TSTP Solution File: LAT306+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT306+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n011.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 18:32:54 EDT 2022
% Result : Theorem 0.55s 0.59s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LAT306+1 : TPTP v8.1.0. Released v3.4.0.
% 0.10/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n011.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 13:47:12 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.55/0.59 % SZS status Theorem
% 0.55/0.59 % SZS output start Proof
% 0.55/0.59 tff(m1_subset_1_type, type, (
% 0.55/0.59 m1_subset_1: ( $i * $i ) > $o)).
% 0.55/0.59 tff(u1_struct_0_type, type, (
% 0.55/0.59 u1_struct_0: $i > $i)).
% 0.55/0.59 tff(g3_lattices_type, type, (
% 0.55/0.59 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.55/0.59 tff(u2_lattices_type, type, (
% 0.55/0.59 u2_lattices: $i > $i)).
% 0.55/0.59 tff(tptp_fun_A_0_type, type, (
% 0.55/0.59 tptp_fun_A_0: $i)).
% 0.55/0.59 tff(u1_lattices_type, type, (
% 0.55/0.59 u1_lattices: $i > $i)).
% 0.55/0.59 tff(k5_lattices_type, type, (
% 0.55/0.59 k5_lattices: $i > $i)).
% 0.55/0.59 tff(k1_lattice2_type, type, (
% 0.55/0.59 k1_lattice2: $i > $i)).
% 0.55/0.59 tff(k6_lattices_type, type, (
% 0.55/0.59 k6_lattices: $i > $i)).
% 0.55/0.59 tff(v3_lattices_type, type, (
% 0.55/0.59 v3_lattices: $i > $o)).
% 0.55/0.59 tff(l3_lattices_type, type, (
% 0.55/0.59 l3_lattices: $i > $o)).
% 0.55/0.59 tff(m1_relset_1_type, type, (
% 0.55/0.59 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.55/0.59 tff(k2_zfmisc_1_type, type, (
% 0.55/0.59 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.55/0.59 tff(m2_relset_1_type, type, (
% 0.55/0.59 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.55/0.59 tff(v1_funct_2_type, type, (
% 0.55/0.59 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.55/0.59 tff(v1_funct_1_type, type, (
% 0.55/0.59 v1_funct_1: $i > $o)).
% 0.55/0.59 tff(l1_lattices_type, type, (
% 0.55/0.59 l1_lattices: $i > $o)).
% 0.55/0.59 tff(l2_lattices_type, type, (
% 0.55/0.59 l2_lattices: $i > $o)).
% 0.55/0.59 tff(v10_lattices_type, type, (
% 0.55/0.59 v10_lattices: $i > $o)).
% 0.55/0.59 tff(v3_struct_0_type, type, (
% 0.55/0.59 v3_struct_0: $i > $o)).
% 0.55/0.59 tff(v14_lattices_type, type, (
% 0.55/0.59 v14_lattices: $i > $o)).
% 0.55/0.59 tff(r1_filter_2_type, type, (
% 0.55/0.59 r1_filter_2: ( $i * $i * $i ) > $o)).
% 0.55/0.59 tff(k18_filter_2_type, type, (
% 0.55/0.59 k18_filter_2: ( $i * $i ) > $i)).
% 0.55/0.59 tff(k17_filter_2_type, type, (
% 0.55/0.59 k17_filter_2: $i > $i)).
% 0.55/0.59 tff(k2_filter_0_type, type, (
% 0.55/0.59 k2_filter_0: ( $i * $i ) > $i)).
% 0.55/0.59 tff(k2_filter_2_type, type, (
% 0.55/0.59 k2_filter_2: ( $i * $i ) > $i)).
% 0.55/0.59 tff(k1_filter_0_type, type, (
% 0.55/0.59 k1_filter_0: $i > $i)).
% 0.55/0.59 tff(v9_lattices_type, type, (
% 0.55/0.59 v9_lattices: $i > $o)).
% 0.55/0.59 tff(v8_lattices_type, type, (
% 0.55/0.59 v8_lattices: $i > $o)).
% 0.55/0.59 tff(v7_lattices_type, type, (
% 0.55/0.59 v7_lattices: $i > $o)).
% 0.55/0.59 tff(v6_lattices_type, type, (
% 0.55/0.59 v6_lattices: $i > $o)).
% 0.55/0.59 tff(v5_lattices_type, type, (
% 0.55/0.59 v5_lattices: $i > $o)).
% 0.55/0.59 tff(v4_lattices_type, type, (
% 0.55/0.59 v4_lattices: $i > $o)).
% 0.55/0.59 tff(v13_lattices_type, type, (
% 0.55/0.59 v13_lattices: $i > $o)).
% 0.55/0.59 tff(k5_filter_2_type, type, (
% 0.55/0.59 k5_filter_2: ( $i * $i ) > $i)).
% 0.55/0.59 tff(k1_zfmisc_1_type, type, (
% 0.55/0.59 k1_zfmisc_1: $i > $i)).
% 0.55/0.59 tff(m2_lattice4_type, type, (
% 0.55/0.59 m2_lattice4: ( $i * $i ) > $o)).
% 0.55/0.59 tff(v1_xboole_0_type, type, (
% 0.55/0.59 v1_xboole_0: $i > $o)).
% 0.55/0.59 tff(m2_filter_2_type, type, (
% 0.55/0.59 m2_filter_2: ( $i * $i ) > $o)).
% 0.55/0.59 tff(l1_struct_0_type, type, (
% 0.55/0.59 l1_struct_0: $i > $o)).
% 0.55/0.59 tff(m1_filter_0_type, type, (
% 0.55/0.59 m1_filter_0: ( $i * $i ) > $o)).
% 0.55/0.59 tff(1,plain,
% 0.55/0.59 (^[A: $i, B: $i, C: $i] : refl((m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(2,plain,
% 0.55/0.59 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[1])).
% 0.55/0.59 tff(3,plain,
% 0.55/0.59 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B)) <=> ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(4,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.55/0.59 tff(5,plain,
% 0.55/0.59 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.55/0.59 tff(6,plain,(
% 0.55/0.59 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.55/0.59 inference(skolemize,[status(sab)],[5])).
% 0.55/0.59 tff(7,plain,
% 0.55/0.59 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.55/0.59 tff(8,plain,
% 0.55/0.59 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.55/0.59 inference(quant_inst,[status(thm)],[])).
% 0.55/0.59 tff(9,plain,
% 0.55/0.59 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.55/0.59 tff(10,plain,
% 0.55/0.59 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(11,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[10])).
% 0.55/0.59 tff(12,plain,
% 0.55/0.59 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(13,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[12])).
% 0.55/0.59 tff(14,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(15,plain,
% 0.55/0.59 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(16,plain,
% 0.55/0.59 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[15])).
% 0.55/0.59 tff(17,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.55/0.59 tff(18,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.55/0.59 tff(19,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.55/0.59 tff(20,plain,(
% 0.55/0.59 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.55/0.59 inference(skolemize,[status(sab)],[19])).
% 0.55/0.59 tff(21,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.55/0.59 tff(22,plain,
% 0.55/0.59 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[21, 11])).
% 0.55/0.59 tff(23,plain,
% 0.55/0.59 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))) <=> (~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(24,plain,
% 0.55/0.59 ((~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))) <=> (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(25,plain,
% 0.55/0.59 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A)))))) <=> (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(26,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v14_lattices(A) => r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t32_filter_2')).
% 0.55/0.59 tff(27,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[26, 25])).
% 0.55/0.59 tff(28,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[27, 24])).
% 0.55/0.59 tff(29,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.55/0.59 tff(30,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[29, 24])).
% 0.55/0.59 tff(31,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[30, 24])).
% 0.55/0.59 tff(32,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.55/0.59 tff(33,plain,
% 0.55/0.59 (~![A: $i] : (r1_filter_2(u1_struct_0(A), k17_filter_2(A), k18_filter_2(A, k6_lattices(A))) | (~v14_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[32, 24])).
% 0.55/0.59 tff(34,plain,(
% 0.55/0.59 ~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.55/0.59 inference(skolemize,[status(sab)],[33])).
% 0.55/0.59 tff(35,plain,
% 0.55/0.59 (~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~v14_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[34, 23])).
% 0.55/0.59 tff(36,plain,
% 0.55/0.59 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 0.55/0.59 inference(or_elim,[status(thm)],[35])).
% 0.55/0.59 tff(37,plain,
% 0.55/0.59 (l3_lattices(A!0)),
% 0.55/0.59 inference(and_elim,[status(thm)],[36])).
% 0.55/0.59 tff(38,plain,
% 0.55/0.59 (((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(39,plain,
% 0.55/0.59 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.55/0.59 inference(quant_inst,[status(thm)],[])).
% 0.55/0.59 tff(40,plain,
% 0.55/0.59 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[39, 38])).
% 0.55/0.59 tff(41,plain,
% 0.55/0.59 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[40, 37, 22])).
% 0.55/0.59 tff(42,plain,
% 0.55/0.59 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.55/0.59 inference(tautology,[status(thm)],[])).
% 0.55/0.59 tff(43,plain,
% 0.55/0.59 (l1_lattices(A!0)),
% 0.55/0.59 inference(unit_resolution,[status(thm)],[42, 41])).
% 0.55/0.59 tff(44,plain,
% 0.55/0.59 (^[A: $i] : refl(((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(45,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[44])).
% 0.55/0.59 tff(46,plain,
% 0.55/0.59 (^[A: $i] : rewrite(((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(47,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[46])).
% 0.55/0.59 tff(48,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(49,plain,
% 0.55/0.59 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l1_lattices(A) => (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.59 inference(bind,[status(th)],[])).
% 0.55/0.59 tff(50,plain,
% 0.55/0.59 (![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.59 inference(quant_intro,[status(thm)],[49])).
% 0.55/0.59 tff(51,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.55/0.59 tff(52,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[51, 50])).
% 0.55/0.59 tff(53,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[52, 48])).
% 0.55/0.59 tff(54,plain,(
% 0.55/0.59 ![A: $i] : ((~l1_lattices(A)) | (v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.59 inference(skolemize,[status(sab)],[53])).
% 0.55/0.59 tff(55,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[54, 47])).
% 0.55/0.59 tff(56,plain,
% 0.55/0.59 (![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.59 inference(modus_ponens,[status(thm)],[55, 45])).
% 0.55/0.59 tff(57,plain,
% 0.55/0.59 (((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.55/0.59 inference(rewrite,[status(thm)],[])).
% 0.55/0.59 tff(58,plain,
% 0.55/0.59 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(59,plain,
% 0.55/0.60 ((~![A: $i] : ((~l1_lattices(A)) | (~((~v1_funct_1(u1_lattices(A))) | (~v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.55/0.60 tff(60,plain,
% 0.55/0.60 ((~l1_lattices(A!0)) | (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[59, 56])).
% 0.55/0.60 tff(61,plain,
% 0.55/0.60 (~((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[60, 43])).
% 0.55/0.60 tff(62,plain,
% 0.55/0.60 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(tautology,[status(thm)],[])).
% 0.55/0.60 tff(63,plain,
% 0.55/0.60 (m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[62, 61])).
% 0.55/0.60 tff(64,plain,
% 0.55/0.60 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(tautology,[status(thm)],[])).
% 0.55/0.60 tff(65,plain,
% 0.55/0.60 ((~(m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[64, 63])).
% 0.55/0.60 tff(66,plain,
% 0.55/0.60 (m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[65, 9])).
% 0.55/0.60 tff(67,plain,
% 0.55/0.60 ((~![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))) | (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))),
% 0.55/0.60 inference(quant_inst,[status(thm)],[])).
% 0.55/0.60 tff(68,plain,
% 0.55/0.60 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[67, 7])).
% 0.55/0.60 tff(69,plain,
% 0.55/0.60 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.55/0.60 inference(tautology,[status(thm)],[])).
% 0.55/0.60 tff(70,plain,
% 0.55/0.60 (l2_lattices(A!0)),
% 0.55/0.60 inference(unit_resolution,[status(thm)],[69, 41])).
% 0.55/0.60 tff(71,plain,
% 0.55/0.60 (^[A: $i] : refl(((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(72,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[71])).
% 0.55/0.60 tff(73,plain,
% 0.55/0.60 (^[A: $i] : rewrite(((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(74,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[73])).
% 0.55/0.60 tff(75,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.60 inference(rewrite,[status(thm)],[])).
% 0.55/0.60 tff(76,plain,
% 0.55/0.60 (^[A: $i] : trans(monotonicity(rewrite(((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) <=> (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> (l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))))), rewrite((l2_lattices(A) => (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), ((l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.60 inference(bind,[status(th)],[])).
% 0.55/0.60 tff(77,plain,
% 0.55/0.60 (![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)))) <=> ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.60 inference(quant_intro,[status(thm)],[76])).
% 0.55/0.60 tff(78,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.55/0.60 tff(79,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.55/0.60 tff(80,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[79, 75])).
% 0.55/0.60 tff(81,plain,(
% 0.55/0.60 ![A: $i] : ((~l2_lattices(A)) | (v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A)) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))),
% 0.55/0.60 inference(skolemize,[status(sab)],[80])).
% 0.55/0.60 tff(82,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[81, 74])).
% 0.55/0.60 tff(83,plain,
% 0.55/0.60 (![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))),
% 0.55/0.60 inference(modus_ponens,[status(thm)],[82, 72])).
% 0.55/0.60 tff(84,plain,
% 0.55/0.60 (((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))) <=> ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(85,plain,
% 0.57/0.60 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))))),
% 0.57/0.60 inference(quant_inst,[status(thm)],[])).
% 0.57/0.60 tff(86,plain,
% 0.57/0.60 ((~![A: $i] : ((~l2_lattices(A)) | (~((~v1_funct_1(u2_lattices(A))) | (~v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) | (~m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))))) | (~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[85, 84])).
% 0.57/0.60 tff(87,plain,
% 0.57/0.60 ((~l2_lattices(A!0)) | (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[86, 83])).
% 0.57/0.60 tff(88,plain,
% 0.57/0.60 (~((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[87, 70])).
% 0.57/0.60 tff(89,plain,
% 0.57/0.60 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(90,plain,
% 0.57/0.60 (m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[89, 88])).
% 0.57/0.60 tff(91,plain,
% 0.57/0.60 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(92,plain,
% 0.57/0.60 ((~(m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)) <=> m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.57/0.60 tff(93,plain,
% 0.57/0.60 (m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[92, 68])).
% 0.57/0.60 tff(94,plain,
% 0.57/0.60 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(95,plain,
% 0.57/0.60 (v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[94, 88])).
% 0.57/0.60 tff(96,plain,
% 0.57/0.60 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u2_lattices(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(97,plain,
% 0.57/0.60 (v1_funct_1(u2_lattices(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[96, 88])).
% 0.57/0.60 tff(98,plain,
% 0.57/0.60 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(99,plain,
% 0.57/0.60 (v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[98, 61])).
% 0.57/0.60 tff(100,plain,
% 0.57/0.60 (((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m2_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0)))) | v1_funct_1(u1_lattices(A!0))),
% 0.57/0.60 inference(tautology,[status(thm)],[])).
% 0.57/0.60 tff(101,plain,
% 0.57/0.60 (v1_funct_1(u1_lattices(A!0))),
% 0.57/0.60 inference(unit_resolution,[status(thm)],[100, 61])).
% 0.57/0.60 tff(102,plain,
% 0.57/0.60 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(103,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[102])).
% 0.57/0.60 tff(104,plain,
% 0.57/0.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), rewrite((v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))) <=> (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(105,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[104])).
% 0.57/0.60 tff(106,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(107,plain,
% 0.57/0.60 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))))),
% 0.57/0.60 inference(bind,[status(th)],[])).
% 0.57/0.60 tff(108,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.57/0.60 inference(quant_intro,[status(thm)],[107])).
% 0.57/0.60 tff(109,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_g3_lattices')).
% 0.57/0.60 tff(110,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[109, 108])).
% 0.57/0.60 tff(111,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[110, 106])).
% 0.57/0.60 tff(112,plain,(
% 0.57/0.60 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | (v3_lattices(g3_lattices(A, B, C)) & l3_lattices(g3_lattices(A, B, C))))),
% 0.57/0.60 inference(skolemize,[status(sab)],[111])).
% 0.57/0.60 tff(113,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.57/0.60 tff(114,plain,
% 0.57/0.60 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))),
% 0.57/0.60 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.57/0.60 tff(115,plain,
% 0.57/0.60 (((~![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)))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(116,plain,
% 0.57/0.60 (((~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)))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(117,plain,
% 0.57/0.60 ((~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.57/0.60 inference(rewrite,[status(thm)],[])).
% 0.57/0.60 tff(118,plain,
% 0.57/0.60 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.57/0.60 inference(monotonicity,[status(thm)],[117])).
% 0.57/0.60 tff(119,plain,
% 0.57/0.60 (((~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)))))))),
% 0.57/0.60 inference(transitivity,[status(thm)],[118, 116])).
% 0.57/0.60 tff(120,plain,
% 0.57/0.60 (((~![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))))))))),
% 0.57/0.60 inference(monotonicity,[status(thm)],[119])).
% 0.57/0.60 tff(121,plain,
% 0.57/0.60 (((~![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)))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[120, 115])).
% 0.57/0.61 tff(122,plain,
% 0.57/0.61 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | (~((~v3_lattices(g3_lattices(A, B, C))) | (~l3_lattices(g3_lattices(A, B, C))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(123,plain,
% 0.57/0.61 ((~![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))))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[122, 121])).
% 0.57/0.61 tff(124,plain,
% 0.57/0.61 ((~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))))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[123, 114, 101, 99, 97, 95])).
% 0.57/0.61 tff(125,plain,
% 0.57/0.61 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[124, 93, 66])).
% 0.57/0.61 tff(126,plain,
% 0.57/0.61 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.61 inference(tautology,[status(thm)],[])).
% 0.57/0.61 tff(127,plain,
% 0.57/0.61 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[126, 125])).
% 0.57/0.61 tff(128,plain,
% 0.57/0.61 (((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.61 inference(tautology,[status(thm)],[])).
% 0.57/0.61 tff(129,plain,
% 0.57/0.61 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[128, 125])).
% 0.57/0.61 tff(130,plain,
% 0.57/0.61 (^[A: $i] : refl(((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(131,plain,
% 0.57/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[130])).
% 0.57/0.61 tff(132,plain,
% 0.57/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(133,plain,
% 0.57/0.61 (^[A: $i] : trans(monotonicity(rewrite((v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))) <=> ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> (l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))))), rewrite((l3_lattices(A) => ((~v3_lattices(A)) | (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))), ((l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(134,plain,
% 0.57/0.61 (![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))))) <=> ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[133])).
% 0.57/0.61 tff(135,axiom,(![A: $i] : (l3_lattices(A) => (v3_lattices(A) => (A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 0.57/0.61 tff(136,plain,
% 0.57/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.57/0.61 tff(137,plain,
% 0.57/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.57/0.61 tff(138,plain,(
% 0.57/0.61 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(skolemize,[status(sab)],[137])).
% 0.57/0.61 tff(139,plain,
% 0.57/0.61 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.57/0.61 tff(140,plain,
% 0.57/0.61 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(141,plain,
% 0.57/0.61 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(142,plain,
% 0.57/0.61 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.57/0.61 inference(monotonicity,[status(thm)],[141])).
% 0.57/0.61 tff(143,plain,
% 0.57/0.61 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[142, 140])).
% 0.57/0.61 tff(144,plain,
% 0.57/0.61 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.57/0.61 inference(quant_inst,[status(thm)],[])).
% 0.57/0.61 tff(145,plain,
% 0.57/0.61 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[144, 143])).
% 0.57/0.61 tff(146,plain,
% 0.57/0.61 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[145, 139])).
% 0.57/0.61 tff(147,plain,
% 0.57/0.61 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.61 inference(unit_resolution,[status(thm)],[146, 129, 127])).
% 0.57/0.61 tff(148,plain,
% 0.57/0.61 (^[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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ((~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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(149,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[148])).
% 0.57/0.61 tff(150,plain,
% 0.57/0.61 (^[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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ((~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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(151,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[150])).
% 0.57/0.61 tff(152,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(transitivity,[status(thm)],[151, 149])).
% 0.57/0.61 tff(153,plain,
% 0.57/0.61 (^[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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))), (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))), (((~(v1_funct_1(B) & v1_funct_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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))))), 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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E)))))) <=> ((~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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))), (((~(v1_funct_1(B) & v1_funct_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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(154,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[153])).
% 0.57/0.61 tff(155,plain,
% 0.57/0.61 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(156,plain,
% 0.57/0.61 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.57/0.61 inference(bind,[status(th)],[])).
% 0.57/0.61 tff(157,plain,
% 0.57/0.61 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.57/0.61 inference(quant_intro,[status(thm)],[156])).
% 0.57/0.61 tff(158,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.57/0.61 tff(159,plain,
% 0.57/0.61 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[158, 157])).
% 0.57/0.61 tff(160,plain,
% 0.57/0.61 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[159, 155])).
% 0.57/0.61 tff(161,plain,(
% 0.57/0.61 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.57/0.61 inference(skolemize,[status(sab)],[160])).
% 0.57/0.61 tff(162,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[161, 154])).
% 0.57/0.61 tff(163,plain,
% 0.57/0.61 (![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))),
% 0.57/0.61 inference(modus_ponens,[status(thm)],[162, 152])).
% 0.57/0.61 tff(164,plain,
% 0.57/0.61 (((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))) <=> ((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | (~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))),
% 0.57/0.61 inference(rewrite,[status(thm)],[])).
% 0.57/0.61 tff(165,plain,
% 0.57/0.61 (((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))) <=> ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(166,plain,
% 0.57/0.62 (((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))) <=> ((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[165])).
% 0.57/0.62 tff(167,plain,
% 0.57/0.62 (((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))) <=> ((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | (~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))),
% 0.57/0.62 inference(transitivity,[status(thm)],[166, 164])).
% 0.57/0.62 tff(168,plain,
% 0.57/0.62 ((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E))))))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(169,plain,
% 0.57/0.62 ((~![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))) | (~((~(C = F)) | (~(A = D)) | (~(B = E))))))) | (~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.57/0.62 tff(170,plain,
% 0.57/0.62 ((~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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[169, 163, 101, 99, 97, 95])).
% 0.57/0.62 tff(171,plain,
% 0.57/0.62 (![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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[170, 93, 66])).
% 0.57/0.62 tff(172,plain,
% 0.57/0.62 (((~![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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))) | ((~(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)))))) | (~((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))) | (~(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)))))) | (~((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(173,plain,
% 0.57/0.62 ((~![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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))) | ((~(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)))))) | (~((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(174,plain,
% 0.57/0.62 ((~![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))) | (~((~(u2_lattices(A!0) = F)) | (~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)))))) | (~(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)))))) | (~((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[173, 172])).
% 0.57/0.62 tff(175,plain,
% 0.57/0.62 (~((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[174, 171, 147])).
% 0.57/0.62 tff(176,plain,
% 0.57/0.62 (((~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.62 inference(tautology,[status(thm)],[])).
% 0.57/0.62 tff(177,plain,
% 0.57/0.62 (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[176, 175])).
% 0.57/0.62 tff(178,plain,
% 0.57/0.62 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 0.57/0.62 inference(symmetry,[status(thm)],[177])).
% 0.57/0.62 tff(179,plain,
% 0.57/0.62 (^[A: $i] : refl((v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(180,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[179])).
% 0.57/0.62 tff(181,plain,
% 0.57/0.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_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) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_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))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(182,plain,
% 0.57/0.62 (![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))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[181])).
% 0.57/0.62 tff(183,plain,
% 0.57/0.62 (![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))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(184,plain,
% 0.57/0.62 (^[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))))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(185,plain,
% 0.57/0.62 (![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))))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[184])).
% 0.57/0.62 tff(186,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')).
% 0.57/0.62 tff(187,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.57/0.62 tff(188,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[187, 183])).
% 0.57/0.62 tff(189,plain,(
% 0.57/0.62 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))))),
% 0.57/0.62 inference(skolemize,[status(sab)],[188])).
% 0.57/0.62 tff(190,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[189, 182])).
% 0.57/0.62 tff(191,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[190, 180])).
% 0.57/0.62 tff(192,plain,
% 0.57/0.62 (v10_lattices(A!0)),
% 0.57/0.62 inference(and_elim,[status(thm)],[36])).
% 0.57/0.62 tff(193,plain,
% 0.57/0.62 (~v3_struct_0(A!0)),
% 0.57/0.62 inference(and_elim,[status(thm)],[36])).
% 0.57/0.62 tff(194,plain,
% 0.57/0.62 (v14_lattices(A!0)),
% 0.57/0.62 inference(or_elim,[status(thm)],[35])).
% 0.57/0.62 tff(195,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~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))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(196,plain,
% 0.57/0.62 ((v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(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))))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(197,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~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)))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[196])).
% 0.57/0.62 tff(198,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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))))),
% 0.57/0.62 inference(transitivity,[status(thm)],[197, 195])).
% 0.57/0.62 tff(199,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))) | (~v14_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(200,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | (k6_lattices(A) = k5_lattices(k1_lattice2(A))) | (~v14_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[199, 198])).
% 0.57/0.62 tff(201,plain,
% 0.57/0.62 (k6_lattices(A!0) = k5_lattices(k1_lattice2(A!0))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[200, 194, 193, 192, 37, 191])).
% 0.57/0.62 tff(202,plain,
% 0.57/0.62 (k5_lattices(k1_lattice2(A!0)) = k6_lattices(A!0)),
% 0.57/0.62 inference(symmetry,[status(thm)],[201])).
% 0.57/0.62 tff(203,plain,
% 0.57/0.62 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) <=> m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[202, 178])).
% 0.57/0.62 tff(204,plain,
% 0.57/0.62 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) <=> m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.62 inference(symmetry,[status(thm)],[203])).
% 0.57/0.62 tff(205,plain,
% 0.57/0.62 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(206,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[205])).
% 0.57/0.62 tff(207,plain,
% 0.57/0.62 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l2_lattices(A)) <=> (~(v3_struct_0(A) | (~l2_lattices(A))))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l2_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l2_lattices(A))))) <=> (v3_struct_0(A) | (~l2_lattices(A)))), ((~((~v3_struct_0(A)) & l2_lattices(A))) <=> (v3_struct_0(A) | (~l2_lattices(A))))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))), (((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(208,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[207])).
% 0.57/0.62 tff(209,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(210,plain,
% 0.57/0.62 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(211,plain,
% 0.57/0.62 (![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[210])).
% 0.57/0.62 tff(212,axiom,(![A: $i] : (((~v3_struct_0(A)) & l2_lattices(A)) => m1_subset_1(k6_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k6_lattices')).
% 0.57/0.62 tff(213,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[212, 211])).
% 0.57/0.62 tff(214,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[213, 209])).
% 0.57/0.62 tff(215,plain,(
% 0.57/0.62 ![A: $i] : ((~((~v3_struct_0(A)) & l2_lattices(A))) | m1_subset_1(k6_lattices(A), u1_struct_0(A)))),
% 0.57/0.62 inference(skolemize,[status(sab)],[214])).
% 0.57/0.62 tff(216,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[215, 208])).
% 0.57/0.62 tff(217,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[216, 206])).
% 0.57/0.62 tff(218,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(219,plain,
% 0.57/0.62 ((v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(220,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.57/0.62 inference(monotonicity,[status(thm)],[219])).
% 0.57/0.62 tff(221,plain,
% 0.57/0.62 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.57/0.62 inference(transitivity,[status(thm)],[220, 218])).
% 0.57/0.62 tff(222,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) | (~l2_lattices(A!0)))),
% 0.57/0.62 inference(quant_inst,[status(thm)],[])).
% 0.57/0.62 tff(223,plain,
% 0.57/0.62 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k6_lattices(A), u1_struct_0(A)) | (~l2_lattices(A)))) | v3_struct_0(A!0) | (~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[222, 221])).
% 0.57/0.62 tff(224,plain,
% 0.57/0.62 ((~l2_lattices(A!0)) | m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[223, 193, 217])).
% 0.57/0.62 tff(225,plain,
% 0.57/0.62 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.57/0.62 inference(unit_resolution,[status(thm)],[224, 70])).
% 0.57/0.62 tff(226,plain,
% 0.57/0.62 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.62 inference(modus_ponens,[status(thm)],[225, 204])).
% 0.57/0.62 tff(227,plain,
% 0.57/0.62 ((k18_filter_2(A!0, k6_lattices(A!0)) = k17_filter_2(A!0)) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.57/0.62 inference(commutativity,[status(thm)],[])).
% 0.57/0.62 tff(228,plain,
% 0.57/0.62 (^[A: $i] : refl((v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(229,plain,
% 0.57/0.62 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[228])).
% 0.57/0.62 tff(230,plain,
% 0.57/0.62 (^[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))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.57/0.62 inference(bind,[status(th)],[])).
% 0.57/0.62 tff(231,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.62 inference(quant_intro,[status(thm)],[230])).
% 0.57/0.62 tff(232,plain,
% 0.57/0.62 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.57/0.62 inference(rewrite,[status(thm)],[])).
% 0.57/0.62 tff(233,plain,
% 0.57/0.62 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(234,plain,
% 0.57/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[233])).
% 0.57/0.63 tff(235,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k17_filter_2(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d8_filter_2')).
% 0.57/0.63 tff(236,plain,
% 0.57/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[235, 234])).
% 0.57/0.63 tff(237,plain,
% 0.57/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[236, 232])).
% 0.57/0.63 tff(238,plain,(
% 0.57/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k17_filter_2(A) = u1_struct_0(A)))),
% 0.57/0.63 inference(skolemize,[status(sab)],[237])).
% 0.57/0.63 tff(239,plain,
% 0.57/0.63 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[238, 231])).
% 0.57/0.63 tff(240,plain,
% 0.57/0.63 (![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[239, 229])).
% 0.57/0.63 tff(241,plain,
% 0.57/0.63 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(242,plain,
% 0.57/0.63 ((v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(243,plain,
% 0.57/0.63 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))))),
% 0.57/0.63 inference(monotonicity,[status(thm)],[242])).
% 0.57/0.63 tff(244,plain,
% 0.57/0.63 (((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0)))),
% 0.57/0.63 inference(transitivity,[status(thm)],[243, 241])).
% 0.57/0.63 tff(245,plain,
% 0.57/0.63 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k17_filter_2(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.57/0.63 inference(quant_inst,[status(thm)],[])).
% 0.57/0.63 tff(246,plain,
% 0.57/0.63 ((~![A: $i] : (v3_struct_0(A) | (k17_filter_2(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k17_filter_2(A!0) = u1_struct_0(A!0))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[245, 244])).
% 0.57/0.63 tff(247,plain,
% 0.57/0.63 (k17_filter_2(A!0) = u1_struct_0(A!0)),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[246, 193, 192, 37, 240])).
% 0.57/0.63 tff(248,plain,
% 0.57/0.63 (u1_struct_0(A!0) = k17_filter_2(A!0)),
% 0.57/0.63 inference(symmetry,[status(thm)],[247])).
% 0.57/0.63 tff(249,plain,
% 0.57/0.63 (^[A: $i] : refl(((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(250,plain,
% 0.57/0.63 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[249])).
% 0.57/0.63 tff(251,plain,
% 0.57/0.63 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(252,plain,
% 0.57/0.63 (^[A: $i] : rewrite((l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(253,plain,
% 0.57/0.63 (![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A)))) <=> ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[252])).
% 0.57/0.63 tff(254,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_lattice2')).
% 0.57/0.63 tff(255,plain,
% 0.57/0.63 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.57/0.63 tff(256,plain,
% 0.57/0.63 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.57/0.63 tff(257,plain,(
% 0.57/0.63 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(skolemize,[status(sab)],[256])).
% 0.57/0.63 tff(258,plain,
% 0.57/0.63 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.57/0.63 tff(259,plain,
% 0.57/0.63 (((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.63 inference(rewrite,[status(thm)],[])).
% 0.57/0.63 tff(260,plain,
% 0.57/0.63 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | ((~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.63 inference(quant_inst,[status(thm)],[])).
% 0.57/0.63 tff(261,plain,
% 0.57/0.63 ((~![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))) | (~l3_lattices(A!0)) | (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.63 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.57/0.63 tff(262,plain,
% 0.57/0.63 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.57/0.63 inference(unit_resolution,[status(thm)],[261, 37, 258])).
% 0.57/0.63 tff(263,plain,
% 0.57/0.63 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.57/0.63 inference(symmetry,[status(thm)],[262])).
% 0.57/0.63 tff(264,plain,
% 0.57/0.63 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v3_struct_0(k1_lattice2(A!0))),
% 0.57/0.63 inference(monotonicity,[status(thm)],[263])).
% 0.57/0.63 tff(265,plain,
% 0.57/0.63 (v3_struct_0(k1_lattice2(A!0)) <=> v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.57/0.63 inference(symmetry,[status(thm)],[264])).
% 0.57/0.63 tff(266,plain,
% 0.57/0.63 ((~v3_struct_0(k1_lattice2(A!0))) <=> (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.57/0.63 inference(monotonicity,[status(thm)],[265])).
% 0.57/0.63 tff(267,plain,
% 0.57/0.63 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))),
% 0.57/0.63 inference(bind,[status(th)],[])).
% 0.57/0.63 tff(268,plain,
% 0.57/0.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.57/0.63 inference(quant_intro,[status(thm)],[267])).
% 0.57/0.63 tff(269,plain,
% 0.57/0.63 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), rewrite(((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))) <=> (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(270,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[269])).
% 0.60/0.63 tff(271,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(272,plain,
% 0.60/0.63 (^[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))), trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)))), (((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)))), ((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)))), (((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)))), ((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)))), (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> (((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), rewrite((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))), ((((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))) <=> ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(273,plain,
% 0.60/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[272])).
% 0.60/0.63 tff(274,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((((((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A))) & v4_lattices(k1_lattice2(A))) & v5_lattices(k1_lattice2(A))) & v6_lattices(k1_lattice2(A))) & v7_lattices(k1_lattice2(A))) & v8_lattices(k1_lattice2(A))) & v9_lattices(k1_lattice2(A))) & v10_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.60/0.63 tff(275,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[274, 273])).
% 0.60/0.63 tff(276,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[275, 271])).
% 0.60/0.63 tff(277,plain,(
% 0.60/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ((~v3_struct_0(k1_lattice2(A))) & v3_lattices(k1_lattice2(A)) & v4_lattices(k1_lattice2(A)) & v5_lattices(k1_lattice2(A)) & v6_lattices(k1_lattice2(A)) & v7_lattices(k1_lattice2(A)) & v8_lattices(k1_lattice2(A)) & v9_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A))))),
% 0.60/0.63 inference(skolemize,[status(sab)],[276])).
% 0.60/0.63 tff(278,plain,
% 0.60/0.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[277, 270])).
% 0.60/0.63 tff(279,plain,
% 0.60/0.63 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[278, 268])).
% 0.60/0.63 tff(280,plain,
% 0.60/0.63 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(281,plain,
% 0.60/0.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(282,plain,
% 0.60/0.63 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~(v3_struct_0(k1_lattice2(A)) | (~v3_lattices(k1_lattice2(A))) | (~v4_lattices(k1_lattice2(A))) | (~v5_lattices(k1_lattice2(A))) | (~v6_lattices(k1_lattice2(A))) | (~v7_lattices(k1_lattice2(A))) | (~v8_lattices(k1_lattice2(A))) | (~v9_lattices(k1_lattice2(A))) | (~v10_lattices(k1_lattice2(A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.60/0.63 tff(283,plain,
% 0.60/0.63 (~(v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[282, 193, 192, 37, 279])).
% 0.60/0.63 tff(284,plain,
% 0.60/0.63 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | (~v3_struct_0(k1_lattice2(A!0)))),
% 0.60/0.63 inference(tautology,[status(thm)],[])).
% 0.60/0.63 tff(285,plain,
% 0.60/0.63 (~v3_struct_0(k1_lattice2(A!0))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[284, 283])).
% 0.60/0.63 tff(286,plain,
% 0.60/0.63 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[285, 266])).
% 0.60/0.63 tff(287,plain,
% 0.60/0.63 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[263])).
% 0.60/0.63 tff(288,plain,
% 0.60/0.63 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.63 inference(symmetry,[status(thm)],[287])).
% 0.60/0.63 tff(289,plain,
% 0.60/0.63 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.60/0.63 inference(tautology,[status(thm)],[])).
% 0.60/0.63 tff(290,plain,
% 0.60/0.63 (v10_lattices(k1_lattice2(A!0))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[289, 283])).
% 0.60/0.63 tff(291,plain,
% 0.60/0.63 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[290, 288])).
% 0.60/0.63 tff(292,plain,
% 0.60/0.63 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(293,plain,
% 0.60/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[292])).
% 0.60/0.63 tff(294,plain,
% 0.60/0.63 (^[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))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(295,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[294])).
% 0.60/0.63 tff(296,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(297,plain,
% 0.60/0.63 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(298,plain,
% 0.60/0.63 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[297])).
% 0.60/0.63 tff(299,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = u1_struct_0(A)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d2_filter_0')).
% 0.60/0.63 tff(300,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.60/0.63 tff(301,plain,
% 0.60/0.63 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[300, 296])).
% 0.60/0.63 tff(302,plain,(
% 0.60/0.63 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = u1_struct_0(A)))),
% 0.60/0.63 inference(skolemize,[status(sab)],[301])).
% 0.60/0.63 tff(303,plain,
% 0.60/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[302, 295])).
% 0.60/0.63 tff(304,plain,
% 0.60/0.63 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[303, 293])).
% 0.60/0.63 tff(305,plain,
% 0.60/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(306,plain,
% 0.60/0.63 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~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))))) <=> ((~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(307,plain,
% 0.60/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~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)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[306])).
% 0.60/0.63 tff(308,plain,
% 0.60/0.63 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~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)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.63 inference(transitivity,[status(thm)],[307, 305])).
% 0.60/0.63 tff(309,plain,
% 0.60/0.63 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~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)))))),
% 0.60/0.63 inference(quant_inst,[status(thm)],[])).
% 0.60/0.63 tff(310,plain,
% 0.60/0.63 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.63 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.60/0.63 tff(311,plain,
% 0.60/0.63 ((~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)))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[310, 304])).
% 0.60/0.63 tff(312,plain,
% 0.60/0.63 (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.63 inference(unit_resolution,[status(thm)],[311, 291, 129, 286])).
% 0.60/0.63 tff(313,plain,
% 0.60/0.63 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v13_lattices(k1_lattice2(A!0))),
% 0.60/0.63 inference(monotonicity,[status(thm)],[263])).
% 0.60/0.63 tff(314,plain,
% 0.60/0.63 (v13_lattices(k1_lattice2(A!0)) <=> v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.63 inference(symmetry,[status(thm)],[313])).
% 0.60/0.63 tff(315,plain,
% 0.60/0.63 (^[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))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(316,plain,
% 0.60/0.63 (![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)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[315])).
% 0.60/0.63 tff(317,plain,
% 0.60/0.63 (^[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)))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(318,plain,
% 0.60/0.63 (![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)))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[317])).
% 0.60/0.63 tff(319,plain,
% 0.60/0.63 (![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))))),
% 0.60/0.63 inference(rewrite,[status(thm)],[])).
% 0.60/0.63 tff(320,plain,
% 0.60/0.63 (^[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))), (((((~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))))))),
% 0.60/0.63 inference(bind,[status(th)],[])).
% 0.60/0.63 tff(321,plain,
% 0.60/0.63 (![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))))),
% 0.60/0.63 inference(quant_intro,[status(thm)],[320])).
% 0.60/0.63 tff(322,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')).
% 0.60/0.64 tff(323,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[322, 321])).
% 0.60/0.64 tff(324,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[323, 319])).
% 0.60/0.64 tff(325,plain,(
% 0.60/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))))),
% 0.60/0.64 inference(skolemize,[status(sab)],[324])).
% 0.60/0.64 tff(326,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[325, 318])).
% 0.60/0.64 tff(327,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (v14_lattices(A) <=> v13_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[326, 316])).
% 0.60/0.64 tff(328,plain,
% 0.60/0.64 (((~![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))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(329,plain,
% 0.60/0.64 ((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))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(330,plain,
% 0.60/0.64 (((~![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)))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[329])).
% 0.60/0.64 tff(331,plain,
% 0.60/0.64 (((~![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))))),
% 0.60/0.64 inference(transitivity,[status(thm)],[330, 328])).
% 0.60/0.64 tff(332,plain,
% 0.60/0.64 ((~![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)))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(333,plain,
% 0.60/0.64 ((~![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)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[332, 331])).
% 0.60/0.64 tff(334,plain,
% 0.60/0.64 (v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[333, 193, 192, 37, 327])).
% 0.60/0.64 tff(335,plain,
% 0.60/0.64 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | (~v14_lattices(A!0)) | v13_lattices(k1_lattice2(A!0))),
% 0.60/0.64 inference(tautology,[status(thm)],[])).
% 0.60/0.64 tff(336,plain,
% 0.60/0.64 ((~(v14_lattices(A!0) <=> v13_lattices(k1_lattice2(A!0)))) | v13_lattices(k1_lattice2(A!0))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[335, 194])).
% 0.60/0.64 tff(337,plain,
% 0.60/0.64 (v13_lattices(k1_lattice2(A!0))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[336, 334])).
% 0.60/0.64 tff(338,plain,
% 0.60/0.64 (v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[337, 314])).
% 0.60/0.64 tff(339,plain,
% 0.60/0.64 (^[A: $i] : refl((v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(340,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[339])).
% 0.60/0.64 tff(341,plain,
% 0.60/0.64 (^[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))))), trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A))))), (((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))))), rewrite(((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))), (((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(342,plain,
% 0.60/0.64 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[341])).
% 0.60/0.64 tff(343,plain,
% 0.60/0.64 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(344,plain,
% 0.60/0.64 (^[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))), trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(345,plain,
% 0.60/0.64 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))))) <=> ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[344])).
% 0.60/0.64 tff(346,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t20_filter_0')).
% 0.60/0.64 tff(347,plain,
% 0.60/0.64 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.60/0.64 tff(348,plain,
% 0.60/0.64 (![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[347, 343])).
% 0.60/0.64 tff(349,plain,(
% 0.60/0.64 ![A: $i] : ((k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))))),
% 0.60/0.64 inference(skolemize,[status(sab)],[348])).
% 0.60/0.64 tff(350,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[349, 342])).
% 0.60/0.64 tff(351,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[350, 340])).
% 0.60/0.64 tff(352,plain,
% 0.60/0.64 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(353,plain,
% 0.60/0.64 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~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)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(354,plain,
% 0.60/0.64 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | ((~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[353])).
% 0.60/0.64 tff(355,plain,
% 0.60/0.64 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.64 inference(transitivity,[status(thm)],[354, 352])).
% 0.60/0.64 tff(356,plain,
% 0.60/0.64 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.64 inference(quant_inst,[status(thm)],[])).
% 0.60/0.64 tff(357,plain,
% 0.60/0.64 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = k2_filter_0(A, k5_lattices(A))) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v13_lattices(A)))) | (~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.60/0.64 tff(358,plain,
% 0.60/0.64 ((~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))) | (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_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)))) | (~v13_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[357, 351])).
% 0.60/0.64 tff(359,plain,
% 0.60/0.64 (k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.64 inference(unit_resolution,[status(thm)],[358, 286, 129, 291, 338])).
% 0.60/0.64 tff(360,plain,
% 0.60/0.64 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k1_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.64 inference(symmetry,[status(thm)],[359])).
% 0.60/0.64 tff(361,plain,
% 0.60/0.64 (k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[263])).
% 0.60/0.64 tff(362,plain,
% 0.60/0.64 (k5_lattices(k1_lattice2(A!0)) = k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.60/0.64 inference(symmetry,[status(thm)],[361])).
% 0.60/0.64 tff(363,plain,
% 0.60/0.64 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[362])).
% 0.60/0.64 tff(364,plain,
% 0.60/0.64 (k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k17_filter_2(A!0)),
% 0.60/0.64 inference(transitivity,[status(thm)],[363, 360, 312, 178, 248])).
% 0.60/0.64 tff(365,plain,
% 0.60/0.64 (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k18_filter_2(A!0, k6_lattices(A!0))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[202])).
% 0.60/0.64 tff(366,plain,
% 0.60/0.64 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0)) <=> m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))),
% 0.60/0.64 inference(monotonicity,[status(thm)],[202])).
% 0.60/0.64 tff(367,plain,
% 0.60/0.64 (m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)) <=> m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))),
% 0.60/0.64 inference(symmetry,[status(thm)],[366])).
% 0.60/0.64 tff(368,plain,
% 0.60/0.64 (m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[225, 367])).
% 0.60/0.64 tff(369,plain,
% 0.60/0.64 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(370,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[369])).
% 0.60/0.64 tff(371,plain,
% 0.60/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(372,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[371])).
% 0.60/0.64 tff(373,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(transitivity,[status(thm)],[372, 370])).
% 0.60/0.64 tff(374,plain,
% 0.60/0.64 (^[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))))), quant_intro(proof_bind(^[B: $i] : rewrite(((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(375,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[374])).
% 0.60/0.64 tff(376,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.64 inference(rewrite,[status(thm)],[])).
% 0.60/0.64 tff(377,plain,
% 0.60/0.64 (^[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, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(bind,[status(th)],[])).
% 0.60/0.64 tff(378,plain,
% 0.60/0.64 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.64 inference(quant_intro,[status(thm)],[377])).
% 0.60/0.64 tff(379,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','t30_filter_2')).
% 0.60/0.64 tff(380,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.60/0.64 tff(381,plain,
% 0.60/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.60/0.64 tff(382,plain,(
% 0.60/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | ((k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B))) & (k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))),
% 0.60/0.64 inference(skolemize,[status(sab)],[381])).
% 0.60/0.64 tff(383,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[382, 375])).
% 0.60/0.64 tff(384,plain,
% 0.60/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))),
% 0.60/0.64 inference(modus_ponens,[status(thm)],[383, 373])).
% 0.60/0.64 tff(385,plain,
% 0.60/0.64 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(386,plain,
% 0.60/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B)))))))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(387,plain,
% 0.60/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (~((~(k18_filter_2(A, B) = k2_filter_2(k1_lattice2(A), k5_filter_2(A, B)))) | (~(k18_filter_2(k1_lattice2(A), k5_filter_2(A, B)) = k2_filter_2(A, B)))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.60/0.65 tff(388,plain,
% 0.60/0.65 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[387, 193, 192, 37, 384])).
% 0.60/0.65 tff(389,plain,
% 0.60/0.65 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(390,plain,
% 0.60/0.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(391,plain,
% 0.60/0.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, B) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, B)) = k2_filter_2(A!0, B))))))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[390, 389])).
% 0.60/0.65 tff(392,plain,
% 0.60/0.65 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[391, 388])).
% 0.60/0.65 tff(393,plain,
% 0.60/0.65 (~((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[392, 368])).
% 0.60/0.65 tff(394,plain,
% 0.60/0.65 (((~(k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (~(k18_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k2_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))) | (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))))),
% 0.60/0.65 inference(tautology,[status(thm)],[])).
% 0.60/0.65 tff(395,plain,
% 0.60/0.65 (k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[394, 393])).
% 0.60/0.65 tff(396,plain,
% 0.60/0.65 (k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))) = k18_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))),
% 0.60/0.65 inference(symmetry,[status(thm)],[395])).
% 0.60/0.65 tff(397,plain,
% 0.60/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(398,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[397])).
% 0.60/0.65 tff(399,plain,
% 0.60/0.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(400,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[399])).
% 0.60/0.65 tff(401,plain,
% 0.60/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(402,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[401])).
% 0.60/0.65 tff(403,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[402, 400])).
% 0.60/0.65 tff(404,plain,
% 0.60/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(405,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[404])).
% 0.60/0.65 tff(406,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(407,plain,
% 0.60/0.65 (^[A: $i] : trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), quant_intro(proof_bind(^[B: $i] : rewrite((m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)) <=> ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(408,plain,
% 0.60/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[407])).
% 0.60/0.65 tff(409,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_subset_1(B, u1_struct_0(A)) => (k5_filter_2(A, B) = B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','d4_filter_2')).
% 0.60/0.65 tff(410,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.60/0.65 tff(411,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[410, 406])).
% 0.60/0.65 tff(412,plain,(
% 0.60/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(skolemize,[status(sab)],[411])).
% 0.60/0.65 tff(413,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[412, 405])).
% 0.60/0.65 tff(414,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)) | (~v10_lattices(A)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[413, 403])).
% 0.60/0.65 tff(415,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[414, 398])).
% 0.60/0.65 tff(416,plain,
% 0.60/0.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(417,plain,
% 0.60/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(418,plain,
% 0.60/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A))) | (k5_filter_2(A, B) = B)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[417, 416])).
% 0.60/0.65 tff(419,plain,
% 0.60/0.65 (![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[418, 193, 192, 37, 415])).
% 0.60/0.65 tff(420,plain,
% 0.60/0.65 (((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))) <=> ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(421,plain,
% 0.60/0.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(422,plain,
% 0.60/0.65 ((~![B: $i] : ((~m1_subset_1(B, u1_struct_0(A!0))) | (k5_filter_2(A!0, B) = B))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[421, 420])).
% 0.60/0.65 tff(423,plain,
% 0.60/0.65 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(A!0))) | (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0)))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[422, 419])).
% 0.60/0.65 tff(424,plain,
% 0.60/0.65 (k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))) = k5_lattices(k1_lattice2(A!0))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[423, 368])).
% 0.60/0.65 tff(425,plain,
% 0.60/0.65 (k5_lattices(k1_lattice2(A!0)) = k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0)))),
% 0.60/0.65 inference(symmetry,[status(thm)],[424])).
% 0.60/0.65 tff(426,plain,
% 0.60/0.65 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_2(k1_lattice2(A!0), k5_filter_2(A!0, k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[263, 425])).
% 0.60/0.65 tff(427,plain,
% 0.60/0.65 (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k18_filter_2(A!0, k6_lattices(A!0))),
% 0.60/0.65 inference(transitivity,[status(thm)],[426, 396, 365])).
% 0.60/0.65 tff(428,plain,
% 0.60/0.65 ((k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) <=> (k18_filter_2(A!0, k6_lattices(A!0)) = k17_filter_2(A!0))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[427, 364])).
% 0.60/0.65 tff(429,plain,
% 0.60/0.65 ((k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.60/0.65 inference(transitivity,[status(thm)],[428, 227])).
% 0.60/0.65 tff(430,plain,
% 0.60/0.65 ((k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))) <=> (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.65 inference(symmetry,[status(thm)],[429])).
% 0.60/0.65 tff(431,plain,
% 0.60/0.65 ((~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) <=> (~(k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[430])).
% 0.60/0.65 tff(432,plain,
% 0.60/0.65 (^[A: $i, B: $i] : refl((m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(433,plain,
% 0.60/0.65 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[432])).
% 0.60/0.65 tff(434,plain,
% 0.60/0.65 (^[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)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), 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)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(435,plain,
% 0.60/0.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[434])).
% 0.60/0.65 tff(436,plain,
% 0.60/0.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(437,plain,
% 0.60/0.65 (^[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_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))) => m2_filter_2(k18_filter_2(A, B), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(438,plain,
% 0.60/0.65 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A)) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[437])).
% 0.60/0.65 tff(439,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => m2_filter_2(k18_filter_2(A, B), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k18_filter_2')).
% 0.60/0.65 tff(440,plain,
% 0.60/0.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[439, 438])).
% 0.60/0.65 tff(441,plain,
% 0.60/0.65 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[440, 436])).
% 0.60/0.65 tff(442,plain,(
% 0.60/0.65 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | m2_filter_2(k18_filter_2(A, B), A))),
% 0.60/0.65 inference(skolemize,[status(sab)],[441])).
% 0.60/0.65 tff(443,plain,
% 0.60/0.65 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[442, 435])).
% 0.60/0.65 tff(444,plain,
% 0.60/0.65 (![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[443, 433])).
% 0.60/0.65 tff(445,plain,
% 0.60/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(446,plain,
% 0.60/0.65 ((m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_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(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(447,plain,
% 0.60/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))))),
% 0.60/0.65 inference(monotonicity,[status(thm)],[446])).
% 0.60/0.65 tff(448,plain,
% 0.60/0.65 (((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))) <=> ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))))),
% 0.60/0.65 inference(transitivity,[status(thm)],[447, 445])).
% 0.60/0.65 tff(449,plain,
% 0.60/0.65 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | v3_struct_0(A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0))) | (~v10_lattices(A!0)) | (~l3_lattices(A!0)))),
% 0.60/0.65 inference(quant_inst,[status(thm)],[])).
% 0.60/0.65 tff(450,plain,
% 0.60/0.65 ((~![A: $i, B: $i] : (m2_filter_2(k18_filter_2(A, B), A) | v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[449, 448])).
% 0.60/0.65 tff(451,plain,
% 0.60/0.65 (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0) | (~m1_subset_1(k6_lattices(A!0), u1_struct_0(A!0)))),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[450, 193, 192, 37, 444])).
% 0.60/0.65 tff(452,plain,
% 0.60/0.65 (m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.60/0.65 inference(unit_resolution,[status(thm)],[451, 225])).
% 0.60/0.65 tff(453,plain,
% 0.60/0.65 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(454,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[453])).
% 0.60/0.65 tff(455,plain,
% 0.60/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(456,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[455])).
% 0.60/0.65 tff(457,plain,
% 0.60/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.65 inference(transitivity,[status(thm)],[456, 454])).
% 0.60/0.65 tff(458,plain,
% 0.60/0.65 (^[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(((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A)))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(459,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[458])).
% 0.60/0.65 tff(460,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.60/0.65 inference(rewrite,[status(thm)],[])).
% 0.60/0.65 tff(461,plain,
% 0.60/0.65 (^[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) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))) <=> ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))))),
% 0.60/0.65 inference(bind,[status(th)],[])).
% 0.60/0.65 tff(462,plain,
% 0.60/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.60/0.65 inference(quant_intro,[status(thm)],[461])).
% 0.60/0.65 tff(463,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) => ((~v1_xboole_0(B)) & m2_lattice4(B, A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_filter_2')).
% 0.60/0.65 tff(464,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[463, 462])).
% 0.60/0.65 tff(465,plain,
% 0.60/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.60/0.65 inference(modus_ponens,[status(thm)],[464, 460])).
% 0.60/0.65 tff(466,plain,(
% 0.60/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_filter_2(B, A)) | ((~v1_xboole_0(B)) & m2_lattice4(B, A))))),
% 0.60/0.65 inference(skolemize,[status(sab)],[465])).
% 0.60/0.66 tff(467,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[466, 459])).
% 0.60/0.66 tff(468,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[467, 457])).
% 0.60/0.66 tff(469,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(470,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(471,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_filter_2(B, A)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[470, 469])).
% 0.60/0.66 tff(472,plain,
% 0.60/0.66 (![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[471, 193, 192, 37, 468])).
% 0.60/0.66 tff(473,plain,
% 0.60/0.66 (((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))) <=> ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(474,plain,
% 0.60/0.66 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | ((~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(475,plain,
% 0.60/0.66 ((~![B: $i] : ((~m2_filter_2(B, A!0)) | (~(v1_xboole_0(B) | (~m2_lattice4(B, A!0)))))) | (~m2_filter_2(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.60/0.66 tff(476,plain,
% 0.60/0.66 (~(v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[475, 472, 452])).
% 0.60/0.66 tff(477,plain,
% 0.60/0.66 ((v1_xboole_0(k18_filter_2(A!0, k6_lattices(A!0))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0))) | m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.60/0.66 inference(tautology,[status(thm)],[])).
% 0.60/0.66 tff(478,plain,
% 0.60/0.66 (m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[477, 476])).
% 0.60/0.66 tff(479,plain,
% 0.60/0.66 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(480,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[479])).
% 0.60/0.66 tff(481,plain,
% 0.60/0.66 (^[A: $i] : refl((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(482,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[481])).
% 0.60/0.66 tff(483,plain,
% 0.60/0.66 (^[A: $i] : rewrite((v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(484,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[483])).
% 0.60/0.66 tff(485,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(transitivity,[status(thm)],[484, 482])).
% 0.60/0.66 tff(486,plain,
% 0.60/0.66 (^[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_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(487,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[486])).
% 0.60/0.66 tff(488,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(489,plain,
% 0.60/0.66 (^[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_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) <=> ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(490,plain,
% 0.60/0.66 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[489])).
% 0.60/0.66 tff(491,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_lattice4(B, A) => m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_m2_lattice4')).
% 0.60/0.66 tff(492,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[491, 490])).
% 0.60/0.66 tff(493,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[492, 488])).
% 0.60/0.66 tff(494,plain,(
% 0.60/0.66 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(skolemize,[status(sab)],[493])).
% 0.60/0.66 tff(495,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[494, 487])).
% 0.60/0.66 tff(496,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))) | (~v10_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[495, 485])).
% 0.60/0.66 tff(497,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[496, 480])).
% 0.60/0.66 tff(498,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(499,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(500,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m2_lattice4(B, A)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A)))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[499, 498])).
% 0.60/0.66 tff(501,plain,
% 0.60/0.66 (![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[500, 193, 192, 37, 497])).
% 0.60/0.66 tff(502,plain,
% 0.60/0.66 (((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(503,plain,
% 0.60/0.66 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | ((~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(504,plain,
% 0.60/0.66 ((~![B: $i] : ((~m2_lattice4(B, A!0)) | m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))) | (~m2_lattice4(k18_filter_2(A!0, k6_lattices(A!0)), A!0)) | m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[503, 502])).
% 0.60/0.66 tff(505,plain,
% 0.60/0.66 (m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[504, 501, 478])).
% 0.60/0.66 tff(506,plain,
% 0.60/0.66 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(507,plain,
% 0.60/0.66 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[506])).
% 0.60/0.66 tff(508,plain,
% 0.60/0.66 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(509,plain,
% 0.60/0.66 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(510,plain,
% 0.60/0.66 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[509])).
% 0.60/0.66 tff(511,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.60/0.66 tff(512,plain,
% 0.60/0.66 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[511, 510])).
% 0.60/0.66 tff(513,plain,
% 0.60/0.66 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[512, 508])).
% 0.60/0.66 tff(514,plain,(
% 0.60/0.66 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(skolemize,[status(sab)],[513])).
% 0.60/0.66 tff(515,plain,
% 0.60/0.66 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[514, 507])).
% 0.60/0.66 tff(516,plain,
% 0.60/0.66 (((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))) <=> ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(517,plain,
% 0.60/0.66 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(518,plain,
% 0.60/0.66 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[517, 516])).
% 0.60/0.66 tff(519,plain,
% 0.60/0.66 (l1_struct_0(A!0)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[518, 515, 70])).
% 0.60/0.66 tff(520,plain,
% 0.60/0.66 (^[A: $i] : refl((v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(521,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[520])).
% 0.60/0.66 tff(522,plain,
% 0.60/0.66 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_struct_0(A)) <=> (~(v3_struct_0(A) | (~l1_struct_0(A))))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (~(~(v3_struct_0(A) | (~l1_struct_0(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_struct_0(A))))) <=> (v3_struct_0(A) | (~l1_struct_0(A)))), ((~((~v3_struct_0(A)) & l1_struct_0(A))) <=> (v3_struct_0(A) | (~l1_struct_0(A))))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))))), rewrite(((~v1_xboole_0(u1_struct_0(A))) | (v3_struct_0(A) | (~l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))), (((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(523,plain,
% 0.60/0.66 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[522])).
% 0.60/0.66 tff(524,plain,
% 0.60/0.66 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(525,plain,
% 0.60/0.66 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(526,plain,
% 0.60/0.66 (![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A)))) <=> ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[525])).
% 0.60/0.66 tff(527,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.60/0.66 tff(528,plain,
% 0.60/0.66 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.60/0.66 tff(529,plain,
% 0.60/0.66 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[528, 524])).
% 0.60/0.66 tff(530,plain,(
% 0.60/0.66 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.60/0.66 inference(skolemize,[status(sab)],[529])).
% 0.60/0.66 tff(531,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[530, 523])).
% 0.60/0.66 tff(532,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[531, 521])).
% 0.60/0.66 tff(533,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(534,plain,
% 0.60/0.66 ((v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0))) <=> (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(535,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[534])).
% 0.60/0.66 tff(536,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0))))),
% 0.60/0.66 inference(transitivity,[status(thm)],[535, 533])).
% 0.60/0.66 tff(537,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | (v3_struct_0(A!0) | (~v1_xboole_0(u1_struct_0(A!0))) | (~l1_struct_0(A!0)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(538,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))) | v3_struct_0(A!0) | (~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.60/0.66 tff(539,plain,
% 0.60/0.66 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[538, 193, 532])).
% 0.60/0.66 tff(540,plain,
% 0.60/0.66 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[539, 519])).
% 0.60/0.66 tff(541,plain,
% 0.60/0.66 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))) <=> m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[248])).
% 0.60/0.66 tff(542,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(543,plain,
% 0.60/0.66 ((v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(544,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[543])).
% 0.60/0.66 tff(545,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0)))),
% 0.60/0.66 inference(transitivity,[status(thm)],[544, 542])).
% 0.60/0.66 tff(546,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k1_filter_0(A!0) = u1_struct_0(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(547,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | (k1_filter_0(A) = u1_struct_0(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k1_filter_0(A!0) = u1_struct_0(A!0))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[546, 545])).
% 0.60/0.66 tff(548,plain,
% 0.60/0.66 (k1_filter_0(A!0) = u1_struct_0(A!0)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[547, 193, 192, 37, 304])).
% 0.60/0.66 tff(549,plain,
% 0.60/0.66 (u1_struct_0(A!0) = k1_filter_0(A!0)),
% 0.60/0.66 inference(symmetry,[status(thm)],[548])).
% 0.60/0.66 tff(550,plain,
% 0.60/0.66 (m1_filter_0(u1_struct_0(A!0), A!0) <=> m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.60/0.66 inference(monotonicity,[status(thm)],[549])).
% 0.60/0.66 tff(551,plain,
% 0.60/0.66 (m1_filter_0(k1_filter_0(A!0), A!0) <=> m1_filter_0(u1_struct_0(A!0), A!0)),
% 0.60/0.66 inference(symmetry,[status(thm)],[550])).
% 0.60/0.66 tff(552,plain,
% 0.60/0.66 (^[A: $i] : refl((v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(553,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[552])).
% 0.60/0.66 tff(554,plain,
% 0.60/0.66 (^[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))) | m1_filter_0(k1_filter_0(A), A)) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(k1_filter_0(A), A)))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(555,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[554])).
% 0.60/0.66 tff(556,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(557,plain,
% 0.60/0.66 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(558,plain,
% 0.60/0.66 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A)) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[557])).
% 0.60/0.66 tff(559,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => m1_filter_0(k1_filter_0(A), A))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','dt_k1_filter_0')).
% 0.60/0.66 tff(560,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[559, 558])).
% 0.60/0.66 tff(561,plain,
% 0.60/0.66 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[560, 556])).
% 0.60/0.66 tff(562,plain,(
% 0.60/0.66 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | m1_filter_0(k1_filter_0(A), A))),
% 0.60/0.66 inference(skolemize,[status(sab)],[561])).
% 0.60/0.66 tff(563,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[562, 555])).
% 0.60/0.66 tff(564,plain,
% 0.60/0.66 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[563, 553])).
% 0.60/0.66 tff(565,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(566,plain,
% 0.60/0.66 ((v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(567,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0)))),
% 0.60/0.66 inference(monotonicity,[status(thm)],[566])).
% 0.60/0.66 tff(568,plain,
% 0.60/0.66 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0))),
% 0.60/0.66 inference(transitivity,[status(thm)],[567, 565])).
% 0.60/0.66 tff(569,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | m1_filter_0(k1_filter_0(A!0), A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(570,plain,
% 0.60/0.66 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k1_filter_0(A), A) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[569, 568])).
% 0.60/0.66 tff(571,plain,
% 0.60/0.66 (m1_filter_0(k1_filter_0(A!0), A!0)),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[570, 193, 192, 37, 564])).
% 0.60/0.66 tff(572,plain,
% 0.60/0.66 (m1_filter_0(u1_struct_0(A!0), A!0)),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[571, 551])).
% 0.60/0.66 tff(573,plain,
% 0.60/0.66 (^[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)))))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(574,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[573])).
% 0.60/0.66 tff(575,plain,
% 0.60/0.66 (^[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)))))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(576,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[575])).
% 0.60/0.66 tff(577,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(transitivity,[status(thm)],[576, 574])).
% 0.60/0.66 tff(578,plain,
% 0.60/0.66 (^[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))))), 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))))))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(579,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[578])).
% 0.60/0.66 tff(580,plain,
% 0.60/0.66 (![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))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(581,plain,
% 0.60/0.66 (^[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((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))))))))),
% 0.60/0.66 inference(bind,[status(th)],[])).
% 0.60/0.66 tff(582,plain,
% 0.60/0.66 (![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))))))),
% 0.60/0.66 inference(quant_intro,[status(thm)],[581])).
% 0.60/0.66 tff(583,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')).
% 0.60/0.66 tff(584,plain,
% 0.60/0.66 (![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))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[583, 582])).
% 0.60/0.66 tff(585,plain,
% 0.60/0.66 (![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))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[584, 580])).
% 0.60/0.66 tff(586,plain,(
% 0.60/0.66 ![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))))))),
% 0.60/0.66 inference(skolemize,[status(sab)],[585])).
% 0.60/0.66 tff(587,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[586, 579])).
% 0.60/0.66 tff(588,plain,
% 0.60/0.66 (![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))))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[587, 577])).
% 0.60/0.66 tff(589,plain,
% 0.60/0.66 (((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : ((~m1_filter_0(B, A)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A))))))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(590,plain,
% 0.60/0.66 ((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0))))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(591,plain,
% 0.60/0.66 ((~![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(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[590, 589])).
% 0.60/0.66 tff(592,plain,
% 0.60/0.66 (![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[591, 193, 192, 37, 588])).
% 0.60/0.66 tff(593,plain,
% 0.60/0.66 (((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))) <=> ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.66 inference(rewrite,[status(thm)],[])).
% 0.60/0.66 tff(594,plain,
% 0.60/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | ((~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))))),
% 0.60/0.66 inference(quant_inst,[status(thm)],[])).
% 0.60/0.66 tff(595,plain,
% 0.60/0.66 ((~![B: $i] : ((~m1_filter_0(B, A!0)) | (~(v1_xboole_0(B) | (~m1_subset_1(B, k1_zfmisc_1(u1_struct_0(A!0)))))))) | (~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.60/0.66 inference(modus_ponens,[status(thm)],[594, 593])).
% 0.60/0.66 tff(596,plain,
% 0.60/0.66 ((~m1_filter_0(u1_struct_0(A!0), A!0)) | (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[595, 592])).
% 0.60/0.66 tff(597,plain,
% 0.60/0.66 (~(v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.60/0.66 inference(unit_resolution,[status(thm)],[596, 572])).
% 0.60/0.66 tff(598,plain,
% 0.60/0.66 ((v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0))))) | m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.67 inference(tautology,[status(thm)],[])).
% 0.60/0.67 tff(599,plain,
% 0.60/0.67 (m1_subset_1(u1_struct_0(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[598, 597])).
% 0.60/0.67 tff(600,plain,
% 0.60/0.67 (m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[599, 541])).
% 0.60/0.67 tff(601,plain,
% 0.60/0.67 (^[A: $i, B: $i, C: $i] : refl((v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(602,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[601])).
% 0.60/0.67 tff(603,plain,
% 0.60/0.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(604,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[603])).
% 0.60/0.67 tff(605,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(606,plain,
% 0.60/0.67 (^[A: $i, B: $i, C: $i] : trans(monotonicity(rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) <=> ((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> (((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))))), rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))), (((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(607,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C))) <=> ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[606])).
% 0.60/0.67 tff(608,axiom,(![A: $i, B: $i, C: $i] : ((((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A))) & m1_subset_1(C, k1_zfmisc_1(A))) => (r1_filter_2(A, B, C) <=> (B = C)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_r1_filter_2')).
% 0.60/0.67 tff(609,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[608, 607])).
% 0.60/0.67 tff(610,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[609, 605])).
% 0.60/0.67 tff(611,plain,(
% 0.60/0.67 ![A: $i, B: $i, C: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, k1_zfmisc_1(A)) & m1_subset_1(C, k1_zfmisc_1(A)))) | (r1_filter_2(A, B, C) <=> (B = C)))),
% 0.60/0.67 inference(skolemize,[status(sab)],[610])).
% 0.60/0.67 tff(612,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[611, 604])).
% 0.60/0.67 tff(613,plain,
% 0.60/0.67 (![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[612, 602])).
% 0.60/0.67 tff(614,plain,
% 0.60/0.67 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(615,plain,
% 0.60/0.67 ((v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0))))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(616,plain,
% 0.60/0.67 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[615])).
% 0.60/0.67 tff(617,plain,
% 0.60/0.67 (((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))) <=> ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))))),
% 0.60/0.67 inference(transitivity,[status(thm)],[616, 614])).
% 0.60/0.67 tff(618,plain,
% 0.60/0.67 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | (v1_xboole_0(u1_struct_0(A!0)) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))))),
% 0.60/0.67 inference(quant_inst,[status(thm)],[])).
% 0.60/0.67 tff(619,plain,
% 0.60/0.67 ((~![A: $i, B: $i, C: $i] : (v1_xboole_0(A) | (r1_filter_2(A, B, C) <=> (B = C)) | (~m1_subset_1(B, k1_zfmisc_1(A))) | (~m1_subset_1(C, k1_zfmisc_1(A))))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[618, 617])).
% 0.60/0.67 tff(620,plain,
% 0.60/0.67 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k18_filter_2(A!0, k6_lattices(A!0)), k1_zfmisc_1(u1_struct_0(A!0)))) | (~m1_subset_1(k17_filter_2(A!0), k1_zfmisc_1(u1_struct_0(A!0)))) | (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[619, 613])).
% 0.60/0.67 tff(621,plain,
% 0.60/0.67 (r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[620, 600, 540, 505])).
% 0.60/0.67 tff(622,plain,
% 0.60/0.67 (~r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.60/0.67 inference(or_elim,[status(thm)],[35])).
% 0.60/0.67 tff(623,plain,
% 0.60/0.67 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))) | r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) | (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.60/0.67 inference(tautology,[status(thm)],[])).
% 0.60/0.67 tff(624,plain,
% 0.60/0.67 ((~(r1_filter_2(u1_struct_0(A!0), k17_filter_2(A!0), k18_filter_2(A!0, k6_lattices(A!0))) <=> (k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))) | (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0))))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[623, 622])).
% 0.60/0.67 tff(625,plain,
% 0.60/0.67 (~(k17_filter_2(A!0) = k18_filter_2(A!0, k6_lattices(A!0)))),
% 0.60/0.67 inference(unit_resolution,[status(thm)],[624, 621])).
% 0.60/0.67 tff(626,plain,
% 0.60/0.67 (~(k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[625, 431])).
% 0.60/0.67 tff(627,plain,
% 0.60/0.67 (^[A: $i, B: $i] : refl((v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(628,plain,
% 0.60/0.67 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[627])).
% 0.60/0.67 tff(629,plain,
% 0.60/0.67 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) <=> (~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) <=> (v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite(((v3_struct_0(A) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(630,plain,
% 0.60/0.67 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[629])).
% 0.60/0.67 tff(631,plain,
% 0.60/0.67 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(632,plain,
% 0.60/0.67 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) <=> ((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))))),
% 0.60/0.67 inference(bind,[status(th)],[])).
% 0.60/0.67 tff(633,plain,
% 0.60/0.67 (![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B))) <=> ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.67 inference(quant_intro,[status(thm)],[632])).
% 0.60/0.67 tff(634,axiom,(![A: $i, B: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) & m1_subset_1(B, u1_struct_0(A))) => (k2_filter_2(A, B) = k2_filter_0(A, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','redefinition_k2_filter_2')).
% 0.60/0.67 tff(635,plain,
% 0.60/0.67 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[634, 633])).
% 0.60/0.67 tff(636,plain,
% 0.60/0.67 (![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[635, 631])).
% 0.60/0.67 tff(637,plain,(
% 0.60/0.67 ![A: $i, B: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B, u1_struct_0(A)))) | (k2_filter_2(A, B) = k2_filter_0(A, B)))),
% 0.60/0.67 inference(skolemize,[status(sab)],[636])).
% 0.60/0.67 tff(638,plain,
% 0.60/0.67 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[637, 630])).
% 0.60/0.67 tff(639,plain,
% 0.60/0.67 (![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))),
% 0.60/0.67 inference(modus_ponens,[status(thm)],[638, 628])).
% 0.60/0.67 tff(640,plain,
% 0.60/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | 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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | 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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(641,plain,
% 0.60/0.67 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | 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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.60/0.67 inference(rewrite,[status(thm)],[])).
% 0.60/0.67 tff(642,plain,
% 0.60/0.67 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | ((~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | 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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))))),
% 0.60/0.67 inference(monotonicity,[status(thm)],[641])).
% 0.60/0.68 tff(643,plain,
% 0.60/0.68 (((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | 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)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))))),
% 0.60/0.68 inference(transitivity,[status(thm)],[642, 640])).
% 0.60/0.68 tff(644,plain,
% 0.60/0.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.60/0.68 inference(quant_inst,[status(thm)],[])).
% 0.60/0.68 tff(645,plain,
% 0.60/0.68 ((~![A: $i, B: $i] : (v3_struct_0(A) | (k2_filter_2(A, B) = k2_filter_0(A, B)) | (~m1_subset_1(B, u1_struct_0(A))) | (~v10_lattices(A)) | (~l3_lattices(A)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.68 inference(modus_ponens,[status(thm)],[644, 643])).
% 0.60/0.68 tff(646,plain,
% 0.60/0.68 ((~m1_subset_1(k5_lattices(k1_lattice2(A!0)), u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (k2_filter_2(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))) = k2_filter_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)), k5_lattices(k1_lattice2(A!0))))),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[645, 639, 129, 286, 291])).
% 0.60/0.68 tff(647,plain,
% 0.60/0.68 ($false),
% 0.60/0.68 inference(unit_resolution,[status(thm)],[646, 626, 226])).
% 0.60/0.68 % SZS output end Proof
%------------------------------------------------------------------------------