, D))) | (~m1_subset_1(F, u1_struct_0(B))))))) | (~((~v3_struct_0(B)) & v10_lattices(B) & v15_lattices(B) & v16_lattices(B) & l3_lattices(B)))))),
% 0.50/0.57 inference(skolemize,[status(sab)],[205])).
% 0.50/0.57 tff(207,plain,
% 0.50/0.57 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[206, 199])).
% 0.50/0.57 tff(208,plain,
% 0.50/0.57 (![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[207, 197])).
% 0.50/0.57 tff(209,plain,
% 0.50/0.57 (v10_lattices(B!1)),
% 0.50/0.57 inference(and_elim,[status(thm)],[21])).
% 0.50/0.57 tff(210,plain,
% 0.50/0.57 (((~![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(211,plain,
% 0.50/0.57 ((v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = 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(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) <=> (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D))))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(212,plain,
% 0.50/0.57 (((~![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = 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(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[211])).
% 0.50/0.57 tff(213,plain,
% 0.50/0.57 (((~![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = 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(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, 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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D))))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[212, 210])).
% 0.50/0.57 tff(214,plain,
% 0.50/0.57 ((~![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | (v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = 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(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D))))))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(215,plain,
% 0.50/0.57 ((~![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(A))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(A, C, D))))))))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[214, 213])).
% 0.50/0.57 tff(216,plain,
% 0.50/0.57 ((~v15_lattices(B!1)) | (~v16_lattices(B!1)) | ![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[215, 160, 209, 46, 208])).
% 0.50/0.57 tff(217,plain,
% 0.50/0.57 (![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[216, 192, 190])).
% 0.50/0.57 tff(218,plain,
% 0.50/0.57 (l3_lattices(A!0)),
% 0.50/0.57 inference(and_elim,[status(thm)],[21])).
% 0.50/0.57 tff(219,plain,
% 0.50/0.57 (v17_lattices(A!0)),
% 0.50/0.57 inference(and_elim,[status(thm)],[21])).
% 0.50/0.57 tff(220,plain,
% 0.50/0.57 (~v3_struct_0(A!0)),
% 0.50/0.57 inference(and_elim,[status(thm)],[21])).
% 0.50/0.57 tff(221,plain,
% 0.50/0.57 (((~![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)))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(222,plain,
% 0.50/0.57 ((~![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)))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(223,plain,
% 0.50/0.57 ((~![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))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.50/0.57 tff(224,plain,
% 0.50/0.57 (~(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)))),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[223, 220, 219, 218, 183])).
% 0.50/0.57 tff(225,plain,
% 0.50/0.57 ((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)),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(226,plain,
% 0.50/0.57 (v16_lattices(A!0)),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[225, 224])).
% 0.50/0.57 tff(227,plain,
% 0.50/0.57 ((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)),
% 0.50/0.57 inference(tautology,[status(thm)],[])).
% 0.50/0.57 tff(228,plain,
% 0.50/0.57 (v15_lattices(A!0)),
% 0.50/0.57 inference(unit_resolution,[status(thm)],[227, 224])).
% 0.50/0.57 tff(229,plain,
% 0.50/0.57 (v10_lattices(A!0)),
% 0.50/0.57 inference(and_elim,[status(thm)],[21])).
% 0.50/0.57 tff(230,plain,
% 0.50/0.57 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(231,plain,
% 0.50/0.57 ((v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : (r2_lattices(A!0, E, F) | (~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D))))))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(rewrite,[status(thm)],[])).
% 0.50/0.57 tff(232,plain,
% 0.50/0.57 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : (r2_lattices(A!0, E, F) | (~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))))),
% 0.50/0.57 inference(monotonicity,[status(thm)],[231])).
% 0.50/0.57 tff(233,plain,
% 0.50/0.57 (((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : (r2_lattices(A!0, E, F) | (~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) <=> ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(transitivity,[status(thm)],[232, 230])).
% 0.50/0.57 tff(234,plain,
% 0.50/0.57 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : (r2_lattices(A!0, E, F) | (~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))),
% 0.50/0.57 inference(quant_inst,[status(thm)],[])).
% 0.50/0.57 tff(235,plain,
% 0.50/0.57 ((~![B: $i] : (v3_struct_0(B) | (~l3_lattices(B)) | (~v10_lattices(B)) | (~v15_lattices(B)) | (~v16_lattices(B)) | (~(g3_lattices(u1_struct_0(B!1), u2_lattices(B!1), u1_lattices(B!1)) = g3_lattices(u1_struct_0(B), u2_lattices(B), u1_lattices(B)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(B))) | ![F: $i] : (r2_lattices(B, E, F) | (~m1_subset_1(F, u1_struct_0(B))) | (~(C = E)) | (~(D = F)) | (~r2_lattices(B!1, C, D)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v15_lattices(A!0)) | (~v16_lattices(A!0)) | (~(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)))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))),
% 0.50/0.57 inference(modus_ponens,[status(thm)],[234, 233])).
% 0.50/0.58 tff(236,plain,
% 0.50/0.58 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))),
% 0.50/0.58 inference(unit_resolution,[status(thm)],[235, 220, 229, 218, 228, 226, 217, 23])).
% 0.50/0.58 tff(237,plain,
% 0.50/0.58 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(238,plain,
% 0.50/0.58 (((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(k7_lattices(B!1, D!3) = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) <=> ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))),
% 0.50/0.58 inference(rewrite,[status(thm)],[])).
% 0.50/0.58 tff(239,plain,
% 0.50/0.58 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(k7_lattices(B!1, D!3) = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))))),
% 0.50/0.58 inference(monotonicity,[status(thm)],[238])).
% 0.50/0.58 tff(240,plain,
% 0.50/0.58 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(k7_lattices(B!1, D!3) = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))),
% 0.52/0.58 inference(transitivity,[status(thm)],[239, 237])).
% 0.52/0.58 tff(241,plain,
% 0.52/0.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(k7_lattices(B!1, D!3) = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D))))))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(242,plain,
% 0.52/0.58 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(C = E)) | (~(D = F)) | r2_lattices(A!0, E, F) | (~r2_lattices(B!1, C, D))))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.52/0.58 tff(243,plain,
% 0.52/0.58 (![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[242, 169, 236])).
% 0.52/0.58 tff(244,plain,
% 0.52/0.58 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(245,plain,
% 0.52/0.58 (((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) <=> ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(246,plain,
% 0.52/0.58 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[245])).
% 0.52/0.58 tff(247,plain,
% 0.52/0.58 (((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))) <=> ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))),
% 0.52/0.58 inference(transitivity,[status(thm)],[246, 244])).
% 0.52/0.58 tff(248,plain,
% 0.52/0.58 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(249,plain,
% 0.52/0.58 ((~![D: $i] : ((~m1_subset_1(D, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D = F)) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D)))))) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | ![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[248, 247])).
% 0.52/0.58 tff(250,plain,
% 0.52/0.58 (![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[249, 162, 243])).
% 0.52/0.58 tff(251,plain,
% 0.52/0.58 (((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F)))) <=> ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F)))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(252,plain,
% 0.52/0.58 (((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(B!1, D!3), F) | (~(k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))) <=> ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F)))),
% 0.52/0.58 inference(rewrite,[status(thm)],[])).
% 0.52/0.58 tff(253,plain,
% 0.52/0.58 (((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(B!1, D!3), F) | (~(k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) <=> ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[252])).
% 0.52/0.58 tff(254,plain,
% 0.52/0.58 (((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(B!1, D!3), F) | (~(k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) <=> ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F)))),
% 0.52/0.58 inference(transitivity,[status(thm)],[253, 251])).
% 0.52/0.58 tff(255,plain,
% 0.52/0.58 ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, k7_lattices(B!1, D!3), F) | (~(k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))),
% 0.52/0.58 inference(quant_inst,[status(thm)],[])).
% 0.52/0.58 tff(256,plain,
% 0.52/0.58 ((~![E: $i] : ((~m1_subset_1(E, u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | r2_lattices(A!0, E, F) | (~(k7_lattices(B!1, D!3) = E)) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[255, 254])).
% 0.52/0.58 tff(257,plain,
% 0.52/0.58 (![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[256, 250, 170])).
% 0.52/0.58 tff(258,plain,
% 0.52/0.58 (C!2 = D!3),
% 0.52/0.58 inference(or_elim,[status(thm)],[161])).
% 0.52/0.58 tff(259,plain,
% 0.52/0.58 (D!3 = C!2),
% 0.52/0.58 inference(symmetry,[status(thm)],[258])).
% 0.52/0.58 tff(260,plain,
% 0.52/0.58 (m1_subset_1(D!3, u1_struct_0(A!0)) <=> m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.52/0.58 inference(monotonicity,[status(thm)],[259])).
% 0.52/0.58 tff(261,plain,
% 0.52/0.58 (m1_subset_1(C!2, u1_struct_0(A!0)) <=> m1_subset_1(D!3, u1_struct_0(A!0))),
% 0.52/0.58 inference(symmetry,[status(thm)],[260])).
% 0.52/0.58 tff(262,plain,
% 0.52/0.58 (m1_subset_1(C!2, u1_struct_0(A!0))),
% 0.52/0.58 inference(and_elim,[status(thm)],[21])).
% 0.52/0.58 tff(263,plain,
% 0.52/0.58 (m1_subset_1(D!3, u1_struct_0(A!0))),
% 0.52/0.58 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.52/0.58 tff(264,plain,
% 0.52/0.58 ((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)),
% 0.52/0.58 inference(tautology,[status(thm)],[])).
% 0.52/0.58 tff(265,plain,
% 0.52/0.58 (v11_lattices(A!0)),
% 0.52/0.58 inference(unit_resolution,[status(thm)],[264, 224])).
% 0.52/0.58 tff(266,plain,
% 0.52/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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))))))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(267,plain,
% 0.52/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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)))))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[266])).
% 0.52/0.58 tff(268,plain,
% 0.52/0.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(269,plain,
% 0.52/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[268])).
% 0.52/0.58 tff(270,plain,
% 0.52/0.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))),
% 0.52/0.58 inference(bind,[status(th)],[])).
% 0.52/0.58 tff(271,plain,
% 0.52/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.58 inference(quant_intro,[status(thm)],[270])).
% 0.52/0.58 tff(272,plain,
% 0.52/0.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.58 inference(transitivity,[status(thm)],[271, 269])).
% 0.52/0.58 tff(273,plain,
% 0.52/0.58 (^[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))))), ((![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))) | (~m1_subset_1(B, u1_struct_0(A)))))), rewrite((![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) | ![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))) | (~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))) | (~m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A)))))), (![B: $i] : (![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)))) <=> ![B: $i] : (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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) | (~l3_lattices(A))) | ![B: $i] : (v3_struct_0(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))) | (~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) | ![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))) | (~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) | ![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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))))),
% 0.52/0.59 inference(bind,[status(th)],[])).
% 0.52/0.59 tff(274,plain,
% 0.52/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.59 inference(quant_intro,[status(thm)],[273])).
% 0.52/0.59 tff(275,plain,
% 0.52/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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)))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(276,plain,
% 0.52/0.59 (^[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))))) <=> (![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))))), ((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))))) <=> (![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))))))), (![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] : (![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)) & 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] : (![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))))))), rewrite((((~v3_struct_0(A)) & l3_lattices(A)) => ![B: $i] : (![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)) & l3_lattices(A))) | ![B: $i] : (![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)) & 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] : (![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)))))))),
% 0.52/0.59 inference(bind,[status(th)],[])).
% 0.52/0.59 tff(277,plain,
% 0.52/0.59 (![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] : (![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)))))),
% 0.52/0.59 inference(quant_intro,[status(thm)],[276])).
% 0.52/0.59 tff(278,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/sandbox/benchmark/theBenchmark.p','d21_lattices')).
% 0.52/0.59 tff(279,plain,
% 0.52/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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)))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[278, 277])).
% 0.52/0.59 tff(280,plain,
% 0.52/0.59 (![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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)))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[279, 275])).
% 0.52/0.59 tff(281,plain,(
% 0.52/0.59 ![A: $i] : ((~((~v3_struct_0(A)) & l3_lattices(A))) | ![B: $i] : (![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)))))),
% 0.52/0.59 inference(skolemize,[status(sab)],[280])).
% 0.52/0.59 tff(282,plain,
% 0.52/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[281, 274])).
% 0.52/0.59 tff(283,plain,
% 0.52/0.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : (v3_struct_0(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))) | (~v10_lattices(A)) | (~v11_lattices(A)) | (~v16_lattices(A)) | (~l3_lattices(A))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[282, 272])).
% 0.52/0.59 tff(284,plain,
% 0.52/0.59 (![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)))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[283, 267])).
% 0.52/0.59 tff(285,plain,
% 0.52/0.59 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(286,plain,
% 0.52/0.59 ((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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(287,plain,
% 0.52/0.59 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))))),
% 0.52/0.59 inference(monotonicity,[status(thm)],[286])).
% 0.52/0.59 tff(288,plain,
% 0.52/0.59 (((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)))))),
% 0.52/0.59 inference(transitivity,[status(thm)],[287, 285])).
% 0.52/0.59 tff(289,plain,
% 0.52/0.59 ((~![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)))))),
% 0.52/0.59 inference(quant_inst,[status(thm)],[])).
% 0.52/0.59 tff(290,plain,
% 0.52/0.59 ((~![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) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.52/0.59 tff(291,plain,
% 0.52/0.59 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[290, 220, 218, 284])).
% 0.52/0.59 tff(292,plain,
% 0.52/0.59 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(293,plain,
% 0.52/0.59 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(294,plain,
% 0.52/0.59 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))))),
% 0.52/0.59 inference(monotonicity,[status(thm)],[293])).
% 0.52/0.59 tff(295,plain,
% 0.52/0.59 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))),
% 0.52/0.59 inference(transitivity,[status(thm)],[294, 292])).
% 0.52/0.59 tff(296,plain,
% 0.52/0.59 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3))))),
% 0.52/0.59 inference(quant_inst,[status(thm)],[])).
% 0.52/0.59 tff(297,plain,
% 0.52/0.59 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_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)) | (~v10_lattices(A!0)) | (~v16_lattices(A!0)) | (~v11_lattices(A!0)) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[296, 295])).
% 0.52/0.59 tff(298,plain,
% 0.52/0.59 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[297, 220, 229, 218, 226, 291, 265, 263])).
% 0.52/0.59 tff(299,plain,
% 0.52/0.59 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)))),
% 0.52/0.59 inference(rewrite,[status(thm)],[])).
% 0.52/0.59 tff(300,plain,
% 0.52/0.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)))),
% 0.52/0.59 inference(quant_inst,[status(thm)],[])).
% 0.52/0.59 tff(301,plain,
% 0.52/0.59 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(A!0))) | ((C = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, C, D!3)))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.59 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.52/0.59 tff(302,plain,
% 0.52/0.59 ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(A!0))) | ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[301, 298])).
% 0.52/0.59 tff(303,plain,
% 0.52/0.59 ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)),
% 0.52/0.59 inference(unit_resolution,[status(thm)],[302, 170])).
% 0.52/0.59 tff(304,plain,
% 0.52/0.59 ((k7_lattices(B!1, D!3) = k7_lattices(A!0, C!2)) <=> (k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3))),
% 0.52/0.59 inference(commutativity,[status(thm)],[])).
% 0.52/0.59 tff(305,plain,
% 0.52/0.59 (k7_lattices(A!0, D!3) = k7_lattices(A!0, C!2)),
% 0.52/0.59 inference(monotonicity,[status(thm)],[259])).
% 0.52/0.60 tff(306,plain,
% 0.52/0.60 ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> (k7_lattices(B!1, D!3) = k7_lattices(A!0, C!2))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[305])).
% 0.52/0.60 tff(307,plain,
% 0.52/0.60 ((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> (k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3))),
% 0.52/0.60 inference(transitivity,[status(thm)],[306, 304])).
% 0.52/0.60 tff(308,plain,
% 0.52/0.60 ((k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3)) <=> (k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3))),
% 0.52/0.60 inference(symmetry,[status(thm)],[307])).
% 0.52/0.60 tff(309,plain,
% 0.52/0.60 ((~(k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3))) <=> (~(k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[308])).
% 0.52/0.60 tff(310,plain,
% 0.52/0.60 (~(k7_lattices(A!0, C!2) = k7_lattices(B!1, D!3))),
% 0.52/0.60 inference(or_elim,[status(thm)],[161])).
% 0.52/0.60 tff(311,plain,
% 0.52/0.60 (~(k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[310, 309])).
% 0.52/0.60 tff(312,plain,
% 0.52/0.60 ((~((k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) <=> r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))) | (k7_lattices(B!1, D!3) = k7_lattices(A!0, D!3)) | (~r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(tautology,[status(thm)],[])).
% 0.52/0.60 tff(313,plain,
% 0.52/0.60 (~r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[312, 311, 303])).
% 0.52/0.60 tff(314,plain,
% 0.52/0.60 ((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)),
% 0.52/0.60 inference(tautology,[status(thm)],[])).
% 0.52/0.60 tff(315,plain,
% 0.52/0.60 (v11_lattices(B!1)),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[314, 188])).
% 0.52/0.60 tff(316,plain,
% 0.52/0.60 (((~![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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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)))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(317,plain,
% 0.52/0.60 ((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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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)))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(318,plain,
% 0.52/0.60 (((~![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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[317])).
% 0.52/0.60 tff(319,plain,
% 0.52/0.60 (((~![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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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)))))),
% 0.52/0.60 inference(transitivity,[status(thm)],[318, 316])).
% 0.52/0.60 tff(320,plain,
% 0.52/0.60 ((~![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)))))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(321,plain,
% 0.52/0.60 ((~![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] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[320, 319])).
% 0.52/0.60 tff(322,plain,
% 0.52/0.60 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[321, 160, 46, 284])).
% 0.52/0.60 tff(323,plain,
% 0.52/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(324,plain,
% 0.52/0.60 (((~m1_subset_1(D!3, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) <=> (v3_struct_0(B!1) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(325,plain,
% 0.52/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[324])).
% 0.52/0.60 tff(326,plain,
% 0.52/0.60 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))),
% 0.52/0.60 inference(transitivity,[status(thm)],[325, 323])).
% 0.52/0.60 tff(327,plain,
% 0.52/0.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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))))) | ((~m1_subset_1(D!3, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3))))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(328,plain,
% 0.52/0.60 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(B!1))) | v3_struct_0(B!1) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_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) | (~m1_subset_1(D!3, u1_struct_0(B!1))) | (~l3_lattices(B!1)) | (~v10_lattices(B!1)) | (~v16_lattices(B!1)) | (~v11_lattices(B!1)) | ![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[327, 326])).
% 0.52/0.60 tff(329,plain,
% 0.52/0.60 (![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[328, 162, 160, 209, 46, 192, 322, 315])).
% 0.52/0.60 tff(330,plain,
% 0.52/0.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(331,plain,
% 0.52/0.60 (((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ((k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))) <=> ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(332,plain,
% 0.52/0.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ((k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[331])).
% 0.52/0.60 tff(333,plain,
% 0.52/0.60 (((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ((k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))) <=> ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(transitivity,[status(thm)],[332, 330])).
% 0.52/0.60 tff(334,plain,
% 0.52/0.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | ((~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | ((k7_lattices(B!1, D!3) = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(335,plain,
% 0.52/0.60 ((~![C: $i] : ((~m1_subset_1(C, u1_struct_0(B!1))) | ((C = k7_lattices(B!1, D!3)) <=> r2_lattices(B!1, C, D!3)))) | (~m1_subset_1(k7_lattices(B!1, D!3), u1_struct_0(B!1))) | r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.52/0.60 tff(336,plain,
% 0.52/0.60 (r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)),
% 0.52/0.60 inference(unit_resolution,[status(thm)],[335, 169, 329])).
% 0.52/0.60 tff(337,plain,
% 0.52/0.60 (((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))) <=> ((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(338,plain,
% 0.52/0.60 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | $false | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(339,plain,
% 0.52/0.60 ((~$true) <=> $false),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(340,plain,
% 0.52/0.60 ((D!3 = D!3) <=> $true),
% 0.52/0.60 inference(rewrite,[status(thm)],[])).
% 0.52/0.60 tff(341,plain,
% 0.52/0.60 ((~(D!3 = D!3)) <=> (~$true)),
% 0.52/0.60 inference(monotonicity,[status(thm)],[340])).
% 0.52/0.60 tff(342,plain,
% 0.52/0.60 ((~(D!3 = D!3)) <=> $false),
% 0.52/0.60 inference(transitivity,[status(thm)],[341, 339])).
% 0.52/0.60 tff(343,plain,
% 0.52/0.60 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~(D!3 = D!3)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | $false | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[342])).
% 0.52/0.60 tff(344,plain,
% 0.52/0.60 (((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~(D!3 = D!3)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)) <=> ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(transitivity,[status(thm)],[343, 338])).
% 0.52/0.60 tff(345,plain,
% 0.52/0.60 (((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~(D!3 = D!3)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))) <=> ((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)))),
% 0.52/0.60 inference(monotonicity,[status(thm)],[344])).
% 0.52/0.60 tff(346,plain,
% 0.52/0.60 (((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~(D!3 = D!3)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))) <=> ((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(transitivity,[status(thm)],[345, 337])).
% 0.52/0.60 tff(347,plain,
% 0.52/0.60 ((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | ((~m1_subset_1(D!3, u1_struct_0(A!0))) | (~(D!3 = D!3)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3))),
% 0.52/0.60 inference(quant_inst,[status(thm)],[])).
% 0.52/0.60 tff(348,plain,
% 0.52/0.60 ((~![F: $i] : ((~m1_subset_1(F, u1_struct_0(A!0))) | (~(D!3 = F)) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), F))) | (~m1_subset_1(D!3, u1_struct_0(A!0))) | (~r2_lattices(B!1, k7_lattices(B!1, D!3), D!3)) | r2_lattices(A!0, k7_lattices(B!1, D!3), D!3)),
% 0.52/0.60 inference(modus_ponens,[status(thm)],[347, 346])).
% 0.52/0.61 tff(349,plain,
% 0.52/0.61 ($false),
% 0.52/0.61 inference(unit_resolution,[status(thm)],[348, 263, 336, 313, 257])).
% 0.52/0.61 % SZS output end Proof
%------------------------------------------------------------------------------