TSTP Solution File: LAT309+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT309+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 18:32:56 EDT 2022
% Result : Theorem 11.66s 7.50s
% Output : Proof 11.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : LAT309+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Thu Sep 1 13:53:13 EDT 2022
% 0.10/0.31 % CPUTime :
% 0.15/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.31 Usage: tptp [options] [-file:]file
% 0.15/0.31 -h, -? prints this message.
% 0.15/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.31 -m, -model generate model.
% 0.15/0.31 -p, -proof generate proof.
% 0.15/0.31 -c, -core generate unsat core of named formulas.
% 0.15/0.31 -st, -statistics display statistics.
% 0.15/0.31 -t:timeout set timeout (in second).
% 0.15/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.31 -<param>:<value> configuration parameter and value.
% 0.15/0.31 -o:<output-file> file to place output in.
% 11.66/7.50 % SZS status Theorem
% 11.66/7.50 % SZS output start Proof
% 11.66/7.50 tff(v1_filter_0_type, type, (
% 11.66/7.50 v1_filter_0: ( $i * $i ) > $o)).
% 11.66/7.50 tff(k1_lattice2_type, type, (
% 11.66/7.50 k1_lattice2: $i > $i)).
% 11.66/7.50 tff(tptp_fun_A_0_type, type, (
% 11.66/7.50 tptp_fun_A_0: $i)).
% 11.66/7.50 tff(k15_filter_2_type, type, (
% 11.66/7.50 k15_filter_2: ( $i * $i ) > $i)).
% 11.66/7.50 tff(tptp_fun_C_27_type, type, (
% 11.66/7.50 tptp_fun_C_27: ( $i * $i ) > $i)).
% 11.66/7.50 tff(g3_lattices_type, type, (
% 11.66/7.50 g3_lattices: ( $i * $i * $i ) > $i)).
% 11.66/7.50 tff(u2_lattices_type, type, (
% 11.66/7.50 u2_lattices: $i > $i)).
% 11.66/7.50 tff(u1_lattices_type, type, (
% 11.66/7.50 u1_lattices: $i > $i)).
% 11.66/7.50 tff(u1_struct_0_type, type, (
% 11.66/7.50 u1_struct_0: $i > $i)).
% 11.66/7.50 tff(tptp_fun_B_1_type, type, (
% 11.66/7.50 tptp_fun_B_1: $i)).
% 11.66/7.50 tff(l3_lattices_type, type, (
% 11.66/7.50 l3_lattices: $i > $o)).
% 11.66/7.50 tff(r2_filter_2_type, type, (
% 11.66/7.50 r2_filter_2: ( $i * $i ) > $o)).
% 11.66/7.50 tff(r2_hidden_type, type, (
% 11.66/7.50 r2_hidden: ( $i * $i ) > $o)).
% 11.66/7.50 tff(m2_filter_2_type, type, (
% 11.66/7.50 m2_filter_2: ( $i * $i ) > $o)).
% 11.66/7.50 tff(k6_lattices_type, type, (
% 11.66/7.50 k6_lattices: $i > $i)).
% 11.66/7.50 tff(v14_lattices_type, type, (
% 11.66/7.50 v14_lattices: $i > $o)).
% 11.66/7.50 tff(m1_subset_1_type, type, (
% 11.66/7.50 m1_subset_1: ( $i * $i ) > $o)).
% 11.66/7.50 tff(v10_lattices_type, type, (
% 11.66/7.50 v10_lattices: $i > $o)).
% 11.66/7.50 tff(v3_struct_0_type, type, (
% 11.66/7.50 v3_struct_0: $i > $o)).
% 11.66/7.50 tff(k7_filter_2_type, type, (
% 11.66/7.50 k7_filter_2: ( $i * $i ) > $i)).
% 11.66/7.50 tff(k1_zfmisc_1_type, type, (
% 11.66/7.50 k1_zfmisc_1: $i > $i)).
% 11.66/7.50 tff(v3_lattices_type, type, (
% 11.66/7.50 v3_lattices: $i > $o)).
% 11.66/7.50 tff(m1_relset_1_type, type, (
% 11.66/7.50 m1_relset_1: ( $i * $i * $i ) > $o)).
% 11.66/7.50 tff(k2_zfmisc_1_type, type, (
% 11.66/7.50 k2_zfmisc_1: ( $i * $i ) > $i)).
% 11.66/7.50 tff(m2_relset_1_type, type, (
% 11.66/7.50 m2_relset_1: ( $i * $i * $i ) > $o)).
% 11.66/7.50 tff(v1_funct_2_type, type, (
% 11.66/7.50 v1_funct_2: ( $i * $i * $i ) > $o)).
% 11.66/7.50 tff(v1_funct_1_type, type, (
% 11.66/7.50 v1_funct_1: $i > $o)).
% 11.66/7.50 tff(l1_lattices_type, type, (
% 11.66/7.50 l1_lattices: $i > $o)).
% 11.66/7.50 tff(l2_lattices_type, type, (
% 11.66/7.50 l2_lattices: $i > $o)).
% 11.66/7.50 tff(v1_xboole_0_type, type, (
% 11.66/7.50 v1_xboole_0: $i > $o)).
% 11.66/7.50 tff(m1_filter_0_type, type, (
% 11.66/7.50 m1_filter_0: ( $i * $i ) > $o)).
% 11.66/7.50 tff(k5_lattices_type, type, (
% 11.66/7.50 k5_lattices: $i > $i)).
% 11.66/7.50 tff(k5_filter_2_type, type, (
% 11.66/7.50 k5_filter_2: ( $i * $i ) > $i)).
% 11.66/7.50 tff(v13_lattices_type, type, (
% 11.66/7.50 v13_lattices: $i > $o)).
% 11.66/7.50 tff(v9_lattices_type, type, (
% 11.66/7.50 v9_lattices: $i > $o)).
% 11.66/7.50 tff(v8_lattices_type, type, (
% 11.66/7.50 v8_lattices: $i > $o)).
% 11.66/7.50 tff(v7_lattices_type, type, (
% 11.66/7.50 v7_lattices: $i > $o)).
% 11.66/7.50 tff(v6_lattices_type, type, (
% 11.66/7.50 v6_lattices: $i > $o)).
% 11.66/7.50 tff(v5_lattices_type, type, (
% 11.66/7.50 v5_lattices: $i > $o)).
% 11.66/7.50 tff(v4_lattices_type, type, (
% 11.66/7.50 v4_lattices: $i > $o)).
% 11.66/7.50 tff(k14_filter_2_type, type, (
% 11.66/7.50 k14_filter_2: ( $i * $i ) > $i)).
% 11.66/7.50 tff(k8_filter_2_type, type, (
% 11.66/7.50 k8_filter_2: ( $i * $i ) > $i)).
% 11.66/7.50 tff(1,plain,
% 11.66/7.50 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 11.66/7.50 inference(bind,[status(th)],[])).
% 11.66/7.50 tff(2,plain,
% 11.66/7.50 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.50 inference(quant_intro,[status(thm)],[1])).
% 11.66/7.50 tff(3,plain,
% 11.66/7.50 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.50 inference(rewrite,[status(thm)],[])).
% 11.66/7.50 tff(4,plain,
% 11.66/7.50 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 11.66/7.50 inference(bind,[status(th)],[])).
% 11.66/7.50 tff(5,plain,
% 11.66/7.50 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.50 inference(quant_intro,[status(thm)],[4])).
% 11.66/7.50 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 11.66/7.51 tff(7,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[6, 5])).
% 11.66/7.51 tff(8,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[7, 3])).
% 11.66/7.51 tff(9,plain,(
% 11.66/7.51 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.51 inference(skolemize,[status(sab)],[8])).
% 11.66/7.51 tff(10,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[9, 2])).
% 11.66/7.51 tff(11,plain,
% 11.66/7.51 ((((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(12,plain,
% 11.66/7.51 ((m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(13,plain,
% 11.66/7.51 ((v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))) <=> (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(14,plain,
% 11.66/7.51 ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) <=> m1_subset_1(B!1, u1_struct_0(A!0))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(15,plain,
% 11.66/7.51 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))),
% 11.66/7.51 inference(monotonicity,[status(thm)],[14, 13])).
% 11.66/7.51 tff(16,plain,
% 11.66/7.51 (((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))) <=> (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 11.66/7.51 inference(transitivity,[status(thm)],[15, 12])).
% 11.66/7.51 tff(17,plain,
% 11.66/7.51 ((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(18,plain,
% 11.66/7.51 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))) <=> (((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)) & (m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))),
% 11.66/7.51 inference(monotonicity,[status(thm)],[17, 16])).
% 11.66/7.51 tff(19,plain,
% 11.66/7.51 (((~(~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))) & ((~(~m1_subset_1(B!1, u1_struct_0(A!0)))) & (v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))))) <=> ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))))),
% 11.66/7.51 inference(transitivity,[status(thm)],[18, 11])).
% 11.66/7.51 tff(20,plain,
% 11.66/7.51 ((~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C)))))))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(21,plain,
% 11.66/7.51 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((v14_lattices(A) & (~(B = k6_lattices(A)))) & ![C: $i] : (m2_filter_2(C, A) => (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))) <=> (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C)))))))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(22,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((v14_lattices(A) & (~(B = k6_lattices(A)))) & ![C: $i] : (m2_filter_2(C, A) => (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t36_filter_2')).
% 11.66/7.51 tff(23,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[22, 21])).
% 11.66/7.51 tff(24,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[23, 20])).
% 11.66/7.51 tff(25,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[24, 20])).
% 11.66/7.51 tff(26,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[25, 20])).
% 11.66/7.51 tff(27,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[26, 20])).
% 11.66/7.51 tff(28,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[27, 20])).
% 11.66/7.51 tff(29,plain,
% 11.66/7.51 (~![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~(v14_lattices(A) & (~(B = k6_lattices(A))) & ![C: $i] : ((~m2_filter_2(C, A)) | (~(r2_hidden(B, C) & r2_filter_2(A, C))))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[28, 20])).
% 11.66/7.51 tff(30,plain,
% 11.66/7.51 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0) & m1_subset_1(B!1, u1_struct_0(A!0)) & v14_lattices(A!0) & (~(B!1 = k6_lattices(A!0))) & ![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[29, 19])).
% 11.66/7.51 tff(31,plain,
% 11.66/7.51 (l3_lattices(A!0)),
% 11.66/7.51 inference(and_elim,[status(thm)],[30])).
% 11.66/7.51 tff(32,plain,
% 11.66/7.51 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(33,plain,
% 11.66/7.51 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.51 inference(quant_inst,[status(thm)],[])).
% 11.66/7.51 tff(34,plain,
% 11.66/7.51 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[33, 32])).
% 11.66/7.51 tff(35,plain,
% 11.66/7.51 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 11.66/7.51 inference(unit_resolution,[status(thm)],[34, 31, 10])).
% 11.66/7.51 tff(36,plain,
% 11.66/7.51 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 11.66/7.51 inference(symmetry,[status(thm)],[35])).
% 11.66/7.51 tff(37,plain,
% 11.66/7.51 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(k1_lattice2(A!0))),
% 11.66/7.51 inference(monotonicity,[status(thm)],[36])).
% 11.66/7.51 tff(38,plain,
% 11.66/7.51 (k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 11.66/7.51 inference(monotonicity,[status(thm)],[37])).
% 11.66/7.51 tff(39,plain,
% 11.66/7.51 (k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.51 inference(symmetry,[status(thm)],[38])).
% 11.66/7.51 tff(40,plain,
% 11.66/7.51 (u1_struct_0(k1_lattice2(A!0)) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.51 inference(symmetry,[status(thm)],[37])).
% 11.66/7.51 tff(41,plain,
% 11.66/7.51 (g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.51 inference(monotonicity,[status(thm)],[40])).
% 11.66/7.51 tff(42,plain,
% 11.66/7.51 (g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.51 inference(symmetry,[status(thm)],[41])).
% 11.66/7.51 tff(43,plain,
% 11.66/7.51 (^[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)))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(44,plain,
% 11.66/7.51 (![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))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[43])).
% 11.66/7.51 tff(45,plain,
% 11.66/7.51 (![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))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(46,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 11.66/7.51 tff(47,plain,
% 11.66/7.51 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[46, 45])).
% 11.66/7.51 tff(48,plain,(
% 11.66/7.51 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 11.66/7.51 inference(skolemize,[status(sab)],[47])).
% 11.66/7.51 tff(49,plain,
% 11.66/7.51 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[48, 44])).
% 11.66/7.51 tff(50,plain,
% 11.66/7.51 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 11.66/7.51 inference(quant_inst,[status(thm)],[])).
% 11.66/7.51 tff(51,plain,
% 11.66/7.51 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.51 inference(unit_resolution,[status(thm)],[50, 49])).
% 11.66/7.51 tff(52,plain,
% 11.66/7.51 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(53,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[52])).
% 11.66/7.51 tff(54,plain,
% 11.66/7.51 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(55,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[54])).
% 11.66/7.51 tff(56,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(57,plain,
% 11.66/7.51 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(58,plain,
% 11.66/7.51 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[57])).
% 11.66/7.51 tff(59,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 11.66/7.51 tff(60,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[59, 58])).
% 11.66/7.51 tff(61,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[60, 56])).
% 11.66/7.51 tff(62,plain,(
% 11.66/7.51 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 11.66/7.51 inference(skolemize,[status(sab)],[61])).
% 11.66/7.51 tff(63,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[62, 55])).
% 11.66/7.51 tff(64,plain,
% 11.66/7.51 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[63, 53])).
% 11.66/7.51 tff(65,plain,
% 11.66/7.51 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(66,plain,
% 11.66/7.51 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 11.66/7.51 inference(quant_inst,[status(thm)],[])).
% 11.66/7.51 tff(67,plain,
% 11.66/7.51 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[66, 65])).
% 11.66/7.51 tff(68,plain,
% 11.66/7.51 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 11.66/7.51 inference(unit_resolution,[status(thm)],[67, 31, 64])).
% 11.66/7.51 tff(69,plain,
% 11.66/7.51 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 11.66/7.51 inference(tautology,[status(thm)],[])).
% 11.66/7.51 tff(70,plain,
% 11.66/7.51 (l1_lattices(A!0)),
% 11.66/7.51 inference(unit_resolution,[status(thm)],[69, 68])).
% 11.66/7.51 tff(71,plain,
% 11.66/7.51 (^[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)))))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(72,plain,
% 11.66/7.51 (![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))))))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[71])).
% 11.66/7.51 tff(73,plain,
% 11.66/7.51 (^[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)))))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(74,plain,
% 11.66/7.51 (![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))))))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[73])).
% 11.66/7.51 tff(75,plain,
% 11.66/7.51 (![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))))),
% 11.66/7.51 inference(rewrite,[status(thm)],[])).
% 11.66/7.51 tff(76,plain,
% 11.66/7.51 (^[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))))))),
% 11.66/7.51 inference(bind,[status(th)],[])).
% 11.66/7.51 tff(77,plain,
% 11.66/7.51 (![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))))),
% 11.66/7.51 inference(quant_intro,[status(thm)],[76])).
% 11.66/7.51 tff(78,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 11.66/7.51 tff(79,plain,
% 11.66/7.51 (![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))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[78, 77])).
% 11.66/7.51 tff(80,plain,
% 11.66/7.51 (![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))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[79, 75])).
% 11.66/7.51 tff(81,plain,(
% 11.66/7.51 ![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))))),
% 11.66/7.51 inference(skolemize,[status(sab)],[80])).
% 11.66/7.51 tff(82,plain,
% 11.66/7.51 (![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))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[81, 74])).
% 11.66/7.51 tff(83,plain,
% 11.66/7.51 (![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))))))),
% 11.66/7.51 inference(modus_ponens,[status(thm)],[82, 72])).
% 11.66/7.51 tff(84,plain,
% 11.66/7.51 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 11.66/7.52 inference(rewrite,[status(thm)],[])).
% 11.66/7.52 tff(85,plain,
% 11.66/7.52 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 11.66/7.52 inference(quant_inst,[status(thm)],[])).
% 11.66/7.52 tff(86,plain,
% 11.66/7.52 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[85, 84])).
% 11.66/7.52 tff(87,plain,
% 11.66/7.52 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[86, 83])).
% 11.66/7.52 tff(88,plain,
% 11.66/7.52 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[87, 70])).
% 11.66/7.52 tff(89,plain,
% 11.66/7.52 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(90,plain,
% 11.66/7.52 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[89, 88])).
% 11.66/7.52 tff(91,plain,
% 11.66/7.52 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(92,plain,
% 11.66/7.52 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[91, 90])).
% 11.66/7.52 tff(93,plain,
% 11.66/7.52 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[92, 51])).
% 11.66/7.52 tff(94,plain,
% 11.66/7.52 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 11.66/7.52 inference(quant_inst,[status(thm)],[])).
% 11.66/7.52 tff(95,plain,
% 11.66/7.52 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[94, 49])).
% 11.66/7.52 tff(96,plain,
% 11.66/7.52 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(97,plain,
% 11.66/7.52 (l2_lattices(A!0)),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[96, 68])).
% 11.66/7.52 tff(98,plain,
% 11.66/7.52 (^[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)))))))),
% 11.66/7.52 inference(bind,[status(th)],[])).
% 11.66/7.52 tff(99,plain,
% 11.66/7.52 (![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))))))),
% 11.66/7.52 inference(quant_intro,[status(thm)],[98])).
% 11.66/7.52 tff(100,plain,
% 11.66/7.52 (^[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)))))))),
% 11.66/7.52 inference(bind,[status(th)],[])).
% 11.66/7.52 tff(101,plain,
% 11.66/7.52 (![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))))))),
% 11.66/7.52 inference(quant_intro,[status(thm)],[100])).
% 11.66/7.52 tff(102,plain,
% 11.66/7.52 (![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))))),
% 11.66/7.52 inference(rewrite,[status(thm)],[])).
% 11.66/7.52 tff(103,plain,
% 11.66/7.52 (^[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))))))),
% 11.66/7.52 inference(bind,[status(th)],[])).
% 11.66/7.52 tff(104,plain,
% 11.66/7.52 (![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))))),
% 11.66/7.52 inference(quant_intro,[status(thm)],[103])).
% 11.66/7.52 tff(105,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 11.66/7.52 tff(106,plain,
% 11.66/7.52 (![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))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[105, 104])).
% 11.66/7.52 tff(107,plain,
% 11.66/7.52 (![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))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[106, 102])).
% 11.66/7.52 tff(108,plain,(
% 11.66/7.52 ![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))))),
% 11.66/7.52 inference(skolemize,[status(sab)],[107])).
% 11.66/7.52 tff(109,plain,
% 11.66/7.52 (![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))))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[108, 101])).
% 11.66/7.52 tff(110,plain,
% 11.66/7.52 (![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))))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[109, 99])).
% 11.66/7.52 tff(111,plain,
% 11.66/7.52 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 11.66/7.52 inference(rewrite,[status(thm)],[])).
% 11.66/7.52 tff(112,plain,
% 11.66/7.52 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 11.66/7.52 inference(quant_inst,[status(thm)],[])).
% 11.66/7.52 tff(113,plain,
% 11.66/7.52 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 11.66/7.52 inference(modus_ponens,[status(thm)],[112, 111])).
% 11.66/7.52 tff(114,plain,
% 11.66/7.52 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[113, 110])).
% 11.66/7.52 tff(115,plain,
% 11.66/7.52 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[114, 97])).
% 11.66/7.52 tff(116,plain,
% 11.66/7.52 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(117,plain,
% 11.66/7.52 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[116, 115])).
% 11.66/7.52 tff(118,plain,
% 11.66/7.52 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(119,plain,
% 11.66/7.52 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[118, 117])).
% 11.66/7.52 tff(120,plain,
% 11.66/7.52 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[119, 95])).
% 11.66/7.52 tff(121,plain,
% 11.66/7.52 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(122,plain,
% 11.66/7.52 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[121, 115])).
% 11.66/7.52 tff(123,plain,
% 11.66/7.52 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(124,plain,
% 11.66/7.52 (v1_funct_1(u2_lattices(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[123, 115])).
% 11.66/7.52 tff(125,plain,
% 11.66/7.52 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(126,plain,
% 11.66/7.52 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[125, 88])).
% 11.66/7.52 tff(127,plain,
% 11.66/7.52 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 11.66/7.52 inference(tautology,[status(thm)],[])).
% 11.66/7.52 tff(128,plain,
% 11.66/7.52 (v1_funct_1(u1_lattices(A!0))),
% 11.66/7.52 inference(unit_resolution,[status(thm)],[127, 88])).
% 11.66/7.52 tff(129,plain,
% 11.66/7.52 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 11.66/7.52 inference(bind,[status(th)],[])).
% 11.66/7.52 tff(130,plain,
% 11.66/7.52 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 11.66/7.52 inference(quant_intro,[status(thm)],[129])).
% 11.66/7.52 tff(131,plain,
% 11.66/7.52 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 11.66/7.52 inference(bind,[status(th)],[])).
% 11.66/7.52 tff(132,plain,
% 11.66/7.52 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 11.66/7.52 inference(quant_intro,[status(thm)],[131])).
% 11.66/7.52 tff(133,plain,
% 11.66/7.52 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 11.66/7.52 inference(rewrite,[status(thm)],[])).
% 11.66/7.52 tff(134,plain,
% 11.66/7.52 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 11.66/7.53 inference(bind,[status(th)],[])).
% 11.66/7.53 tff(135,plain,
% 11.66/7.53 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 11.66/7.53 inference(quant_intro,[status(thm)],[134])).
% 11.66/7.53 tff(136,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 11.66/7.53 tff(137,plain,
% 11.66/7.53 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 11.66/7.53 inference(modus_ponens,[status(thm)],[136, 135])).
% 11.66/7.53 tff(138,plain,
% 11.66/7.53 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 11.66/7.53 inference(modus_ponens,[status(thm)],[137, 133])).
% 11.66/7.53 tff(139,plain,(
% 11.66/7.53 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 11.66/7.53 inference(skolemize,[status(sab)],[138])).
% 11.66/7.53 tff(140,plain,
% 11.66/7.53 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 11.66/7.53 inference(modus_ponens,[status(thm)],[139, 132])).
% 11.66/7.53 tff(141,plain,
% 11.66/7.53 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 11.66/7.53 inference(modus_ponens,[status(thm)],[140, 130])).
% 11.66/7.53 tff(142,plain,
% 11.66/7.53 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(rewrite,[status(thm)],[])).
% 11.66/7.53 tff(143,plain,
% 11.66/7.53 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(rewrite,[status(thm)],[])).
% 11.66/7.53 tff(144,plain,
% 11.66/7.53 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.53 inference(rewrite,[status(thm)],[])).
% 11.66/7.53 tff(145,plain,
% 11.66/7.53 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(monotonicity,[status(thm)],[144])).
% 11.66/7.53 tff(146,plain,
% 11.66/7.53 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(transitivity,[status(thm)],[145, 143])).
% 11.66/7.53 tff(147,plain,
% 11.66/7.53 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.66/7.53 inference(monotonicity,[status(thm)],[146])).
% 11.66/7.53 tff(148,plain,
% 11.66/7.53 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(transitivity,[status(thm)],[147, 142])).
% 11.66/7.53 tff(149,plain,
% 11.66/7.53 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.53 inference(quant_inst,[status(thm)],[])).
% 11.66/7.53 tff(150,plain,
% 11.66/7.53 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.54 inference(modus_ponens,[status(thm)],[149, 148])).
% 11.66/7.54 tff(151,plain,
% 11.66/7.54 ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[150, 141, 128, 126, 124, 122])).
% 11.66/7.54 tff(152,plain,
% 11.66/7.54 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[151, 120, 93])).
% 11.66/7.54 tff(153,plain,
% 11.66/7.54 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.54 inference(tautology,[status(thm)],[])).
% 11.66/7.54 tff(154,plain,
% 11.66/7.54 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[153, 152])).
% 11.66/7.54 tff(155,plain,
% 11.66/7.54 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.54 inference(tautology,[status(thm)],[])).
% 11.66/7.54 tff(156,plain,
% 11.66/7.54 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[155, 152])).
% 11.66/7.54 tff(157,plain,
% 11.66/7.54 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))))),
% 11.66/7.54 inference(bind,[status(th)],[])).
% 11.66/7.54 tff(158,plain,
% 11.66/7.54 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(quant_intro,[status(thm)],[157])).
% 11.66/7.54 tff(159,plain,
% 11.66/7.54 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(rewrite,[status(thm)],[])).
% 11.66/7.54 tff(160,plain,
% 11.66/7.54 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))))),
% 11.66/7.54 inference(bind,[status(th)],[])).
% 11.66/7.54 tff(161,plain,
% 11.66/7.54 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(quant_intro,[status(thm)],[160])).
% 11.66/7.54 tff(162,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 11.66/7.54 tff(163,plain,
% 11.66/7.54 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(modus_ponens,[status(thm)],[162, 161])).
% 11.66/7.54 tff(164,plain,
% 11.66/7.54 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(modus_ponens,[status(thm)],[163, 159])).
% 11.66/7.54 tff(165,plain,(
% 11.66/7.54 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(skolemize,[status(sab)],[164])).
% 11.66/7.54 tff(166,plain,
% 11.66/7.54 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))),
% 11.66/7.54 inference(modus_ponens,[status(thm)],[165, 158])).
% 11.66/7.54 tff(167,plain,
% 11.66/7.54 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.54 inference(rewrite,[status(thm)],[])).
% 11.66/7.54 tff(168,plain,
% 11.66/7.54 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.54 inference(rewrite,[status(thm)],[])).
% 11.66/7.54 tff(169,plain,
% 11.66/7.54 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.66/7.54 inference(monotonicity,[status(thm)],[168])).
% 11.66/7.54 tff(170,plain,
% 11.66/7.54 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.66/7.54 inference(transitivity,[status(thm)],[169, 167])).
% 11.66/7.54 tff(171,plain,
% 11.66/7.54 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.66/7.54 inference(quant_inst,[status(thm)],[])).
% 11.66/7.54 tff(172,plain,
% 11.66/7.54 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~l3_lattices(A)) | (~v3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.66/7.54 inference(modus_ponens,[status(thm)],[171, 170])).
% 11.66/7.54 tff(173,plain,
% 11.66/7.54 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[172, 166])).
% 11.66/7.54 tff(174,plain,
% 11.66/7.54 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.54 inference(unit_resolution,[status(thm)],[173, 156, 154])).
% 11.66/7.54 tff(175,plain,
% 11.66/7.54 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.66/7.54 inference(transitivity,[status(thm)],[174, 42])).
% 11.66/7.54 tff(176,plain,
% 11.66/7.54 (^[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)))))))),
% 11.66/7.54 inference(bind,[status(th)],[])).
% 11.66/7.54 tff(177,plain,
% 11.66/7.54 (![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))))))),
% 11.66/7.54 inference(quant_intro,[status(thm)],[176])).
% 11.66/7.54 tff(178,plain,
% 11.66/7.54 (^[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)))))))),
% 11.66/7.54 inference(bind,[status(th)],[])).
% 11.66/7.54 tff(179,plain,
% 11.66/7.54 (![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))))))),
% 11.66/7.54 inference(quant_intro,[status(thm)],[178])).
% 11.66/7.54 tff(180,plain,
% 11.66/7.54 (![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))))))),
% 11.66/7.54 inference(transitivity,[status(thm)],[179, 177])).
% 11.66/7.54 tff(181,plain,
% 11.66/7.54 (^[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))))))))),
% 11.66/7.54 inference(bind,[status(th)],[])).
% 11.66/7.54 tff(182,plain,
% 11.66/7.54 (![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))))))),
% 11.66/7.54 inference(quant_intro,[status(thm)],[181])).
% 11.66/7.54 tff(183,plain,
% 11.66/7.54 (![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))))),
% 11.66/7.54 inference(rewrite,[status(thm)],[])).
% 11.66/7.54 tff(184,plain,
% 11.66/7.54 (^[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))))))),
% 11.76/7.55 inference(bind,[status(th)],[])).
% 11.76/7.55 tff(185,plain,
% 11.76/7.55 (![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))))),
% 11.76/7.55 inference(quant_intro,[status(thm)],[184])).
% 11.76/7.55 tff(186,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 11.76/7.55 tff(187,plain,
% 11.76/7.55 (![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))))),
% 11.76/7.55 inference(modus_ponens,[status(thm)],[186, 185])).
% 11.76/7.55 tff(188,plain,
% 11.76/7.55 (![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))))),
% 11.76/7.55 inference(modus_ponens,[status(thm)],[187, 183])).
% 11.76/7.55 tff(189,plain,(
% 11.76/7.55 ![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))))),
% 11.76/7.55 inference(skolemize,[status(sab)],[188])).
% 11.76/7.55 tff(190,plain,
% 11.76/7.55 (![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))))))),
% 11.76/7.55 inference(modus_ponens,[status(thm)],[189, 182])).
% 11.76/7.55 tff(191,plain,
% 11.76/7.55 (![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))))))),
% 11.76/7.55 inference(modus_ponens,[status(thm)],[190, 180])).
% 11.76/7.55 tff(192,plain,
% 11.76/7.55 (((~![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(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 11.76/7.55 inference(rewrite,[status(thm)],[])).
% 11.76/7.55 tff(193,plain,
% 11.76/7.55 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 11.76/7.55 inference(rewrite,[status(thm)],[])).
% 11.76/7.55 tff(194,plain,
% 11.76/7.55 (((~![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(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))))),
% 11.76/7.55 inference(monotonicity,[status(thm)],[193])).
% 11.76/7.55 tff(195,plain,
% 11.76/7.55 (((~![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(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 11.76/7.55 inference(transitivity,[status(thm)],[194, 192])).
% 11.76/7.55 tff(196,plain,
% 11.76/7.55 ((~![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(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 11.76/7.55 inference(quant_inst,[status(thm)],[])).
% 11.76/7.56 tff(197,plain,
% 11.76/7.56 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[196, 195])).
% 11.76/7.56 tff(198,plain,
% 11.76/7.56 ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[197, 191, 128, 126, 124, 122])).
% 11.76/7.56 tff(199,plain,
% 11.76/7.56 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[198, 120, 93])).
% 11.76/7.56 tff(200,plain,
% 11.76/7.56 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.76/7.56 inference(rewrite,[status(thm)],[])).
% 11.76/7.56 tff(201,plain,
% 11.76/7.56 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.76/7.56 inference(quant_inst,[status(thm)],[])).
% 11.76/7.56 tff(202,plain,
% 11.76/7.56 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[201, 200])).
% 11.76/7.56 tff(203,plain,
% 11.76/7.56 ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(k1_lattice2(A!0)), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[202, 199])).
% 11.76/7.56 tff(204,plain,
% 11.76/7.56 (~((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[203, 175])).
% 11.76/7.56 tff(205,plain,
% 11.76/7.56 (((~(u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0)))),
% 11.76/7.56 inference(tautology,[status(thm)],[])).
% 11.76/7.56 tff(206,plain,
% 11.76/7.56 (u1_struct_0(A!0) = u1_struct_0(k1_lattice2(A!0))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[205, 204])).
% 11.76/7.56 tff(207,plain,
% 11.76/7.56 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[206])).
% 11.76/7.56 tff(208,plain,
% 11.76/7.56 (k1_zfmisc_1(u1_struct_0(A!0)) = k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.76/7.56 inference(transitivity,[status(thm)],[207, 39])).
% 11.76/7.56 tff(209,plain,
% 11.76/7.56 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[208])).
% 11.76/7.56 tff(210,plain,
% 11.76/7.56 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 11.76/7.56 inference(symmetry,[status(thm)],[209])).
% 11.76/7.56 tff(211,plain,
% 11.76/7.56 (^[A: $i] : refl((v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(212,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[211])).
% 11.76/7.56 tff(213,plain,
% 11.76/7.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(214,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[213])).
% 11.76/7.56 tff(215,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 11.76/7.56 inference(rewrite,[status(thm)],[])).
% 11.76/7.56 tff(216,plain,
% 11.76/7.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(217,plain,
% 11.76/7.56 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[216])).
% 11.76/7.56 tff(218,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => (k6_lattices(A) = k5_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t79_lattice2')).
% 11.76/7.56 tff(219,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[218, 217])).
% 11.76/7.56 tff(220,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[219, 215])).
% 11.76/7.56 tff(221,plain,(
% 11.76/7.56 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 11.76/7.56 inference(skolemize,[status(sab)],[220])).
% 11.76/7.56 tff(222,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[221, 214])).
% 11.76/7.56 tff(223,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[222, 212])).
% 11.76/7.56 tff(224,plain,
% 11.76/7.56 (v14_lattices(A!0)),
% 11.76/7.56 inference(and_elim,[status(thm)],[30])).
% 11.76/7.56 tff(225,plain,
% 11.76/7.56 (v10_lattices(A!0)),
% 11.76/7.56 inference(and_elim,[status(thm)],[30])).
% 11.76/7.56 tff(226,plain,
% 11.76/7.56 (~v3_struct_0(A!0)),
% 11.76/7.56 inference(and_elim,[status(thm)],[30])).
% 11.76/7.56 tff(227,plain,
% 11.76/7.56 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 11.76/7.56 inference(rewrite,[status(thm)],[])).
% 11.76/7.56 tff(228,plain,
% 11.76/7.56 ((v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 11.76/7.56 inference(rewrite,[status(thm)],[])).
% 11.76/7.56 tff(229,plain,
% 11.76/7.56 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0))))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[228])).
% 11.76/7.56 tff(230,plain,
% 11.76/7.56 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)))),
% 11.76/7.56 inference(transitivity,[status(thm)],[229, 227])).
% 11.76/7.56 tff(231,plain,
% 11.76/7.56 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~v14_lattices(A!0)))),
% 11.76/7.56 inference(quant_inst,[status(thm)],[])).
% 11.76/7.56 tff(232,plain,
% 11.76/7.56 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[231, 230])).
% 11.76/7.56 tff(233,plain,
% 11.76/7.56 (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))),
% 11.76/7.56 inference(unit_resolution,[status(thm)],[232, 226, 225, 31, 224, 223])).
% 11.76/7.56 tff(234,plain,
% 11.76/7.56 (k5_lattices(k1_lattice2(A!0)) = k6_lattices(A!0)),
% 11.76/7.56 inference(symmetry,[status(thm)],[233])).
% 11.76/7.56 tff(235,plain,
% 11.76/7.56 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[36])).
% 11.76/7.56 tff(236,plain,
% 11.76/7.56 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k6_lattices(A!0)),
% 11.76/7.56 inference(transitivity,[status(thm)],[235, 234])).
% 11.76/7.56 tff(237,plain,
% 11.76/7.56 ((B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> (B!1 = k6_lattices(A!0))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[236])).
% 11.76/7.56 tff(238,plain,
% 11.76/7.56 ((B!1 = k6_lattices(A!0)) <=> (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.76/7.56 inference(symmetry,[status(thm)],[237])).
% 11.76/7.56 tff(239,plain,
% 11.76/7.56 ((~(B!1 = k6_lattices(A!0))) <=> (~(B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.76/7.56 inference(monotonicity,[status(thm)],[238])).
% 11.76/7.56 tff(240,plain,
% 11.76/7.56 (~(B!1 = k6_lattices(A!0))),
% 11.76/7.56 inference(and_elim,[status(thm)],[30])).
% 11.76/7.56 tff(241,plain,
% 11.76/7.56 (~(B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.76/7.56 inference(modus_ponens,[status(thm)],[240, 239])).
% 11.76/7.56 tff(242,plain,
% 11.76/7.56 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(243,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[242])).
% 11.76/7.56 tff(244,plain,
% 11.76/7.56 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(245,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[244])).
% 11.76/7.56 tff(246,plain,
% 11.76/7.56 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(247,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[246])).
% 11.76/7.56 tff(248,plain,
% 11.76/7.56 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.56 inference(transitivity,[status(thm)],[247, 245])).
% 11.76/7.56 tff(249,plain,
% 11.76/7.56 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 11.76/7.56 inference(bind,[status(th)],[])).
% 11.76/7.56 tff(250,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.56 inference(quant_intro,[status(thm)],[249])).
% 11.76/7.56 tff(251,plain,
% 11.76/7.56 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.56 inference(rewrite,[status(thm)],[])).
% 11.76/7.56 tff(252,plain,
% 11.76/7.56 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(253,plain,
% 11.76/7.57 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[252])).
% 11.76/7.57 tff(254,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 11.76/7.57 tff(255,plain,
% 11.76/7.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[254, 253])).
% 11.76/7.57 tff(256,plain,
% 11.76/7.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[255, 251])).
% 11.76/7.57 tff(257,plain,(
% 11.76/7.57 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.57 inference(skolemize,[status(sab)],[256])).
% 11.76/7.57 tff(258,plain,
% 11.76/7.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[257, 250])).
% 11.76/7.57 tff(259,plain,
% 11.76/7.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[258, 248])).
% 11.76/7.57 tff(260,plain,
% 11.76/7.57 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[259, 243])).
% 11.76/7.57 tff(261,plain,
% 11.76/7.57 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(262,plain,
% 11.76/7.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 11.76/7.57 inference(quant_inst,[status(thm)],[])).
% 11.76/7.57 tff(263,plain,
% 11.76/7.57 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[262, 261])).
% 11.76/7.57 tff(264,plain,
% 11.76/7.57 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 11.76/7.57 inference(unit_resolution,[status(thm)],[263, 226, 225, 31, 260])).
% 11.76/7.57 tff(265,plain,
% 11.76/7.57 (m1_subset_1(B!1, u1_struct_0(A!0))),
% 11.76/7.57 inference(and_elim,[status(thm)],[30])).
% 11.76/7.57 tff(266,plain,
% 11.76/7.57 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(267,plain,
% 11.76/7.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1))),
% 11.76/7.57 inference(quant_inst,[status(thm)],[])).
% 11.76/7.57 tff(268,plain,
% 11.76/7.57 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (k5_filter_2(A!0, B!1) = B!1)),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[267, 266])).
% 11.76/7.57 tff(269,plain,
% 11.76/7.57 (k5_filter_2(A!0, B!1) = B!1),
% 11.76/7.57 inference(unit_resolution,[status(thm)],[268, 265, 264])).
% 11.76/7.57 tff(270,plain,
% 11.76/7.57 (B!1 = k5_filter_2(A!0, B!1)),
% 11.76/7.57 inference(symmetry,[status(thm)],[269])).
% 11.76/7.57 tff(271,plain,
% 11.76/7.57 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 11.76/7.57 inference(monotonicity,[status(thm)],[270, 37])).
% 11.76/7.57 tff(272,plain,
% 11.76/7.57 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) <=> m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.76/7.57 inference(symmetry,[status(thm)],[271])).
% 11.76/7.57 tff(273,plain,
% 11.76/7.57 (^[A: $i, B: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(274,plain,
% 11.76/7.57 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[273])).
% 11.76/7.57 tff(275,plain,
% 11.76/7.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(276,plain,
% 11.76/7.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[275])).
% 11.76/7.57 tff(277,plain,
% 11.76/7.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(278,plain,
% 11.76/7.57 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(279,plain,
% 11.76/7.57 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A)))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[278])).
% 11.76/7.57 tff(280,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k5_filter_2')).
% 11.76/7.57 tff(281,plain,
% 11.76/7.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[280, 279])).
% 11.76/7.57 tff(282,plain,
% 11.76/7.57 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[281, 277])).
% 11.76/7.57 tff(283,plain,(
% 11.76/7.57 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))))),
% 11.76/7.57 inference(skolemize,[status(sab)],[282])).
% 11.76/7.57 tff(284,plain,
% 11.76/7.57 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[283, 276])).
% 11.76/7.57 tff(285,plain,
% 11.76/7.57 (![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[284, 274])).
% 11.76/7.57 tff(286,plain,
% 11.76/7.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(287,plain,
% 11.76/7.57 ((v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(288,plain,
% 11.76/7.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))))),
% 11.76/7.57 inference(monotonicity,[status(thm)],[287])).
% 11.76/7.57 tff(289,plain,
% 11.76/7.57 (((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))))),
% 11.76/7.57 inference(transitivity,[status(thm)],[288, 286])).
% 11.76/7.57 tff(290,plain,
% 11.76/7.57 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 11.76/7.57 inference(quant_inst,[status(thm)],[])).
% 11.76/7.57 tff(291,plain,
% 11.76/7.57 ((~![A: $i, B: $i] : (v3_struct_0(A) | m1_subset_1(k5_filter_2(A, B), u1_struct_0(k1_lattice2(A))) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~m1_subset_1(B!1, u1_struct_0(A!0))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[290, 289])).
% 11.76/7.57 tff(292,plain,
% 11.76/7.57 (m1_subset_1(k5_filter_2(A!0, B!1), u1_struct_0(k1_lattice2(A!0)))),
% 11.76/7.57 inference(unit_resolution,[status(thm)],[291, 226, 225, 31, 265, 285])).
% 11.76/7.57 tff(293,plain,
% 11.76/7.57 (m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.76/7.57 inference(modus_ponens,[status(thm)],[292, 272])).
% 11.76/7.57 tff(294,plain,
% 11.76/7.57 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v13_lattices(k1_lattice2(A!0))),
% 11.76/7.57 inference(monotonicity,[status(thm)],[36])).
% 11.76/7.57 tff(295,plain,
% 11.76/7.57 (v13_lattices(k1_lattice2(A!0)) <=> v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.76/7.57 inference(symmetry,[status(thm)],[294])).
% 11.76/7.57 tff(296,plain,
% 11.76/7.57 (^[A: $i] : refl((v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(297,plain,
% 11.76/7.57 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[296])).
% 11.76/7.57 tff(298,plain,
% 11.76/7.57 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(299,plain,
% 11.76/7.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 11.76/7.57 inference(quant_intro,[status(thm)],[298])).
% 11.76/7.57 tff(300,plain,
% 11.76/7.57 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 11.76/7.57 inference(rewrite,[status(thm)],[])).
% 11.76/7.57 tff(301,plain,
% 11.76/7.57 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))))),
% 11.76/7.57 inference(bind,[status(th)],[])).
% 11.76/7.57 tff(302,plain,
% 11.76/7.57 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[301])).
% 11.78/7.58 tff(303,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t64_lattice2')).
% 11.78/7.58 tff(304,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[303, 302])).
% 11.78/7.58 tff(305,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[304, 300])).
% 11.78/7.58 tff(306,plain,(
% 11.78/7.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(skolemize,[status(sab)],[305])).
% 11.78/7.58 tff(307,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[306, 299])).
% 11.78/7.58 tff(308,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[307, 297])).
% 11.78/7.58 tff(309,plain,
% 11.78/7.58 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 11.78/7.58 inference(rewrite,[status(thm)],[])).
% 11.78/7.58 tff(310,plain,
% 11.78/7.58 ((v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 11.78/7.58 inference(rewrite,[status(thm)],[])).
% 11.78/7.58 tff(311,plain,
% 11.78/7.58 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))))),
% 11.78/7.58 inference(monotonicity,[status(thm)],[310])).
% 11.78/7.58 tff(312,plain,
% 11.78/7.58 (((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))))),
% 11.78/7.58 inference(transitivity,[status(thm)],[311, 309])).
% 11.78/7.58 tff(313,plain,
% 11.78/7.58 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 11.78/7.58 inference(quant_inst,[status(thm)],[])).
% 11.78/7.58 tff(314,plain,
% 11.78/7.58 ((~![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[313, 312])).
% 11.78/7.58 tff(315,plain,
% 11.78/7.58 (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[314, 226, 225, 31, 308])).
% 11.78/7.58 tff(316,plain,
% 11.78/7.58 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | (~v14_lattices(A!0)) | v13_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(tautology,[status(thm)],[])).
% 11.78/7.58 tff(317,plain,
% 11.78/7.58 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | v13_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[316, 224])).
% 11.78/7.58 tff(318,plain,
% 11.78/7.58 (v13_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[317, 315])).
% 11.78/7.58 tff(319,plain,
% 11.78/7.58 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[318, 295])).
% 11.78/7.58 tff(320,plain,
% 11.78/7.58 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 11.78/7.58 inference(monotonicity,[status(thm)],[36])).
% 11.78/7.58 tff(321,plain,
% 11.78/7.58 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.58 inference(symmetry,[status(thm)],[320])).
% 11.78/7.58 tff(322,plain,
% 11.78/7.58 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.78/7.58 inference(monotonicity,[status(thm)],[321])).
% 11.78/7.58 tff(323,plain,
% 11.78/7.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 11.78/7.58 inference(bind,[status(th)],[])).
% 11.78/7.58 tff(324,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[323])).
% 11.78/7.58 tff(325,plain,
% 11.78/7.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 11.78/7.58 inference(bind,[status(th)],[])).
% 11.78/7.58 tff(326,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[325])).
% 11.78/7.58 tff(327,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(rewrite,[status(thm)],[])).
% 11.78/7.58 tff(328,plain,
% 11.78/7.58 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 11.78/7.58 inference(bind,[status(th)],[])).
% 11.78/7.58 tff(329,plain,
% 11.78/7.58 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[328])).
% 11.78/7.58 tff(330,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 11.78/7.58 tff(331,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[330, 329])).
% 11.78/7.58 tff(332,plain,
% 11.78/7.58 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[331, 327])).
% 11.78/7.58 tff(333,plain,(
% 11.78/7.58 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 11.78/7.58 inference(skolemize,[status(sab)],[332])).
% 11.78/7.58 tff(334,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[333, 326])).
% 11.78/7.58 tff(335,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[334, 324])).
% 11.78/7.58 tff(336,plain,
% 11.78/7.58 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 11.78/7.58 inference(rewrite,[status(thm)],[])).
% 11.78/7.58 tff(337,plain,
% 11.78/7.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 11.78/7.58 inference(quant_inst,[status(thm)],[])).
% 11.78/7.58 tff(338,plain,
% 11.78/7.58 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[337, 336])).
% 11.78/7.58 tff(339,plain,
% 11.78/7.58 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[338, 226, 225, 31, 335])).
% 11.78/7.58 tff(340,plain,
% 11.78/7.58 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 11.78/7.58 inference(tautology,[status(thm)],[])).
% 11.78/7.58 tff(341,plain,
% 11.78/7.58 (~v3_struct_0(k1_lattice2(A!0))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[340, 339])).
% 11.78/7.58 tff(342,plain,
% 11.78/7.58 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[341, 322])).
% 11.78/7.58 tff(343,plain,
% 11.78/7.58 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(monotonicity,[status(thm)],[36])).
% 11.78/7.58 tff(344,plain,
% 11.78/7.58 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.58 inference(symmetry,[status(thm)],[343])).
% 11.78/7.58 tff(345,plain,
% 11.78/7.58 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(tautology,[status(thm)],[])).
% 11.78/7.58 tff(346,plain,
% 11.78/7.58 (v10_lattices(k1_lattice2(A!0))),
% 11.78/7.58 inference(unit_resolution,[status(thm)],[345, 339])).
% 11.78/7.58 tff(347,plain,
% 11.78/7.58 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.58 inference(modus_ponens,[status(thm)],[346, 344])).
% 11.78/7.58 tff(348,plain,
% 11.78/7.58 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 11.78/7.58 inference(bind,[status(th)],[])).
% 11.78/7.58 tff(349,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[348])).
% 11.78/7.58 tff(350,plain,
% 11.78/7.58 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 11.78/7.58 inference(bind,[status(th)],[])).
% 11.78/7.58 tff(351,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.58 inference(quant_intro,[status(thm)],[350])).
% 11.78/7.58 tff(352,plain,
% 11.78/7.58 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.58 inference(transitivity,[status(thm)],[351, 349])).
% 11.78/7.58 tff(353,plain,
% 11.78/7.58 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))), ((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), rewrite((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))), ((v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), (![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 11.78/7.59 inference(bind,[status(th)],[])).
% 11.78/7.59 tff(354,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.59 inference(quant_intro,[status(thm)],[353])).
% 11.78/7.59 tff(355,plain,
% 11.78/7.59 (^[A: $i] : rewrite(((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((~(~v3_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~(~(B = k5_lattices(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 11.78/7.59 inference(bind,[status(th)],[])).
% 11.78/7.59 tff(356,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((~(~v3_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~(~(B = k5_lattices(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 11.78/7.59 inference(quant_intro,[status(thm)],[355])).
% 11.78/7.59 tff(357,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 11.78/7.59 inference(rewrite,[status(thm)],[])).
% 11.78/7.59 tff(358,plain,
% 11.78/7.59 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : trans(monotonicity(rewrite((~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))) <=> (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> (m1_subset_1(B, u1_struct_0(A)) => (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), rewrite((m1_subset_1(B, u1_struct_0(A)) => (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))), ((m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))))),
% 11.78/7.59 inference(bind,[status(th)],[])).
% 11.78/7.59 tff(359,plain,
% 11.78/7.59 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A)))))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 11.78/7.59 inference(quant_intro,[status(thm)],[358])).
% 11.78/7.59 tff(360,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (~((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) & (~(B = k5_lattices(A)))) & ![C: $i] : (m1_filter_0(C, A) => (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t24_filter_0')).
% 11.78/7.59 tff(361,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 11.78/7.59 inference(modus_ponens,[status(thm)],[360, 359])).
% 11.78/7.59 tff(362,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) & (~(B = k5_lattices(A))) & ![C: $i] : ((~m1_filter_0(C, A)) | (~(r2_hidden(B, C) & v1_filter_0(C, A))))))))),
% 11.78/7.59 inference(modus_ponens,[status(thm)],[361, 357])).
% 11.78/7.59 tff(363,plain,(
% 11.78/7.59 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((~(~v3_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~(~(B = k5_lattices(A)))) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A))))))))),
% 11.78/7.59 inference(skolemize,[status(sab)],[362])).
% 11.78/7.59 tff(364,plain,
% 11.78/7.59 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~(r2_hidden(B, tptp_fun_C_27(B, A)) & v1_filter_0(tptp_fun_C_27(B, A), A)))))))),
% 11.78/7.59 inference(modus_ponens,[status(thm)],[363, 356])).
% 11.78/7.59 tff(365,plain,
% 11.78/7.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.59 inference(modus_ponens,[status(thm)],[364, 354])).
% 11.78/7.59 tff(366,plain,
% 11.78/7.59 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))),
% 11.78/7.59 inference(modus_ponens,[status(thm)],[365, 352])).
% 11.78/7.59 tff(367,plain,
% 11.78/7.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.78/7.59 inference(rewrite,[status(thm)],[])).
% 11.78/7.59 tff(368,plain,
% 11.78/7.59 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.78/7.59 inference(rewrite,[status(thm)],[])).
% 11.78/7.59 tff(369,plain,
% 11.78/7.59 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.78/7.60 inference(monotonicity,[status(thm)],[368])).
% 11.78/7.60 tff(370,plain,
% 11.78/7.60 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.78/7.60 inference(transitivity,[status(thm)],[369, 367])).
% 11.78/7.60 tff(371,plain,
% 11.78/7.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.78/7.60 inference(quant_inst,[status(thm)],[])).
% 11.78/7.60 tff(372,plain,
% 11.78/7.60 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (v3_struct_0(A) | (B = k5_lattices(A)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~((~m1_filter_0(tptp_fun_C_27(B, A), A)) | (~r2_hidden(B, tptp_fun_C_27(B, A))) | (~v1_filter_0(tptp_fun_C_27(B, A), A))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.60 inference(modus_ponens,[status(thm)],[371, 370])).
% 11.78/7.60 tff(373,plain,
% 11.78/7.60 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.60 inference(unit_resolution,[status(thm)],[372, 366])).
% 11.78/7.60 tff(374,plain,
% 11.78/7.60 (![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.60 inference(unit_resolution,[status(thm)],[373, 347, 156, 342])).
% 11.78/7.60 tff(375,plain,
% 11.78/7.60 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.60 inference(rewrite,[status(thm)],[])).
% 11.78/7.60 tff(376,plain,
% 11.78/7.60 (((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.61 inference(rewrite,[status(thm)],[])).
% 11.78/7.61 tff(377,plain,
% 11.78/7.61 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.78/7.61 inference(monotonicity,[status(thm)],[376])).
% 11.78/7.61 tff(378,plain,
% 11.78/7.61 (((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) <=> ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.61 inference(transitivity,[status(thm)],[377, 375])).
% 11.78/7.61 tff(379,plain,
% 11.78/7.61 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.78/7.61 inference(quant_inst,[status(thm)],[])).
% 11.78/7.61 tff(380,plain,
% 11.78/7.61 ((~![B: $i] : ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~((~m1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B, tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[379, 378])).
% 11.78/7.62 tff(381,plain,
% 11.78/7.62 ((B!1 = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(B!1, u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.78/7.62 inference(unit_resolution,[status(thm)],[380, 156, 342, 347, 374, 319])).
% 11.78/7.62 tff(382,plain,
% 11.78/7.62 (~((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.78/7.62 inference(unit_resolution,[status(thm)],[381, 293, 241])).
% 11.78/7.62 tff(383,plain,
% 11.78/7.62 (((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.62 inference(tautology,[status(thm)],[])).
% 11.78/7.62 tff(384,plain,
% 11.78/7.62 (m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.78/7.62 inference(unit_resolution,[status(thm)],[383, 382])).
% 11.78/7.62 tff(385,plain,
% 11.78/7.62 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 11.78/7.62 inference(bind,[status(th)],[])).
% 11.78/7.62 tff(386,plain,
% 11.78/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(quant_intro,[status(thm)],[385])).
% 11.78/7.62 tff(387,plain,
% 11.78/7.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))),
% 11.78/7.62 inference(bind,[status(th)],[])).
% 11.78/7.62 tff(388,plain,
% 11.78/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(quant_intro,[status(thm)],[387])).
% 11.78/7.62 tff(389,plain,
% 11.78/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(transitivity,[status(thm)],[388, 386])).
% 11.78/7.62 tff(390,plain,
% 11.78/7.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))))),
% 11.78/7.62 inference(bind,[status(th)],[])).
% 11.78/7.62 tff(391,plain,
% 11.78/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(quant_intro,[status(thm)],[390])).
% 11.78/7.62 tff(392,plain,
% 11.78/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 11.78/7.62 inference(rewrite,[status(thm)],[])).
% 11.78/7.62 tff(393,plain,
% 11.78/7.62 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(bind,[status(th)],[])).
% 11.78/7.62 tff(394,plain,
% 11.78/7.62 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 11.78/7.62 inference(quant_intro,[status(thm)],[393])).
% 11.78/7.62 tff(395,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_0(B, A) => ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m1_filter_0')).
% 11.78/7.62 tff(396,plain,
% 11.78/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[395, 394])).
% 11.78/7.62 tff(397,plain,
% 11.78/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[396, 392])).
% 11.78/7.62 tff(398,plain,(
% 11.78/7.62 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_filter_0(B, A)) | ((~v1_xboole_0(B)) & m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 11.78/7.62 inference(skolemize,[status(sab)],[397])).
% 11.78/7.62 tff(399,plain,
% 11.78/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[398, 391])).
% 11.78/7.62 tff(400,plain,
% 11.78/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[399, 389])).
% 11.78/7.62 tff(401,plain,
% 11.78/7.62 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 11.78/7.62 inference(rewrite,[status(thm)],[])).
% 11.78/7.62 tff(402,plain,
% 11.78/7.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))))),
% 11.78/7.62 inference(quant_inst,[status(thm)],[])).
% 11.78/7.62 tff(403,plain,
% 11.78/7.62 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.78/7.62 inference(modus_ponens,[status(thm)],[402, 401])).
% 11.78/7.62 tff(404,plain,
% 11.78/7.62 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.78/7.62 inference(unit_resolution,[status(thm)],[403, 400])).
% 11.78/7.62 tff(405,plain,
% 11.78/7.62 (![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.78/7.62 inference(unit_resolution,[status(thm)],[404, 347, 156, 342])).
% 11.78/7.62 tff(406,plain,
% 11.78/7.62 (((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.83/7.62 inference(rewrite,[status(thm)],[])).
% 11.83/7.62 tff(407,plain,
% 11.83/7.62 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | ((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))),
% 11.83/7.62 inference(quant_inst,[status(thm)],[])).
% 11.83/7.62 tff(408,plain,
% 11.83/7.62 ((~![B: $i] : ((~m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))))) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 11.83/7.62 inference(modus_ponens,[status(thm)],[407, 406])).
% 11.83/7.62 tff(409,plain,
% 11.83/7.62 (~(v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.83/7.62 inference(unit_resolution,[status(thm)],[408, 405, 384])).
% 11.83/7.62 tff(410,plain,
% 11.83/7.62 ((v1_xboole_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) | m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.62 inference(tautology,[status(thm)],[])).
% 11.83/7.62 tff(411,plain,
% 11.83/7.62 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.62 inference(unit_resolution,[status(thm)],[410, 409])).
% 11.83/7.62 tff(412,plain,
% 11.83/7.62 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))),
% 11.83/7.62 inference(modus_ponens,[status(thm)],[411, 210])).
% 11.83/7.62 tff(413,plain,
% 11.83/7.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))),
% 11.83/7.62 inference(bind,[status(th)],[])).
% 11.83/7.62 tff(414,plain,
% 11.83/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.62 inference(quant_intro,[status(thm)],[413])).
% 11.83/7.62 tff(415,plain,
% 11.83/7.62 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.83/7.62 inference(bind,[status(th)],[])).
% 11.83/7.62 tff(416,plain,
% 11.83/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.62 inference(quant_intro,[status(thm)],[415])).
% 11.83/7.62 tff(417,plain,
% 11.83/7.62 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.83/7.62 inference(bind,[status(th)],[])).
% 11.83/7.62 tff(418,plain,
% 11.83/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.62 inference(quant_intro,[status(thm)],[417])).
% 11.83/7.62 tff(419,plain,
% 11.83/7.62 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.62 inference(transitivity,[status(thm)],[418, 416])).
% 11.83/7.62 tff(420,plain,
% 11.83/7.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 11.83/7.62 inference(bind,[status(th)],[])).
% 11.83/7.62 tff(421,plain,
% 11.83/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.62 inference(quant_intro,[status(thm)],[420])).
% 11.83/7.62 tff(422,plain,
% 11.83/7.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.62 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(423,plain,
% 11.83/7.63 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))))),
% 11.83/7.63 inference(bind,[status(th)],[])).
% 11.83/7.63 tff(424,plain,
% 11.83/7.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.63 inference(quant_intro,[status(thm)],[423])).
% 11.83/7.63 tff(425,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))) => (k7_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d6_filter_2')).
% 11.83/7.63 tff(426,plain,
% 11.83/7.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[425, 424])).
% 11.83/7.63 tff(427,plain,
% 11.83/7.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[426, 422])).
% 11.83/7.63 tff(428,plain,(
% 11.83/7.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.63 inference(skolemize,[status(sab)],[427])).
% 11.83/7.63 tff(429,plain,
% 11.83/7.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[428, 421])).
% 11.83/7.63 tff(430,plain,
% 11.83/7.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[429, 419])).
% 11.83/7.63 tff(431,plain,
% 11.83/7.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[430, 414])).
% 11.83/7.63 tff(432,plain,
% 11.83/7.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 11.83/7.63 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(433,plain,
% 11.83/7.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B)))),
% 11.83/7.63 inference(quant_inst,[status(thm)],[])).
% 11.83/7.63 tff(434,plain,
% 11.83/7.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (k7_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[433, 432])).
% 11.83/7.63 tff(435,plain,
% 11.83/7.63 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))),
% 11.83/7.63 inference(unit_resolution,[status(thm)],[434, 226, 225, 31, 431])).
% 11.83/7.63 tff(436,plain,
% 11.83/7.63 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.63 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(437,plain,
% 11.83/7.63 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.63 inference(quant_inst,[status(thm)],[])).
% 11.83/7.63 tff(438,plain,
% 11.83/7.63 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[437, 436])).
% 11.83/7.63 tff(439,plain,
% 11.83/7.63 ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(A!0)))) | (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.63 inference(unit_resolution,[status(thm)],[438, 435])).
% 11.83/7.63 tff(440,plain,
% 11.83/7.63 (k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.83/7.63 inference(unit_resolution,[status(thm)],[439, 412])).
% 11.83/7.63 tff(441,plain,
% 11.83/7.63 (m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)) <=> m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.83/7.63 inference(monotonicity,[status(thm)],[35])).
% 11.83/7.63 tff(442,plain,
% 11.83/7.63 (m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 11.83/7.63 inference(symmetry,[status(thm)],[441])).
% 11.83/7.63 tff(443,plain,
% 11.83/7.63 (m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[384, 442])).
% 11.83/7.63 tff(444,plain,
% 11.83/7.63 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 11.83/7.63 inference(bind,[status(th)],[])).
% 11.83/7.63 tff(445,plain,
% 11.83/7.63 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.83/7.63 inference(quant_intro,[status(thm)],[444])).
% 11.83/7.63 tff(446,plain,
% 11.83/7.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 11.83/7.63 inference(bind,[status(th)],[])).
% 11.83/7.63 tff(447,plain,
% 11.83/7.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.83/7.63 inference(quant_intro,[status(thm)],[446])).
% 11.83/7.63 tff(448,plain,
% 11.83/7.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 11.83/7.63 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(449,plain,
% 11.83/7.63 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))))),
% 11.83/7.63 inference(bind,[status(th)],[])).
% 11.83/7.63 tff(450,plain,
% 11.83/7.63 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 11.83/7.63 inference(quant_intro,[status(thm)],[449])).
% 11.83/7.63 tff(451,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => (k14_filter_2(A, B) = k8_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k14_filter_2')).
% 11.83/7.63 tff(452,plain,
% 11.83/7.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[451, 450])).
% 11.83/7.63 tff(453,plain,
% 11.83/7.63 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[452, 448])).
% 11.83/7.63 tff(454,plain,(
% 11.83/7.63 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | (k14_filter_2(A, B) = k8_filter_2(A, B)))),
% 11.83/7.63 inference(skolemize,[status(sab)],[453])).
% 11.83/7.63 tff(455,plain,
% 11.83/7.63 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[454, 447])).
% 11.83/7.63 tff(456,plain,
% 11.83/7.63 (![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.83/7.63 inference(modus_ponens,[status(thm)],[455, 445])).
% 11.83/7.63 tff(457,plain,
% 11.83/7.63 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.83/7.63 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(458,plain,
% 11.83/7.63 ((v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.83/7.63 inference(rewrite,[status(thm)],[])).
% 11.83/7.63 tff(459,plain,
% 11.83/7.63 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.83/7.63 inference(monotonicity,[status(thm)],[458])).
% 11.83/7.63 tff(460,plain,
% 11.83/7.63 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.83/7.63 inference(transitivity,[status(thm)],[459, 457])).
% 11.83/7.63 tff(461,plain,
% 11.83/7.63 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 11.83/7.64 inference(quant_inst,[status(thm)],[])).
% 11.83/7.64 tff(462,plain,
% 11.83/7.64 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k14_filter_2(A, B) = k8_filter_2(A, B)) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[461, 460])).
% 11.83/7.64 tff(463,plain,
% 11.83/7.64 ((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))) | (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.64 inference(unit_resolution,[status(thm)],[462, 226, 225, 31, 456])).
% 11.83/7.64 tff(464,plain,
% 11.83/7.64 (k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.64 inference(unit_resolution,[status(thm)],[463, 443])).
% 11.83/7.64 tff(465,plain,
% 11.83/7.64 (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.64 inference(symmetry,[status(thm)],[464])).
% 11.83/7.64 tff(466,plain,
% 11.83/7.64 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0)))) <=> m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.64 inference(monotonicity,[status(thm)],[39])).
% 11.83/7.64 tff(467,plain,
% 11.83/7.64 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 11.83/7.64 inference(symmetry,[status(thm)],[466])).
% 11.83/7.64 tff(468,plain,
% 11.83/7.64 (m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[411, 467])).
% 11.83/7.64 tff(469,plain,
% 11.83/7.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))),
% 11.83/7.64 inference(bind,[status(th)],[])).
% 11.83/7.64 tff(470,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(quant_intro,[status(thm)],[469])).
% 11.83/7.64 tff(471,plain,
% 11.83/7.64 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.83/7.64 inference(bind,[status(th)],[])).
% 11.83/7.64 tff(472,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(quant_intro,[status(thm)],[471])).
% 11.83/7.64 tff(473,plain,
% 11.83/7.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 11.83/7.64 inference(bind,[status(th)],[])).
% 11.83/7.64 tff(474,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(quant_intro,[status(thm)],[473])).
% 11.83/7.64 tff(475,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(transitivity,[status(thm)],[474, 472])).
% 11.83/7.64 tff(476,plain,
% 11.83/7.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 11.83/7.64 inference(bind,[status(th)],[])).
% 11.83/7.64 tff(477,plain,
% 11.83/7.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(quant_intro,[status(thm)],[476])).
% 11.83/7.64 tff(478,plain,
% 11.83/7.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(rewrite,[status(thm)],[])).
% 11.83/7.64 tff(479,plain,
% 11.83/7.64 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))))),
% 11.83/7.64 inference(bind,[status(th)],[])).
% 11.83/7.64 tff(480,plain,
% 11.83/7.64 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(quant_intro,[status(thm)],[479])).
% 11.83/7.64 tff(481,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => (k8_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d7_filter_2')).
% 11.83/7.64 tff(482,plain,
% 11.83/7.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[481, 480])).
% 11.83/7.64 tff(483,plain,
% 11.83/7.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[482, 478])).
% 11.83/7.64 tff(484,plain,(
% 11.83/7.64 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(skolemize,[status(sab)],[483])).
% 11.83/7.64 tff(485,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[484, 477])).
% 11.83/7.64 tff(486,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[485, 475])).
% 11.83/7.64 tff(487,plain,
% 11.83/7.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[486, 470])).
% 11.83/7.64 tff(488,plain,
% 11.83/7.64 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 11.83/7.64 inference(rewrite,[status(thm)],[])).
% 11.83/7.64 tff(489,plain,
% 11.83/7.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B)))),
% 11.83/7.64 inference(quant_inst,[status(thm)],[])).
% 11.83/7.64 tff(490,plain,
% 11.83/7.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A))))) | (k8_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[489, 488])).
% 11.83/7.64 tff(491,plain,
% 11.83/7.64 (![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))),
% 11.83/7.64 inference(unit_resolution,[status(thm)],[490, 226, 225, 31, 487])).
% 11.83/7.64 tff(492,plain,
% 11.83/7.64 (((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.64 inference(rewrite,[status(thm)],[])).
% 11.83/7.64 tff(493,plain,
% 11.83/7.64 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.83/7.64 inference(quant_inst,[status(thm)],[])).
% 11.83/7.64 tff(494,plain,
% 11.83/7.64 ((~![B: $i] : ((~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, B) = B))) | (~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.64 inference(modus_ponens,[status(thm)],[493, 492])).
% 11.83/7.64 tff(495,plain,
% 11.83/7.64 ((~m1_subset_1(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_zfmisc_1(u1_struct_0(k1_lattice2(A!0))))) | (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.83/7.64 inference(unit_resolution,[status(thm)],[494, 491])).
% 11.83/7.64 tff(496,plain,
% 11.83/7.64 (k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.83/7.64 inference(unit_resolution,[status(thm)],[495, 468])).
% 11.83/7.64 tff(497,plain,
% 11.83/7.64 (tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k8_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.64 inference(symmetry,[status(thm)],[496])).
% 11.85/7.64 tff(498,plain,
% 11.85/7.64 (tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.64 inference(transitivity,[status(thm)],[497, 465])).
% 11.85/7.64 tff(499,plain,
% 11.85/7.64 (m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0) <=> m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 11.85/7.64 inference(monotonicity,[status(thm)],[498])).
% 11.85/7.64 tff(500,plain,
% 11.85/7.64 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) <=> m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 11.85/7.64 inference(symmetry,[status(thm)],[499])).
% 11.85/7.64 tff(501,plain,
% 11.85/7.64 (^[A: $i, B: $i] : refl((m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))),
% 11.85/7.64 inference(bind,[status(th)],[])).
% 11.85/7.64 tff(502,plain,
% 11.85/7.64 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.85/7.64 inference(quant_intro,[status(thm)],[501])).
% 11.85/7.64 tff(503,plain,
% 11.85/7.64 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) <=> (~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))))), rewrite((~(~(v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))))),
% 11.85/7.64 inference(bind,[status(th)],[])).
% 11.85/7.64 tff(504,plain,
% 11.85/7.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.85/7.64 inference(quant_intro,[status(thm)],[503])).
% 11.85/7.64 tff(505,plain,
% 11.85/7.64 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(506,plain,
% 11.85/7.65 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))))),
% 11.85/7.65 inference(bind,[status(th)],[])).
% 11.85/7.65 tff(507,plain,
% 11.85/7.65 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 11.85/7.65 inference(quant_intro,[status(thm)],[506])).
% 11.85/7.65 tff(508,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_filter_0(B, k1_lattice2(A))) => m2_filter_2(k14_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k14_filter_2')).
% 11.85/7.65 tff(509,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[508, 507])).
% 11.85/7.65 tff(510,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[509, 505])).
% 11.85/7.65 tff(511,plain,(
% 11.85/7.65 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_filter_0(B, k1_lattice2(A)))) | m2_filter_2(k14_filter_2(A, B), A))),
% 11.85/7.65 inference(skolemize,[status(sab)],[510])).
% 11.85/7.65 tff(512,plain,
% 11.85/7.65 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[511, 504])).
% 11.85/7.65 tff(513,plain,
% 11.85/7.65 (![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[512, 502])).
% 11.85/7.65 tff(514,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(515,plain,
% 11.85/7.65 ((m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(516,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))))),
% 11.85/7.65 inference(monotonicity,[status(thm)],[515])).
% 11.85/7.65 tff(517,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 11.85/7.65 inference(transitivity,[status(thm)],[516, 514])).
% 11.85/7.65 tff(518,plain,
% 11.85/7.65 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | v3_struct_0(A!0) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0))))),
% 11.85/7.65 inference(quant_inst,[status(thm)],[])).
% 11.85/7.65 tff(519,plain,
% 11.85/7.65 ((~![A: $i, B: $i] : (m2_filter_2(k14_filter_2(A, B), A) | v3_struct_0(A) | (~v10_lattices(A)) | (~l3_lattices(A)) | (~m1_filter_0(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[518, 517])).
% 11.85/7.65 tff(520,plain,
% 11.85/7.65 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0) | (~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k1_lattice2(A!0)))),
% 11.85/7.65 inference(unit_resolution,[status(thm)],[519, 226, 225, 31, 513])).
% 11.85/7.65 tff(521,plain,
% 11.85/7.65 (m2_filter_2(k14_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), A!0)),
% 11.85/7.65 inference(unit_resolution,[status(thm)],[520, 443])).
% 11.85/7.65 tff(522,plain,
% 11.85/7.65 (m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[521, 500])).
% 11.85/7.65 tff(523,plain,
% 11.85/7.65 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 11.85/7.65 inference(bind,[status(th)],[])).
% 11.85/7.65 tff(524,plain,
% 11.85/7.65 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.85/7.65 inference(quant_intro,[status(thm)],[523])).
% 11.85/7.65 tff(525,plain,
% 11.85/7.65 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) <=> (~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) <=> (v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite(((v3_struct_0(A) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 11.85/7.65 inference(bind,[status(th)],[])).
% 11.85/7.65 tff(526,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.85/7.65 inference(quant_intro,[status(thm)],[525])).
% 11.85/7.65 tff(527,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(528,plain,
% 11.85/7.65 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))))),
% 11.85/7.65 inference(bind,[status(th)],[])).
% 11.85/7.65 tff(529,plain,
% 11.85/7.65 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 11.85/7.65 inference(quant_intro,[status(thm)],[528])).
% 11.85/7.65 tff(530,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m2_filter_2(B, A)) => (k15_filter_2(A, B) = k7_filter_2(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k15_filter_2')).
% 11.85/7.65 tff(531,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[530, 529])).
% 11.85/7.65 tff(532,plain,
% 11.85/7.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[531, 527])).
% 11.85/7.65 tff(533,plain,(
% 11.85/7.65 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m2_filter_2(B, A))) | (k15_filter_2(A, B) = k7_filter_2(A, B)))),
% 11.85/7.65 inference(skolemize,[status(sab)],[532])).
% 11.85/7.65 tff(534,plain,
% 11.85/7.65 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[533, 526])).
% 11.85/7.65 tff(535,plain,
% 11.85/7.65 (![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 11.85/7.65 inference(modus_ponens,[status(thm)],[534, 524])).
% 11.85/7.65 tff(536,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(537,plain,
% 11.85/7.65 ((v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.65 inference(rewrite,[status(thm)],[])).
% 11.85/7.65 tff(538,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.85/7.65 inference(monotonicity,[status(thm)],[537])).
% 11.85/7.65 tff(539,plain,
% 11.85/7.65 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.65 inference(transitivity,[status(thm)],[538, 536])).
% 11.85/7.65 tff(540,plain,
% 11.85/7.65 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 11.85/7.65 inference(quant_inst,[status(thm)],[])).
% 11.85/7.65 tff(541,plain,
% 11.85/7.65 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k15_filter_2(A, B) = k7_filter_2(A, B)) | (~m2_filter_2(B, A)) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[540, 539])).
% 11.85/7.66 tff(542,plain,
% 11.85/7.66 (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k7_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.66 inference(unit_resolution,[status(thm)],[541, 226, 225, 31, 535, 522])).
% 11.85/7.66 tff(543,plain,
% 11.85/7.66 (k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.85/7.66 inference(transitivity,[status(thm)],[542, 440])).
% 11.85/7.66 tff(544,plain,
% 11.85/7.66 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)) <=> v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.85/7.66 inference(monotonicity,[status(thm)],[543, 35])).
% 11.85/7.66 tff(545,plain,
% 11.85/7.66 (v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 11.85/7.66 inference(symmetry,[status(thm)],[544])).
% 11.85/7.66 tff(546,plain,
% 11.85/7.66 (((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.85/7.66 inference(tautology,[status(thm)],[])).
% 11.85/7.66 tff(547,plain,
% 11.85/7.66 (v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 11.85/7.66 inference(unit_resolution,[status(thm)],[546, 382])).
% 11.85/7.66 tff(548,plain,
% 11.85/7.66 (v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[547, 545])).
% 11.85/7.66 tff(549,plain,
% 11.85/7.66 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))),
% 11.85/7.66 inference(bind,[status(th)],[])).
% 11.85/7.66 tff(550,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(quant_intro,[status(thm)],[549])).
% 11.85/7.66 tff(551,plain,
% 11.85/7.66 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 11.85/7.66 inference(bind,[status(th)],[])).
% 11.85/7.66 tff(552,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(quant_intro,[status(thm)],[551])).
% 11.85/7.66 tff(553,plain,
% 11.85/7.66 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))))),
% 11.85/7.66 inference(bind,[status(th)],[])).
% 11.85/7.66 tff(554,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(quant_intro,[status(thm)],[553])).
% 11.85/7.66 tff(555,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(transitivity,[status(thm)],[554, 552])).
% 11.85/7.66 tff(556,plain,
% 11.85/7.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))))),
% 11.85/7.66 inference(bind,[status(th)],[])).
% 11.85/7.66 tff(557,plain,
% 11.85/7.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(quant_intro,[status(thm)],[556])).
% 11.85/7.66 tff(558,plain,
% 11.85/7.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(rewrite,[status(thm)],[])).
% 11.85/7.66 tff(559,plain,
% 11.85/7.66 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))))),
% 11.85/7.66 inference(bind,[status(th)],[])).
% 11.85/7.66 tff(560,plain,
% 11.85/7.66 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(quant_intro,[status(thm)],[559])).
% 11.85/7.66 tff(561,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t33_filter_2')).
% 11.85/7.66 tff(562,plain,
% 11.85/7.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[561, 560])).
% 11.85/7.66 tff(563,plain,
% 11.85/7.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[562, 558])).
% 11.85/7.66 tff(564,plain,(
% 11.85/7.66 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(skolemize,[status(sab)],[563])).
% 11.85/7.66 tff(565,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[564, 557])).
% 11.85/7.66 tff(566,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))) | (~v10_lattices(A)))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[565, 555])).
% 11.85/7.66 tff(567,plain,
% 11.85/7.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[566, 550])).
% 11.85/7.66 tff(568,plain,
% 11.85/7.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 11.85/7.66 inference(rewrite,[status(thm)],[])).
% 11.85/7.66 tff(569,plain,
% 11.85/7.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0)))))),
% 11.85/7.66 inference(quant_inst,[status(thm)],[])).
% 11.85/7.66 tff(570,plain,
% 11.85/7.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (r2_filter_2(A, B) <=> v1_filter_0(k15_filter_2(A, B), k1_lattice2(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[569, 568])).
% 11.85/7.66 tff(571,plain,
% 11.85/7.66 (![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))),
% 11.85/7.66 inference(unit_resolution,[status(thm)],[570, 226, 225, 31, 567])).
% 11.85/7.66 tff(572,plain,
% 11.85/7.66 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 11.85/7.66 inference(rewrite,[status(thm)],[])).
% 11.85/7.66 tff(573,plain,
% 11.85/7.66 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))))),
% 11.85/7.66 inference(quant_inst,[status(thm)],[])).
% 11.85/7.66 tff(574,plain,
% 11.85/7.66 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (r2_filter_2(A!0, B) <=> v1_filter_0(k15_filter_2(A!0, B), k1_lattice2(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 11.85/7.66 inference(modus_ponens,[status(thm)],[573, 572])).
% 11.85/7.66 tff(575,plain,
% 11.85/7.66 (r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 11.85/7.67 inference(unit_resolution,[status(thm)],[574, 571, 522])).
% 11.85/7.67 tff(576,plain,
% 11.85/7.67 (((~m1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v1_filter_0(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.67 inference(tautology,[status(thm)],[])).
% 11.85/7.67 tff(577,plain,
% 11.85/7.67 (r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.67 inference(unit_resolution,[status(thm)],[576, 382])).
% 11.85/7.67 tff(578,plain,
% 11.85/7.67 (^[C: $i] : refl(((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))),
% 11.85/7.67 inference(bind,[status(th)],[])).
% 11.85/7.67 tff(579,plain,
% 11.85/7.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 11.85/7.67 inference(quant_intro,[status(thm)],[578])).
% 11.85/7.67 tff(580,plain,
% 11.85/7.67 (^[C: $i] : trans(monotonicity(trans(monotonicity(rewrite((r2_hidden(B!1, C) & r2_filter_2(A!0, C)) <=> (~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))), ((~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))) <=> (~(~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))))), rewrite((~(~((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))) <=> ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))), ((~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))) <=> ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C))))), (((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))))), rewrite(((~m2_filter_2(C, A!0)) | ((~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))), (((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))))),
% 11.85/7.67 inference(bind,[status(th)],[])).
% 11.85/7.67 tff(581,plain,
% 11.85/7.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C)))) <=> ![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 11.85/7.67 inference(quant_intro,[status(thm)],[580])).
% 11.85/7.67 tff(582,plain,
% 11.85/7.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~(r2_hidden(B!1, C) & r2_filter_2(A!0, C))))),
% 11.85/7.67 inference(and_elim,[status(thm)],[30])).
% 11.85/7.67 tff(583,plain,
% 11.85/7.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 11.85/7.67 inference(modus_ponens,[status(thm)],[582, 581])).
% 11.85/7.67 tff(584,plain,
% 11.85/7.67 (![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))),
% 11.85/7.67 inference(modus_ponens,[status(thm)],[583, 579])).
% 11.85/7.67 tff(585,plain,
% 11.85/7.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.67 inference(rewrite,[status(thm)],[])).
% 11.85/7.67 tff(586,plain,
% 11.85/7.67 (((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.67 inference(rewrite,[status(thm)],[])).
% 11.85/7.67 tff(587,plain,
% 11.85/7.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 11.85/7.67 inference(monotonicity,[status(thm)],[586])).
% 11.85/7.67 tff(588,plain,
% 11.85/7.67 (((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.67 inference(transitivity,[status(thm)],[587, 585])).
% 11.85/7.67 tff(589,plain,
% 11.85/7.67 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 11.85/7.67 inference(quant_inst,[status(thm)],[])).
% 11.85/7.67 tff(590,plain,
% 11.85/7.67 ((~![C: $i] : ((~m2_filter_2(C, A!0)) | (~r2_hidden(B!1, C)) | (~r2_filter_2(A!0, C)))) | (~r2_hidden(B!1, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.85/7.67 inference(modus_ponens,[status(thm)],[589, 588])).
% 11.85/7.67 tff(591,plain,
% 11.85/7.67 ((~m2_filter_2(tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), A!0)) | (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 11.85/7.67 inference(unit_resolution,[status(thm)],[590, 584, 577])).
% 11.85/7.67 tff(592,plain,
% 11.85/7.67 (~r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 11.85/7.67 inference(unit_resolution,[status(thm)],[591, 522])).
% 11.85/7.67 tff(593,plain,
% 11.85/7.67 ((~(r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))) | r2_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0)))),
% 11.85/7.71 inference(tautology,[status(thm)],[])).
% 11.85/7.71 tff(594,plain,
% 11.85/7.71 (~v1_filter_0(k15_filter_2(A!0, tptp_fun_C_27(B!1, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))), k1_lattice2(A!0))),
% 11.85/7.71 inference(unit_resolution,[status(thm)],[593, 592, 575])).
% 11.85/7.71 tff(595,plain,
% 11.85/7.71 ($false),
% 11.85/7.71 inference(unit_resolution,[status(thm)],[594, 548])).
% 11.85/7.71 % SZS output end Proof
%------------------------------------------------------------------------------