TSTP Solution File: LAT302+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : LAT302+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n018.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 18:32:51 EDT 2022
% Result : Theorem 0.51s 0.62s
% Output : Proof 0.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LAT302+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n018.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Sep 1 13:45:57 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.51/0.62 % SZS status Theorem
% 0.51/0.62 % SZS output start Proof
% 0.51/0.62 tff(m1_filter_0_type, type, (
% 0.51/0.62 m1_filter_0: ( $i * $i ) > $o)).
% 0.51/0.62 tff(g3_lattices_type, type, (
% 0.51/0.62 g3_lattices: ( $i * $i * $i ) > $i)).
% 0.51/0.62 tff(u2_lattices_type, type, (
% 0.51/0.62 u2_lattices: $i > $i)).
% 0.51/0.62 tff(tptp_fun_A_0_type, type, (
% 0.51/0.62 tptp_fun_A_0: $i)).
% 0.51/0.62 tff(u1_lattices_type, type, (
% 0.51/0.62 u1_lattices: $i > $i)).
% 0.51/0.62 tff(u1_struct_0_type, type, (
% 0.51/0.62 u1_struct_0: $i > $i)).
% 0.51/0.62 tff(k1_tarski_type, type, (
% 0.51/0.62 k1_tarski: $i > $i)).
% 0.51/0.62 tff(k5_lattices_type, type, (
% 0.51/0.62 k5_lattices: $i > $i)).
% 0.51/0.62 tff(m1_filter_2_type, type, (
% 0.51/0.62 m1_filter_2: ( $i * $i ) > $o)).
% 0.51/0.62 tff(v3_struct_0_type, type, (
% 0.51/0.62 v3_struct_0: $i > $o)).
% 0.51/0.62 tff(k1_lattice2_type, type, (
% 0.51/0.62 k1_lattice2: $i > $i)).
% 0.51/0.62 tff(l3_lattices_type, type, (
% 0.51/0.62 l3_lattices: $i > $o)).
% 0.51/0.62 tff(v10_lattices_type, type, (
% 0.51/0.62 v10_lattices: $i > $o)).
% 0.51/0.62 tff(v13_lattices_type, type, (
% 0.51/0.62 v13_lattices: $i > $o)).
% 0.51/0.62 tff(m2_filter_2_type, type, (
% 0.51/0.62 m2_filter_2: ( $i * $i ) > $o)).
% 0.51/0.62 tff(k6_domain_1_type, type, (
% 0.51/0.62 k6_domain_1: ( $i * $i ) > $i)).
% 0.51/0.62 tff(v9_lattices_type, type, (
% 0.51/0.62 v9_lattices: $i > $o)).
% 0.51/0.62 tff(v8_lattices_type, type, (
% 0.51/0.62 v8_lattices: $i > $o)).
% 0.51/0.62 tff(v7_lattices_type, type, (
% 0.51/0.62 v7_lattices: $i > $o)).
% 0.51/0.62 tff(v6_lattices_type, type, (
% 0.51/0.62 v6_lattices: $i > $o)).
% 0.51/0.62 tff(v5_lattices_type, type, (
% 0.51/0.62 v5_lattices: $i > $o)).
% 0.51/0.62 tff(v4_lattices_type, type, (
% 0.51/0.62 v4_lattices: $i > $o)).
% 0.51/0.62 tff(v3_lattices_type, type, (
% 0.51/0.62 v3_lattices: $i > $o)).
% 0.51/0.62 tff(m1_relset_1_type, type, (
% 0.51/0.62 m1_relset_1: ( $i * $i * $i ) > $o)).
% 0.51/0.62 tff(k2_zfmisc_1_type, type, (
% 0.51/0.62 k2_zfmisc_1: ( $i * $i ) > $i)).
% 0.51/0.62 tff(m2_relset_1_type, type, (
% 0.51/0.62 m2_relset_1: ( $i * $i * $i ) > $o)).
% 0.51/0.62 tff(v1_funct_2_type, type, (
% 0.51/0.62 v1_funct_2: ( $i * $i * $i ) > $o)).
% 0.51/0.62 tff(v1_funct_1_type, type, (
% 0.51/0.62 v1_funct_1: $i > $o)).
% 0.51/0.62 tff(l1_lattices_type, type, (
% 0.51/0.62 l1_lattices: $i > $o)).
% 0.51/0.62 tff(l2_lattices_type, type, (
% 0.51/0.62 l2_lattices: $i > $o)).
% 0.51/0.62 tff(m1_subset_1_type, type, (
% 0.51/0.62 m1_subset_1: ( $i * $i ) > $o)).
% 0.51/0.62 tff(v1_xboole_0_type, type, (
% 0.51/0.62 v1_xboole_0: $i > $o)).
% 0.51/0.62 tff(l1_struct_0_type, type, (
% 0.51/0.62 l1_struct_0: $i > $o)).
% 0.51/0.62 tff(k6_lattices_type, type, (
% 0.51/0.62 k6_lattices: $i > $i)).
% 0.51/0.62 tff(v14_lattices_type, type, (
% 0.51/0.62 v14_lattices: $i > $o)).
% 0.51/0.62 tff(1,plain,
% 0.51/0.62 (^[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)))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(2,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[1])).
% 0.51/0.62 tff(3,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(4,plain,
% 0.51/0.62 (^[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)))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(5,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[4])).
% 0.51/0.62 tff(6,axiom,(![A: $i] : (l3_lattices(A) => (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','d2_lattice2')).
% 0.51/0.62 tff(7,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.51/0.62 tff(8,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.51/0.62 tff(9,plain,(
% 0.51/0.62 ![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.51/0.62 inference(skolemize,[status(sab)],[8])).
% 0.51/0.62 tff(10,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (k1_lattice2(A) = g3_lattices(u1_struct_0(A), u1_lattices(A), u2_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.51/0.62 tff(11,plain,
% 0.51/0.62 ((~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) | (~v13_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))) <=> (~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) | (~v13_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(12,plain,
% 0.51/0.62 ((~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))) <=> (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(13,plain,
% 0.51/0.62 ((~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A)))) <=> (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(14,axiom,(~![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) => m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t26_filter_2')).
% 0.51/0.62 tff(15,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.51/0.62 tff(16,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[15, 12])).
% 0.51/0.62 tff(17,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.51/0.62 tff(18,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[17, 12])).
% 0.51/0.62 tff(19,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[18, 12])).
% 0.51/0.62 tff(20,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[19, 12])).
% 0.51/0.62 tff(21,plain,
% 0.51/0.62 (~![A: $i] : (m2_filter_2(k6_domain_1(u1_struct_0(A), k5_lattices(A)), A) | (~v13_lattices(A)) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[20, 12])).
% 0.51/0.62 tff(22,plain,(
% 0.51/0.62 ~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) | (~v13_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.51/0.62 inference(skolemize,[status(sab)],[21])).
% 0.51/0.62 tff(23,plain,
% 0.51/0.62 (~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) | (~v13_lattices(A!0)) | (~((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[22, 11])).
% 0.51/0.62 tff(24,plain,
% 0.51/0.62 ((~v3_struct_0(A!0)) & v10_lattices(A!0) & l3_lattices(A!0)),
% 0.51/0.62 inference(or_elim,[status(thm)],[23])).
% 0.51/0.62 tff(25,plain,
% 0.51/0.62 (l3_lattices(A!0)),
% 0.51/0.62 inference(and_elim,[status(thm)],[24])).
% 0.51/0.62 tff(26,plain,
% 0.51/0.62 (((~![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))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(27,plain,
% 0.51/0.62 ((~![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))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(28,plain,
% 0.51/0.62 ((~![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)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.51/0.62 tff(29,plain,
% 0.51/0.62 (k1_lattice2(A!0) = g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[28, 25, 10])).
% 0.51/0.62 tff(30,plain,
% 0.51/0.62 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = k1_lattice2(A!0)),
% 0.51/0.62 inference(symmetry,[status(thm)],[29])).
% 0.51/0.62 tff(31,plain,
% 0.51/0.62 (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))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[30])).
% 0.51/0.62 tff(32,plain,
% 0.51/0.62 (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)))),
% 0.51/0.62 inference(symmetry,[status(thm)],[31])).
% 0.51/0.62 tff(33,plain,
% 0.51/0.62 ((~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))))),
% 0.51/0.62 inference(monotonicity,[status(thm)],[32])).
% 0.51/0.62 tff(34,plain,
% 0.51/0.62 (^[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)))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(35,plain,
% 0.51/0.62 (![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))))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[34])).
% 0.51/0.62 tff(36,plain,
% 0.51/0.62 (^[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))))), 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))))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(37,plain,
% 0.51/0.62 (![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))))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[36])).
% 0.51/0.62 tff(38,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(39,plain,
% 0.51/0.62 (^[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))), 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))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(40,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[39])).
% 0.51/0.62 tff(41,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/sandbox/benchmark/theBenchmark.p','fc6_lattice2')).
% 0.51/0.62 tff(42,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.51/0.62 tff(43,plain,
% 0.51/0.62 (![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))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[42, 38])).
% 0.51/0.62 tff(44,plain,(
% 0.51/0.62 ![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))))),
% 0.51/0.62 inference(skolemize,[status(sab)],[43])).
% 0.51/0.62 tff(45,plain,
% 0.51/0.62 (![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))))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[44, 37])).
% 0.51/0.62 tff(46,plain,
% 0.51/0.62 (![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))))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[45, 35])).
% 0.51/0.62 tff(47,plain,
% 0.51/0.62 (v10_lattices(A!0)),
% 0.51/0.62 inference(and_elim,[status(thm)],[24])).
% 0.51/0.62 tff(48,plain,
% 0.51/0.62 (~v3_struct_0(A!0)),
% 0.51/0.62 inference(and_elim,[status(thm)],[24])).
% 0.51/0.62 tff(49,plain,
% 0.51/0.62 (((~![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))))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(50,plain,
% 0.51/0.62 ((~![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))))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(51,plain,
% 0.51/0.62 ((~![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)))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[50, 49])).
% 0.51/0.62 tff(52,plain,
% 0.51/0.62 (~(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))))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[51, 48, 47, 25, 46])).
% 0.51/0.62 tff(53,plain,
% 0.51/0.62 ((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)))),
% 0.51/0.62 inference(tautology,[status(thm)],[])).
% 0.51/0.62 tff(54,plain,
% 0.51/0.62 (~v3_struct_0(k1_lattice2(A!0))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[53, 52])).
% 0.51/0.62 tff(55,plain,
% 0.51/0.62 (~v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[54, 33])).
% 0.51/0.62 tff(56,plain,
% 0.51/0.62 (^[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)))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(57,plain,
% 0.51/0.62 (![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))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[56])).
% 0.51/0.62 tff(58,plain,
% 0.51/0.62 (![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))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(59,axiom,(![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m2_relset_1')).
% 0.51/0.62 tff(60,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.51/0.62 tff(61,plain,(
% 0.51/0.62 ![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.51/0.62 inference(skolemize,[status(sab)],[60])).
% 0.51/0.62 tff(62,plain,
% 0.51/0.62 (![A: $i, B: $i, C: $i] : (m2_relset_1(C, A, B) <=> m1_relset_1(C, A, B))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[61, 57])).
% 0.51/0.62 tff(63,plain,
% 0.51/0.62 ((~![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)))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(64,plain,
% 0.51/0.62 (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))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[63, 62])).
% 0.51/0.62 tff(65,plain,
% 0.51/0.62 (^[A: $i] : refl(((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(66,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[65])).
% 0.51/0.62 tff(67,plain,
% 0.51/0.62 (^[A: $i] : rewrite(((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(68,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[67])).
% 0.51/0.62 tff(69,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(70,plain,
% 0.51/0.62 (^[A: $i] : rewrite((l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(71,plain,
% 0.51/0.62 (![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A))) <=> ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.51/0.62 inference(quant_intro,[status(thm)],[70])).
% 0.51/0.62 tff(72,axiom,(![A: $i] : (l3_lattices(A) => (l1_lattices(A) & l2_lattices(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l3_lattices')).
% 0.51/0.62 tff(73,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[72, 71])).
% 0.51/0.62 tff(74,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[73, 69])).
% 0.51/0.62 tff(75,plain,(
% 0.51/0.62 ![A: $i] : ((~l3_lattices(A)) | (l1_lattices(A) & l2_lattices(A)))),
% 0.51/0.62 inference(skolemize,[status(sab)],[74])).
% 0.51/0.62 tff(76,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[75, 68])).
% 0.51/0.62 tff(77,plain,
% 0.51/0.62 (![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[76, 66])).
% 0.51/0.62 tff(78,plain,
% 0.51/0.62 (((~![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)))))),
% 0.51/0.62 inference(rewrite,[status(thm)],[])).
% 0.51/0.62 tff(79,plain,
% 0.51/0.62 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | ((~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))))),
% 0.51/0.62 inference(quant_inst,[status(thm)],[])).
% 0.51/0.62 tff(80,plain,
% 0.51/0.62 ((~![A: $i] : ((~l3_lattices(A)) | (~((~l1_lattices(A)) | (~l2_lattices(A)))))) | (~l3_lattices(A!0)) | (~((~l1_lattices(A!0)) | (~l2_lattices(A!0))))),
% 0.51/0.62 inference(modus_ponens,[status(thm)],[79, 78])).
% 0.51/0.62 tff(81,plain,
% 0.51/0.62 (~((~l1_lattices(A!0)) | (~l2_lattices(A!0)))),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[80, 25, 77])).
% 0.51/0.62 tff(82,plain,
% 0.51/0.62 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l1_lattices(A!0)),
% 0.51/0.62 inference(tautology,[status(thm)],[])).
% 0.51/0.62 tff(83,plain,
% 0.51/0.62 (l1_lattices(A!0)),
% 0.51/0.62 inference(unit_resolution,[status(thm)],[82, 81])).
% 0.51/0.62 tff(84,plain,
% 0.51/0.62 (^[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)))))))),
% 0.51/0.62 inference(bind,[status(th)],[])).
% 0.51/0.62 tff(85,plain,
% 0.51/0.62 (![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))))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[84])).
% 0.51/0.63 tff(86,plain,
% 0.51/0.63 (^[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)))))))),
% 0.51/0.63 inference(bind,[status(th)],[])).
% 0.51/0.63 tff(87,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[86])).
% 0.51/0.63 tff(88,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(89,plain,
% 0.51/0.63 (^[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))))))),
% 0.51/0.63 inference(bind,[status(th)],[])).
% 0.51/0.63 tff(90,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[89])).
% 0.51/0.63 tff(91,axiom,(![A: $i] : (l1_lattices(A) => ((v1_funct_1(u1_lattices(A)) & v1_funct_2(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u1_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u1_lattices')).
% 0.51/0.63 tff(92,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[91, 90])).
% 0.51/0.63 tff(93,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[92, 88])).
% 0.51/0.63 tff(94,plain,(
% 0.51/0.63 ![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))))),
% 0.51/0.63 inference(skolemize,[status(sab)],[93])).
% 0.51/0.63 tff(95,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[94, 87])).
% 0.51/0.63 tff(96,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[95, 85])).
% 0.51/0.63 tff(97,plain,
% 0.51/0.63 (((~![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))))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(98,plain,
% 0.51/0.63 ((~![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))))))),
% 0.51/0.63 inference(quant_inst,[status(thm)],[])).
% 0.51/0.63 tff(99,plain,
% 0.51/0.63 ((~![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)))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[98, 97])).
% 0.51/0.63 tff(100,plain,
% 0.51/0.63 ((~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)))))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[99, 96])).
% 0.51/0.63 tff(101,plain,
% 0.51/0.63 (~((~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))))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[100, 83])).
% 0.51/0.63 tff(102,plain,
% 0.51/0.63 (((~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))),
% 0.51/0.63 inference(tautology,[status(thm)],[])).
% 0.51/0.63 tff(103,plain,
% 0.51/0.63 (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))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[102, 101])).
% 0.51/0.63 tff(104,plain,
% 0.51/0.63 ((~(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))),
% 0.51/0.63 inference(tautology,[status(thm)],[])).
% 0.51/0.63 tff(105,plain,
% 0.51/0.63 ((~(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))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[104, 103])).
% 0.51/0.63 tff(106,plain,
% 0.51/0.63 (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))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[105, 64])).
% 0.51/0.63 tff(107,plain,
% 0.51/0.63 ((~![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)))),
% 0.51/0.63 inference(quant_inst,[status(thm)],[])).
% 0.51/0.63 tff(108,plain,
% 0.51/0.63 (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))),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[107, 62])).
% 0.51/0.63 tff(109,plain,
% 0.51/0.63 (((~l1_lattices(A!0)) | (~l2_lattices(A!0))) | l2_lattices(A!0)),
% 0.51/0.63 inference(tautology,[status(thm)],[])).
% 0.51/0.63 tff(110,plain,
% 0.51/0.63 (l2_lattices(A!0)),
% 0.51/0.63 inference(unit_resolution,[status(thm)],[109, 81])).
% 0.51/0.63 tff(111,plain,
% 0.51/0.63 (^[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)))))))),
% 0.51/0.63 inference(bind,[status(th)],[])).
% 0.51/0.63 tff(112,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[111])).
% 0.51/0.63 tff(113,plain,
% 0.51/0.63 (^[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)))))))),
% 0.51/0.63 inference(bind,[status(th)],[])).
% 0.51/0.63 tff(114,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[113])).
% 0.51/0.63 tff(115,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(116,plain,
% 0.51/0.63 (^[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))))))),
% 0.51/0.63 inference(bind,[status(th)],[])).
% 0.51/0.63 tff(117,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(quant_intro,[status(thm)],[116])).
% 0.51/0.63 tff(118,axiom,(![A: $i] : (l2_lattices(A) => ((v1_funct_1(u2_lattices(A)) & v1_funct_2(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))) & m2_relset_1(u2_lattices(A), k2_zfmisc_1(u1_struct_0(A), u1_struct_0(A)), u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_u2_lattices')).
% 0.51/0.63 tff(119,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[118, 117])).
% 0.51/0.63 tff(120,plain,
% 0.51/0.63 (![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))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[119, 115])).
% 0.51/0.63 tff(121,plain,(
% 0.51/0.63 ![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))))),
% 0.51/0.63 inference(skolemize,[status(sab)],[120])).
% 0.51/0.63 tff(122,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[121, 114])).
% 0.51/0.63 tff(123,plain,
% 0.51/0.63 (![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))))))),
% 0.51/0.63 inference(modus_ponens,[status(thm)],[122, 112])).
% 0.51/0.63 tff(124,plain,
% 0.51/0.63 (((~![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))))))),
% 0.51/0.63 inference(rewrite,[status(thm)],[])).
% 0.51/0.63 tff(125,plain,
% 0.51/0.63 ((~![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))))))),
% 0.61/0.63 inference(quant_inst,[status(thm)],[])).
% 0.61/0.63 tff(126,plain,
% 0.61/0.63 ((~![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)))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.61/0.63 tff(127,plain,
% 0.61/0.63 ((~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)))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[126, 123])).
% 0.61/0.63 tff(128,plain,
% 0.61/0.63 (~((~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))))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[127, 110])).
% 0.61/0.63 tff(129,plain,
% 0.61/0.63 (((~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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(130,plain,
% 0.61/0.63 (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))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[129, 128])).
% 0.61/0.63 tff(131,plain,
% 0.61/0.63 ((~(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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(132,plain,
% 0.61/0.63 ((~(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))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[131, 130])).
% 0.61/0.63 tff(133,plain,
% 0.61/0.63 (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))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[132, 108])).
% 0.61/0.63 tff(134,plain,
% 0.61/0.63 (((~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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(135,plain,
% 0.61/0.63 (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))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[134, 128])).
% 0.61/0.63 tff(136,plain,
% 0.61/0.63 (((~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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(137,plain,
% 0.61/0.63 (v1_funct_1(u2_lattices(A!0))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[136, 128])).
% 0.61/0.63 tff(138,plain,
% 0.61/0.63 (((~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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(139,plain,
% 0.61/0.63 (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))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[138, 101])).
% 0.61/0.63 tff(140,plain,
% 0.61/0.63 (((~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))),
% 0.61/0.63 inference(tautology,[status(thm)],[])).
% 0.61/0.63 tff(141,plain,
% 0.61/0.63 (v1_funct_1(u1_lattices(A!0))),
% 0.61/0.63 inference(unit_resolution,[status(thm)],[140, 101])).
% 0.61/0.63 tff(142,plain,
% 0.61/0.63 (^[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)))))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(143,plain,
% 0.61/0.63 (![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))))))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[142])).
% 0.61/0.63 tff(144,plain,
% 0.61/0.63 (^[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))))))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(145,plain,
% 0.61/0.63 (![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))))))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[144])).
% 0.61/0.63 tff(146,plain,
% 0.61/0.63 (![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))))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(147,plain,
% 0.61/0.63 (^[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))))))),
% 0.61/0.63 inference(bind,[status(th)],[])).
% 0.61/0.63 tff(148,plain,
% 0.61/0.63 (![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))))),
% 0.61/0.63 inference(quant_intro,[status(thm)],[147])).
% 0.61/0.63 tff(149,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/sandbox/benchmark/theBenchmark.p','dt_g3_lattices')).
% 0.61/0.63 tff(150,plain,
% 0.61/0.63 (![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))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[149, 148])).
% 0.61/0.63 tff(151,plain,
% 0.61/0.63 (![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))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[150, 146])).
% 0.61/0.63 tff(152,plain,(
% 0.61/0.63 ![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))))),
% 0.61/0.63 inference(skolemize,[status(sab)],[151])).
% 0.61/0.63 tff(153,plain,
% 0.61/0.63 (![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))))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[152, 145])).
% 0.61/0.63 tff(154,plain,
% 0.61/0.63 (![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))))))),
% 0.61/0.63 inference(modus_ponens,[status(thm)],[153, 143])).
% 0.61/0.63 tff(155,plain,
% 0.61/0.63 (((~![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)))))))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(156,plain,
% 0.61/0.63 (((~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)))))))),
% 0.61/0.63 inference(rewrite,[status(thm)],[])).
% 0.61/0.63 tff(157,plain,
% 0.61/0.63 ((~((~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))))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(158,plain,
% 0.61/0.64 (((~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)))))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[157])).
% 0.61/0.64 tff(159,plain,
% 0.61/0.64 (((~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)))))))),
% 0.61/0.64 inference(transitivity,[status(thm)],[158, 156])).
% 0.61/0.64 tff(160,plain,
% 0.61/0.64 (((~![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))))))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[159])).
% 0.61/0.64 tff(161,plain,
% 0.61/0.64 (((~![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)))))))),
% 0.61/0.64 inference(transitivity,[status(thm)],[160, 155])).
% 0.61/0.64 tff(162,plain,
% 0.61/0.64 ((~![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)))))))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(163,plain,
% 0.61/0.64 ((~![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))))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[162, 161])).
% 0.61/0.64 tff(164,plain,
% 0.61/0.64 ((~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))))))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[163, 154, 141, 139, 137, 135])).
% 0.61/0.64 tff(165,plain,
% 0.61/0.64 (~((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[164, 133, 106])).
% 0.61/0.64 tff(166,plain,
% 0.61/0.64 (((~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)))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(167,plain,
% 0.61/0.64 (l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[166, 165])).
% 0.61/0.64 tff(168,plain,
% 0.61/0.64 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v10_lattices(k1_lattice2(A!0))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.64 tff(169,plain,
% 0.61/0.64 (v10_lattices(k1_lattice2(A!0)) <=> v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.64 inference(symmetry,[status(thm)],[168])).
% 0.61/0.64 tff(170,plain,
% 0.61/0.64 ((v3_struct_0(k1_lattice2(A!0)) | (~v3_lattices(k1_lattice2(A!0))) | (~v4_lattices(k1_lattice2(A!0))) | (~v5_lattices(k1_lattice2(A!0))) | (~v6_lattices(k1_lattice2(A!0))) | (~v7_lattices(k1_lattice2(A!0))) | (~v8_lattices(k1_lattice2(A!0))) | (~v9_lattices(k1_lattice2(A!0))) | (~v10_lattices(k1_lattice2(A!0)))) | v10_lattices(k1_lattice2(A!0))),
% 0.61/0.64 inference(tautology,[status(thm)],[])).
% 0.61/0.64 tff(171,plain,
% 0.61/0.64 (v10_lattices(k1_lattice2(A!0))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[170, 52])).
% 0.61/0.64 tff(172,plain,
% 0.61/0.64 (v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[171, 169])).
% 0.61/0.64 tff(173,plain,
% 0.61/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(174,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[173])).
% 0.61/0.64 tff(175,plain,
% 0.61/0.64 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(176,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[175])).
% 0.61/0.64 tff(177,plain,
% 0.61/0.64 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(178,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[177])).
% 0.61/0.64 tff(179,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(transitivity,[status(thm)],[178, 176])).
% 0.61/0.64 tff(180,plain,
% 0.61/0.64 (^[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))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(181,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[180])).
% 0.61/0.64 tff(182,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(183,plain,
% 0.61/0.64 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(184,plain,
% 0.61/0.64 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[183])).
% 0.61/0.64 tff(185,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_m1_filter_2')).
% 0.61/0.64 tff(186,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.61/0.64 tff(187,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[186, 182])).
% 0.61/0.64 tff(188,plain,(
% 0.61/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[187])).
% 0.61/0.64 tff(189,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[188, 181])).
% 0.61/0.64 tff(190,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[189, 179])).
% 0.61/0.64 tff(191,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[190, 174])).
% 0.61/0.64 tff(192,plain,
% 0.61/0.64 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(193,plain,
% 0.61/0.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(194,plain,
% 0.61/0.64 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m1_filter_2(B, A) <=> m1_filter_0(B, A)))) | v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.61/0.64 tff(195,plain,
% 0.61/0.64 (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | ![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[194, 191])).
% 0.61/0.64 tff(196,plain,
% 0.61/0.64 (![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[195, 172, 167, 55])).
% 0.61/0.64 tff(197,plain,
% 0.61/0.64 ((~![B: $i] : (m1_filter_2(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(B, g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(198,plain,
% 0.61/0.64 (m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[197, 196])).
% 0.61/0.64 tff(199,plain,
% 0.61/0.64 (^[A: $i] : refl((v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(200,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[199])).
% 0.61/0.64 tff(201,plain,
% 0.61/0.64 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & l1_lattices(A)) <=> (~(v3_struct_0(A) | (~l1_lattices(A))))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l1_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l1_lattices(A))))) <=> (v3_struct_0(A) | (~l1_lattices(A)))), ((~((~v3_struct_0(A)) & l1_lattices(A))) <=> (v3_struct_0(A) | (~l1_lattices(A))))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))), rewrite(((v3_struct_0(A) | (~l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))), (((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(202,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[201])).
% 0.61/0.64 tff(203,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(204,plain,
% 0.61/0.64 (^[A: $i] : rewrite((((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(205,plain,
% 0.61/0.64 (![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[204])).
% 0.61/0.64 tff(206,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_lattices(A)) => m1_subset_1(k5_lattices(A), u1_struct_0(A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_k5_lattices')).
% 0.61/0.64 tff(207,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[206, 205])).
% 0.61/0.64 tff(208,plain,
% 0.61/0.64 (![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[207, 203])).
% 0.61/0.64 tff(209,plain,(
% 0.61/0.64 ![A: $i] : ((~((~v3_struct_0(A)) & l1_lattices(A))) | m1_subset_1(k5_lattices(A), u1_struct_0(A)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[208])).
% 0.61/0.64 tff(210,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[209, 202])).
% 0.61/0.64 tff(211,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[210, 200])).
% 0.61/0.64 tff(212,plain,
% 0.61/0.64 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(213,plain,
% 0.61/0.64 ((v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0))) <=> (v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(214,plain,
% 0.61/0.64 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[213])).
% 0.61/0.64 tff(215,plain,
% 0.61/0.64 (((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)))),
% 0.61/0.64 inference(transitivity,[status(thm)],[214, 212])).
% 0.61/0.64 tff(216,plain,
% 0.61/0.64 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | (v3_struct_0(A!0) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)) | (~l1_lattices(A!0)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(217,plain,
% 0.61/0.64 ((~![A: $i] : (v3_struct_0(A) | m1_subset_1(k5_lattices(A), u1_struct_0(A)) | (~l1_lattices(A)))) | v3_struct_0(A!0) | (~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[216, 215])).
% 0.61/0.64 tff(218,plain,
% 0.61/0.64 ((~l1_lattices(A!0)) | m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[217, 48, 211])).
% 0.61/0.64 tff(219,plain,
% 0.61/0.64 (m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[218, 83])).
% 0.61/0.64 tff(220,plain,
% 0.61/0.64 (^[A: $i] : refl((l1_struct_0(A) | (~l2_lattices(A))) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(221,plain,
% 0.61/0.64 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[220])).
% 0.61/0.64 tff(222,plain,
% 0.61/0.64 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A))) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(223,plain,
% 0.61/0.64 (^[A: $i] : rewrite((l2_lattices(A) => l1_struct_0(A)) <=> (l1_struct_0(A) | (~l2_lattices(A))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(224,plain,
% 0.61/0.64 (![A: $i] : (l2_lattices(A) => l1_struct_0(A)) <=> ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[223])).
% 0.61/0.64 tff(225,axiom,(![A: $i] : (l2_lattices(A) => l1_struct_0(A))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','dt_l2_lattices')).
% 0.61/0.64 tff(226,plain,
% 0.61/0.64 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[225, 224])).
% 0.61/0.64 tff(227,plain,
% 0.61/0.64 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[226, 222])).
% 0.61/0.64 tff(228,plain,(
% 0.61/0.64 ![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(skolemize,[status(sab)],[227])).
% 0.61/0.64 tff(229,plain,
% 0.61/0.64 (![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[228, 221])).
% 0.61/0.64 tff(230,plain,
% 0.61/0.64 (((~![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)))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(231,plain,
% 0.61/0.64 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | (l1_struct_0(A!0) | (~l2_lattices(A!0)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(232,plain,
% 0.61/0.64 ((~![A: $i] : (l1_struct_0(A) | (~l2_lattices(A)))) | l1_struct_0(A!0) | (~l2_lattices(A!0))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.61/0.64 tff(233,plain,
% 0.61/0.64 (l1_struct_0(A!0)),
% 0.61/0.64 inference(unit_resolution,[status(thm)],[232, 229, 110])).
% 0.61/0.64 tff(234,plain,
% 0.61/0.64 (^[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))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(235,plain,
% 0.61/0.64 (![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)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[234])).
% 0.61/0.64 tff(236,plain,
% 0.61/0.64 (^[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)))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(237,plain,
% 0.61/0.64 (![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)))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[236])).
% 0.61/0.64 tff(238,plain,
% 0.61/0.64 (![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))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(239,plain,
% 0.61/0.64 (^[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)))))),
% 0.61/0.64 inference(bind,[status(th)],[])).
% 0.61/0.64 tff(240,plain,
% 0.61/0.64 (![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))))),
% 0.61/0.64 inference(quant_intro,[status(thm)],[239])).
% 0.61/0.64 tff(241,axiom,(![A: $i] : (((~v3_struct_0(A)) & l1_struct_0(A)) => (~v1_xboole_0(u1_struct_0(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','fc1_struct_0')).
% 0.61/0.64 tff(242,plain,
% 0.61/0.64 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.61/0.64 tff(243,plain,
% 0.61/0.64 (![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[242, 238])).
% 0.61/0.64 tff(244,plain,(
% 0.61/0.64 ![A: $i] : ((~v1_xboole_0(u1_struct_0(A))) | (~((~v3_struct_0(A)) & l1_struct_0(A))))),
% 0.61/0.64 inference(skolemize,[status(sab)],[243])).
% 0.61/0.64 tff(245,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[244, 237])).
% 0.61/0.64 tff(246,plain,
% 0.61/0.64 (![A: $i] : (v3_struct_0(A) | (~v1_xboole_0(u1_struct_0(A))) | (~l1_struct_0(A)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[245, 235])).
% 0.61/0.64 tff(247,plain,
% 0.61/0.64 (((~![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))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(248,plain,
% 0.61/0.64 ((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))))),
% 0.61/0.64 inference(rewrite,[status(thm)],[])).
% 0.61/0.64 tff(249,plain,
% 0.61/0.64 (((~![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)))))),
% 0.61/0.64 inference(monotonicity,[status(thm)],[248])).
% 0.61/0.64 tff(250,plain,
% 0.61/0.64 (((~![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))))),
% 0.61/0.64 inference(transitivity,[status(thm)],[249, 247])).
% 0.61/0.64 tff(251,plain,
% 0.61/0.64 ((~![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)))),
% 0.61/0.64 inference(quant_inst,[status(thm)],[])).
% 0.61/0.64 tff(252,plain,
% 0.61/0.64 ((~![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)))),
% 0.61/0.64 inference(modus_ponens,[status(thm)],[251, 250])).
% 0.61/0.64 tff(253,plain,
% 0.61/0.64 ((~l1_struct_0(A!0)) | (~v1_xboole_0(u1_struct_0(A!0)))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[252, 48, 246])).
% 0.61/0.65 tff(254,plain,
% 0.61/0.65 (~v1_xboole_0(u1_struct_0(A!0))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[253, 233])).
% 0.61/0.65 tff(255,plain,
% 0.61/0.65 (^[A: $i, B: $i] : refl((v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(256,plain,
% 0.61/0.65 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[255])).
% 0.61/0.65 tff(257,plain,
% 0.61/0.65 (^[A: $i, B: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v1_xboole_0(A)) & m1_subset_1(B, A)) <=> (~(v1_xboole_0(A) | (~m1_subset_1(B, A))))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))))), rewrite((~(~(v1_xboole_0(A) | (~m1_subset_1(B, A))))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A)))), ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) <=> (v1_xboole_0(A) | (~m1_subset_1(B, A))))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ((v1_xboole_0(A) | (~m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))))), rewrite(((v1_xboole_0(A) | (~m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))), (((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(258,plain,
% 0.61/0.65 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[257])).
% 0.61/0.65 tff(259,plain,
% 0.61/0.65 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(260,plain,
% 0.61/0.65 (^[A: $i, B: $i] : rewrite((((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B))) <=> ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(261,plain,
% 0.61/0.65 (![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B))) <=> ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[260])).
% 0.61/0.65 tff(262,axiom,(![A: $i, B: $i] : (((~v1_xboole_0(A)) & m1_subset_1(B, A)) => (k6_domain_1(A, B) = k1_tarski(B)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','redefinition_k6_domain_1')).
% 0.61/0.65 tff(263,plain,
% 0.61/0.65 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[262, 261])).
% 0.61/0.65 tff(264,plain,
% 0.61/0.65 (![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[263, 259])).
% 0.61/0.65 tff(265,plain,(
% 0.61/0.65 ![A: $i, B: $i] : ((~((~v1_xboole_0(A)) & m1_subset_1(B, A))) | (k6_domain_1(A, B) = k1_tarski(B)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[264])).
% 0.61/0.65 tff(266,plain,
% 0.61/0.65 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[265, 258])).
% 0.61/0.65 tff(267,plain,
% 0.61/0.65 (![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[266, 256])).
% 0.61/0.65 tff(268,plain,
% 0.61/0.65 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(269,plain,
% 0.61/0.65 ((v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0)))) <=> (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(270,plain,
% 0.61/0.65 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0)))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[269])).
% 0.61/0.65 tff(271,plain,
% 0.61/0.65 (((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))))) <=> ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))))),
% 0.61/0.65 inference(transitivity,[status(thm)],[270, 268])).
% 0.61/0.65 tff(272,plain,
% 0.61/0.65 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | (v1_xboole_0(u1_struct_0(A!0)) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(273,plain,
% 0.61/0.65 ((~![A: $i, B: $i] : (v1_xboole_0(A) | (k6_domain_1(A, B) = k1_tarski(B)) | (~m1_subset_1(B, A)))) | v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.61/0.65 tff(274,plain,
% 0.61/0.65 (v1_xboole_0(u1_struct_0(A!0)) | (~m1_subset_1(k5_lattices(A!0), u1_struct_0(A!0))) | (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0)))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[273, 267])).
% 0.61/0.65 tff(275,plain,
% 0.61/0.65 (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k1_tarski(k5_lattices(A!0))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[274, 254, 219])).
% 0.61/0.65 tff(276,plain,
% 0.61/0.65 (k1_tarski(k5_lattices(A!0)) = k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0))),
% 0.61/0.65 inference(symmetry,[status(thm)],[275])).
% 0.61/0.65 tff(277,plain,
% 0.61/0.65 (m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[276, 30])).
% 0.61/0.65 tff(278,plain,
% 0.61/0.65 (m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)) <=> m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.65 inference(symmetry,[status(thm)],[277])).
% 0.61/0.65 tff(279,plain,
% 0.61/0.65 ((~m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0))) <=> (~m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[278])).
% 0.61/0.65 tff(280,plain,
% 0.61/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(281,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[280])).
% 0.61/0.65 tff(282,plain,
% 0.61/0.65 (^[A: $i] : refl((v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(283,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[282])).
% 0.61/0.65 tff(284,plain,
% 0.61/0.65 (^[A: $i] : rewrite((v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(285,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[284])).
% 0.61/0.65 tff(286,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(transitivity,[status(thm)],[285, 283])).
% 0.61/0.65 tff(287,plain,
% 0.61/0.65 (^[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] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(288,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[287])).
% 0.61/0.65 tff(289,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(290,plain,
% 0.61/0.65 (^[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))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(291,plain,
% 0.61/0.65 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[290])).
% 0.61/0.65 tff(292,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t21_filter_2')).
% 0.61/0.65 tff(293,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[292, 291])).
% 0.61/0.65 tff(294,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[293, 289])).
% 0.61/0.65 tff(295,plain,(
% 0.61/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(skolemize,[status(sab)],[294])).
% 0.61/0.65 tff(296,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[295, 288])).
% 0.61/0.65 tff(297,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[296, 286])).
% 0.61/0.65 tff(298,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[297, 281])).
% 0.61/0.65 tff(299,plain,
% 0.61/0.65 (((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(300,plain,
% 0.61/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0))))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(301,plain,
% 0.61/0.65 ((~![A: $i] : (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | ![B: $i] : (m2_filter_2(B, A) <=> m1_filter_2(B, k1_lattice2(A))))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | ![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.61/0.65 tff(302,plain,
% 0.61/0.65 (![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0)))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[301, 48, 47, 25, 298])).
% 0.61/0.65 tff(303,plain,
% 0.61/0.65 ((~![B: $i] : (m2_filter_2(B, A!0) <=> m1_filter_2(B, k1_lattice2(A!0)))) | (m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) <=> m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(304,plain,
% 0.61/0.65 (m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) <=> m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[303, 302])).
% 0.61/0.65 tff(305,plain,
% 0.61/0.65 (~m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0)),
% 0.61/0.65 inference(or_elim,[status(thm)],[23])).
% 0.61/0.65 tff(306,plain,
% 0.61/0.65 ((~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) <=> m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)))) | m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) | (~m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)))),
% 0.61/0.65 inference(tautology,[status(thm)],[])).
% 0.61/0.65 tff(307,plain,
% 0.61/0.65 ((~(m2_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), A!0) <=> m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)))) | (~m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0)))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[306, 305])).
% 0.61/0.65 tff(308,plain,
% 0.61/0.65 (~m1_filter_2(k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)), k1_lattice2(A!0))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[307, 304])).
% 0.61/0.65 tff(309,plain,
% 0.61/0.65 (~m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[308, 279])).
% 0.61/0.65 tff(310,plain,
% 0.61/0.65 (^[A: $i] : refl((v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(311,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[310])).
% 0.61/0.65 tff(312,plain,
% 0.61/0.65 (^[A: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))) <=> (v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(313,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[312])).
% 0.61/0.65 tff(314,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(315,plain,
% 0.61/0.65 (^[A: $i] : 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)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(316,plain,
% 0.61/0.65 (![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[315])).
% 0.61/0.65 tff(317,axiom,(![A: $i] : (((((~v3_struct_0(A)) & v10_lattices(A)) & v13_lattices(A)) & l3_lattices(A)) => (k5_lattices(A) = k6_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t78_lattice2')).
% 0.61/0.65 tff(318,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.61/0.65 tff(319,plain,
% 0.61/0.65 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[318, 314])).
% 0.61/0.65 tff(320,plain,(
% 0.61/0.65 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A))) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))))),
% 0.61/0.65 inference(skolemize,[status(sab)],[319])).
% 0.61/0.65 tff(321,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[320, 313])).
% 0.61/0.65 tff(322,plain,
% 0.61/0.65 (![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[321, 311])).
% 0.61/0.65 tff(323,plain,
% 0.61/0.65 (v13_lattices(A!0)),
% 0.61/0.65 inference(or_elim,[status(thm)],[23])).
% 0.61/0.65 tff(324,plain,
% 0.61/0.65 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(325,plain,
% 0.61/0.65 ((v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~v13_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0))) <=> ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(326,plain,
% 0.61/0.65 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~v13_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | ((~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0)))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[325])).
% 0.61/0.65 tff(327,plain,
% 0.61/0.65 (((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~v13_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))))),
% 0.61/0.65 inference(transitivity,[status(thm)],[326, 324])).
% 0.61/0.65 tff(328,plain,
% 0.61/0.65 ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))) | (~v13_lattices(A!0)) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.61/0.65 inference(quant_inst,[status(thm)],[])).
% 0.61/0.65 tff(329,plain,
% 0.61/0.65 ((~![A: $i] : (v3_struct_0(A) | (k5_lattices(A) = k6_lattices(k1_lattice2(A))) | (~v13_lattices(A)) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (~v13_lattices(A!0)) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.61/0.65 tff(330,plain,
% 0.61/0.65 (k5_lattices(A!0) = k6_lattices(k1_lattice2(A!0))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[329, 323, 48, 47, 25, 322])).
% 0.61/0.65 tff(331,plain,
% 0.61/0.65 (k6_lattices(k1_lattice2(A!0)) = k5_lattices(A!0)),
% 0.61/0.65 inference(symmetry,[status(thm)],[330])).
% 0.61/0.65 tff(332,plain,
% 0.61/0.65 (k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k6_lattices(k1_lattice2(A!0))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[30])).
% 0.61/0.65 tff(333,plain,
% 0.61/0.65 (k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = k5_lattices(A!0)),
% 0.61/0.65 inference(transitivity,[status(thm)],[332, 331])).
% 0.61/0.65 tff(334,plain,
% 0.61/0.65 (((~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)))),
% 0.61/0.65 inference(tautology,[status(thm)],[])).
% 0.61/0.65 tff(335,plain,
% 0.61/0.65 (v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.61/0.65 inference(unit_resolution,[status(thm)],[334, 165])).
% 0.61/0.65 tff(336,plain,
% 0.61/0.65 (^[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))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(337,plain,
% 0.61/0.65 (![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)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[336])).
% 0.61/0.65 tff(338,plain,
% 0.61/0.65 (![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)))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(339,plain,
% 0.61/0.65 (^[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)))))),
% 0.61/0.65 inference(bind,[status(th)],[])).
% 0.61/0.65 tff(340,plain,
% 0.61/0.65 (![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)))),
% 0.61/0.65 inference(quant_intro,[status(thm)],[339])).
% 0.61/0.65 tff(341,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/sandbox/benchmark/theBenchmark.p','abstractness_v3_lattices')).
% 0.61/0.65 tff(342,plain,
% 0.61/0.65 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[341, 340])).
% 0.61/0.65 tff(343,plain,
% 0.61/0.65 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[342, 338])).
% 0.61/0.65 tff(344,plain,(
% 0.61/0.65 ![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.65 inference(skolemize,[status(sab)],[343])).
% 0.61/0.65 tff(345,plain,
% 0.61/0.65 (![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))),
% 0.61/0.65 inference(modus_ponens,[status(thm)],[344, 337])).
% 0.61/0.65 tff(346,plain,
% 0.61/0.65 (((~![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))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(347,plain,
% 0.61/0.65 (((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) <=> ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.65 inference(rewrite,[status(thm)],[])).
% 0.61/0.65 tff(348,plain,
% 0.61/0.65 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.61/0.65 inference(monotonicity,[status(thm)],[347])).
% 0.61/0.65 tff(349,plain,
% 0.61/0.65 (((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[348, 346])).
% 0.61/0.66 tff(350,plain,
% 0.61/0.66 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | ((g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(351,plain,
% 0.61/0.66 ((~![A: $i] : ((A = g3_lattices(u1_struct_0(A), u2_lattices(A), u1_lattices(A))) | (~v3_lattices(A)) | (~l3_lattices(A)))) | (~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[350, 349])).
% 0.61/0.66 tff(352,plain,
% 0.61/0.66 ((~v3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~l3_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[351, 345])).
% 0.61/0.66 tff(353,plain,
% 0.61/0.66 (g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.61/0.66 inference(unit_resolution,[status(thm)],[352, 167, 335])).
% 0.61/0.66 tff(354,plain,
% 0.61/0.66 (^[A: $i, B: $i, C: $i] : refl(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(355,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[354])).
% 0.61/0.66 tff(356,plain,
% 0.61/0.66 (^[A: $i, B: $i, C: $i] : rewrite(((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(357,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[356])).
% 0.61/0.66 tff(358,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[357, 355])).
% 0.61/0.66 tff(359,plain,
% 0.61/0.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(rewrite((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> (~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))))), rewrite((~(~((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)))), ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : rewrite(((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> (((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))))), rewrite((((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F)))))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))), (((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(360,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[359])).
% 0.61/0.66 tff(361,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(362,plain,
% 0.61/0.66 (^[A: $i, B: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C))), ((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A))), (((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))), ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) <=> (v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)))), quant_intro(proof_bind(^[D: $i, E: $i, F: $i] : trans(monotonicity(rewrite((((A = D) & (B = E)) & (C = F)) <=> ((A = D) & (B = E) & (C = F))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))))), rewrite(((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => ((A = D) & (B = E) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))), (((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), (![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))) <=> ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))))), rewrite(((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))), (((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))))),
% 0.61/0.66 inference(bind,[status(th)],[])).
% 0.61/0.66 tff(363,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F)))) <=> ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.66 inference(quant_intro,[status(thm)],[362])).
% 0.61/0.66 tff(364,axiom,(![A: $i, B: $i, C: $i] : ((((((v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A)) & m1_relset_1(B, k2_zfmisc_1(A, A), A)) & v1_funct_1(C)) & v1_funct_2(C, k2_zfmisc_1(A, A), A)) & m1_relset_1(C, k2_zfmisc_1(A, A), A)) => ![D: $i, E: $i, F: $i] : ((g3_lattices(A, B, C) = g3_lattices(D, E, F)) => (((A = D) & (B = E)) & (C = F))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','free_g3_lattices')).
% 0.61/0.66 tff(365,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[364, 363])).
% 0.61/0.66 tff(366,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[365, 361])).
% 0.61/0.66 tff(367,plain,(
% 0.61/0.66 ![A: $i, B: $i, C: $i] : ((~(v1_funct_1(B) & v1_funct_2(B, k2_zfmisc_1(A, A), A) & m1_relset_1(B, k2_zfmisc_1(A, A), A) & v1_funct_1(C) & v1_funct_2(C, k2_zfmisc_1(A, A), A) & m1_relset_1(C, k2_zfmisc_1(A, A), A))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | ((A = D) & (B = E) & (C = F))))),
% 0.61/0.66 inference(skolemize,[status(sab)],[366])).
% 0.61/0.66 tff(368,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[367, 360])).
% 0.61/0.66 tff(369,plain,
% 0.61/0.66 (![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[368, 358])).
% 0.61/0.66 tff(370,plain,
% 0.61/0.66 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(371,plain,
% 0.61/0.66 (((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) <=> ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.61/0.66 inference(rewrite,[status(thm)],[])).
% 0.61/0.66 tff(372,plain,
% 0.61/0.66 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))))),
% 0.61/0.66 inference(monotonicity,[status(thm)],[371])).
% 0.61/0.66 tff(373,plain,
% 0.61/0.66 (((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))) <=> ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.61/0.66 inference(transitivity,[status(thm)],[372, 370])).
% 0.61/0.66 tff(374,plain,
% 0.61/0.66 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | ((~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F))))))),
% 0.61/0.66 inference(quant_inst,[status(thm)],[])).
% 0.61/0.66 tff(375,plain,
% 0.61/0.66 ((~![A: $i, B: $i, C: $i] : ((~v1_funct_1(C)) | (~v1_funct_1(B)) | (~v1_funct_2(B, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(B, k2_zfmisc_1(A, A), A)) | (~v1_funct_2(C, k2_zfmisc_1(A, A), A)) | (~m1_relset_1(C, k2_zfmisc_1(A, A), A)) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(A, B, C) = g3_lattices(D, E, F))) | (~((~(A = D)) | (~(B = E)) | (~(C = F))))))) | (~v1_funct_1(u1_lattices(A!0))) | (~v1_funct_2(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~v1_funct_1(u2_lattices(A!0))) | (~v1_funct_2(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 0.61/0.66 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.61/0.66 tff(376,plain,
% 0.61/0.66 ((~m1_relset_1(u1_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | (~m1_relset_1(u2_lattices(A!0), k2_zfmisc_1(u1_struct_0(A!0), u1_struct_0(A!0)), u1_struct_0(A!0))) | ![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[375, 369, 141, 139, 137, 135])).
% 0.65/0.67 tff(377,plain,
% 0.65/0.67 (![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[376, 133, 106])).
% 0.65/0.67 tff(378,plain,
% 0.65/0.67 (((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))) <=> ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(379,plain,
% 0.65/0.67 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))))),
% 0.65/0.67 inference(quant_inst,[status(thm)],[])).
% 0.65/0.67 tff(380,plain,
% 0.65/0.67 ((~![D: $i, E: $i, F: $i] : ((~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(D, E, F))) | (~((~(u1_struct_0(A!0) = D)) | (~(u1_lattices(A!0) = E)) | (~(u2_lattices(A!0) = F)))))) | (~(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)) = g3_lattices(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.65/0.67 tff(381,plain,
% 0.65/0.67 (~((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[380, 377, 353])).
% 0.65/0.67 tff(382,plain,
% 0.65/0.67 (((~(u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u1_lattices(A!0) = u2_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | (~(u2_lattices(A!0) = u1_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) | (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.67 inference(tautology,[status(thm)],[])).
% 0.65/0.67 tff(383,plain,
% 0.65/0.67 (u1_struct_0(A!0) = u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[382, 381])).
% 0.65/0.67 tff(384,plain,
% 0.65/0.67 (u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) = u1_struct_0(A!0)),
% 0.65/0.67 inference(symmetry,[status(thm)],[383])).
% 0.65/0.67 tff(385,plain,
% 0.65/0.67 (k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) = k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0))),
% 0.65/0.67 inference(monotonicity,[status(thm)],[384, 333])).
% 0.65/0.67 tff(386,plain,
% 0.65/0.67 (k6_domain_1(u1_struct_0(A!0), k5_lattices(A!0)) = k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.67 inference(symmetry,[status(thm)],[385])).
% 0.65/0.67 tff(387,plain,
% 0.65/0.67 (k1_tarski(k5_lattices(A!0)) = k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.67 inference(transitivity,[status(thm)],[276, 386])).
% 0.65/0.67 tff(388,plain,
% 0.65/0.67 (m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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)))),
% 0.65/0.67 inference(monotonicity,[status(thm)],[387])).
% 0.65/0.67 tff(389,plain,
% 0.65/0.67 (m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) <=> m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.67 inference(symmetry,[status(thm)],[388])).
% 0.65/0.67 tff(390,plain,
% 0.65/0.67 (v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> v14_lattices(k1_lattice2(A!0))),
% 0.65/0.67 inference(monotonicity,[status(thm)],[30])).
% 0.65/0.67 tff(391,plain,
% 0.65/0.67 (v14_lattices(k1_lattice2(A!0)) <=> v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.67 inference(symmetry,[status(thm)],[390])).
% 0.65/0.67 tff(392,plain,
% 0.65/0.67 (^[A: $i] : refl((v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(393,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[392])).
% 0.65/0.67 tff(394,plain,
% 0.65/0.67 (^[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))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))))), rewrite(((v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))), (((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(395,plain,
% 0.65/0.67 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[394])).
% 0.65/0.67 tff(396,plain,
% 0.65/0.67 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(397,plain,
% 0.65/0.67 (^[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)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(398,plain,
% 0.65/0.67 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A)))) <=> ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[397])).
% 0.65/0.67 tff(399,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t63_lattice2')).
% 0.65/0.67 tff(400,plain,
% 0.65/0.67 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.65/0.67 tff(401,plain,
% 0.65/0.67 (![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[400, 396])).
% 0.65/0.67 tff(402,plain,(
% 0.65/0.67 ![A: $i] : ((~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))))),
% 0.65/0.67 inference(skolemize,[status(sab)],[401])).
% 0.65/0.67 tff(403,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[402, 395])).
% 0.65/0.67 tff(404,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[403, 393])).
% 0.65/0.67 tff(405,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(406,plain,
% 0.65/0.67 ((v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_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)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(407,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))))),
% 0.65/0.67 inference(monotonicity,[status(thm)],[406])).
% 0.65/0.67 tff(408,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))) <=> ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))))),
% 0.65/0.67 inference(transitivity,[status(thm)],[407, 405])).
% 0.65/0.67 tff(409,plain,
% 0.65/0.67 ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | (v3_struct_0(A!0) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)))),
% 0.65/0.67 inference(quant_inst,[status(thm)],[])).
% 0.65/0.67 tff(410,plain,
% 0.65/0.67 ((~![A: $i] : (v3_struct_0(A) | (v13_lattices(A) <=> v14_lattices(k1_lattice2(A))) | (~l3_lattices(A)) | (~v10_lattices(A)))) | v3_struct_0(A!0) | (~l3_lattices(A!0)) | (~v10_lattices(A!0)) | (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.65/0.67 tff(411,plain,
% 0.65/0.67 (v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[410, 48, 47, 25, 404])).
% 0.65/0.67 tff(412,plain,
% 0.65/0.67 ((~(v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))) | (~v13_lattices(A!0)) | v14_lattices(k1_lattice2(A!0))),
% 0.65/0.67 inference(tautology,[status(thm)],[])).
% 0.65/0.67 tff(413,plain,
% 0.65/0.67 ((~(v13_lattices(A!0) <=> v14_lattices(k1_lattice2(A!0)))) | v14_lattices(k1_lattice2(A!0))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[412, 323])).
% 0.65/0.67 tff(414,plain,
% 0.65/0.67 (v14_lattices(k1_lattice2(A!0))),
% 0.65/0.67 inference(unit_resolution,[status(thm)],[413, 411])).
% 0.65/0.67 tff(415,plain,
% 0.65/0.67 (v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[414, 391])).
% 0.65/0.67 tff(416,plain,
% 0.65/0.67 (^[A: $i] : refl((v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(417,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[416])).
% 0.65/0.67 tff(418,plain,
% 0.65/0.67 (^[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) & v14_lattices(A) & l3_lattices(A)) <=> (~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))))), rewrite((~(~(v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) <=> (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A))))), ((m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))))), rewrite((m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A))) | (v3_struct_0(A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) <=> (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))), ((m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(419,plain,
% 0.65/0.67 (![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[418])).
% 0.65/0.67 tff(420,plain,
% 0.65/0.67 (![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)))) <=> ![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(421,plain,
% 0.65/0.67 (^[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)) & 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)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)) <=> (((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))), ((((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)) <=> ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)))), (((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))) <=> (((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))))), rewrite((((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A)) => ((~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))) <=> (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_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)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))) <=> (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))))),
% 0.65/0.67 inference(bind,[status(th)],[])).
% 0.65/0.67 tff(422,plain,
% 0.65/0.67 (![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A))) <=> ![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))),
% 0.65/0.67 inference(quant_intro,[status(thm)],[421])).
% 0.65/0.67 tff(423,axiom,(![A: $i] : ((((~v3_struct_0(A)) & v10_lattices(A)) & l3_lattices(A)) => (((((~v3_struct_0(A)) & v10_lattices(A)) & v14_lattices(A)) & l3_lattices(A)) => m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t13_filter_0')).
% 0.65/0.67 tff(424,plain,
% 0.65/0.67 (![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[423, 422])).
% 0.65/0.67 tff(425,plain,
% 0.65/0.67 (![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[424, 420])).
% 0.65/0.67 tff(426,plain,(
% 0.65/0.67 ![A: $i] : (m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~((~v3_struct_0(A)) & v10_lattices(A) & l3_lattices(A))) | (~((~v3_struct_0(A)) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A))))),
% 0.65/0.67 inference(skolemize,[status(sab)],[425])).
% 0.65/0.67 tff(427,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[426, 419])).
% 0.65/0.67 tff(428,plain,
% 0.65/0.67 (![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[427, 417])).
% 0.65/0.67 tff(429,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(430,plain,
% 0.65/0.67 ((v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~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)))) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.65/0.67 inference(rewrite,[status(thm)],[])).
% 0.65/0.67 tff(431,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~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)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))))),
% 0.65/0.67 inference(monotonicity,[status(thm)],[430])).
% 0.65/0.67 tff(432,plain,
% 0.65/0.67 (((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~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)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))) <=> ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.65/0.67 inference(transitivity,[status(thm)],[431, 429])).
% 0.65/0.67 tff(433,plain,
% 0.65/0.67 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_lattices(A)))) | (v3_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~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)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))))),
% 0.65/0.67 inference(quant_inst,[status(thm)],[])).
% 0.65/0.67 tff(434,plain,
% 0.65/0.67 ((~![A: $i] : (v3_struct_0(A) | m1_filter_0(k6_domain_1(u1_struct_0(A), k6_lattices(A)), A) | (~l3_lattices(A)) | (~v10_lattices(A)) | (~v14_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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.67 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.65/0.67 tff(435,plain,
% 0.65/0.67 ((~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))) | m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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))) | (~v10_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))) | (~v14_lattices(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[434, 428])).
% 0.65/0.68 tff(436,plain,
% 0.65/0.68 (m1_filter_0(k6_domain_1(u1_struct_0(g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))), k6_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)))),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[435, 55, 167, 172, 415])).
% 0.65/0.68 tff(437,plain,
% 0.65/0.68 (m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0)))),
% 0.65/0.68 inference(modus_ponens,[status(thm)],[436, 389])).
% 0.65/0.68 tff(438,plain,
% 0.65/0.68 ((~(m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) <=> m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))) | m1_filter_2(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))) | (~m1_filter_0(k1_tarski(k5_lattices(A!0)), g3_lattices(u1_struct_0(A!0), u1_lattices(A!0), u2_lattices(A!0))))),
% 0.65/0.68 inference(tautology,[status(thm)],[])).
% 0.65/0.68 tff(439,plain,
% 0.65/0.68 ($false),
% 0.65/0.68 inference(unit_resolution,[status(thm)],[438, 437, 309, 198])).
% 0.65/0.68 % SZS output end Proof
%------------------------------------------------------------------------------